Antiferromagnetic Spin Fluctuations and the Pseudogap in the Paramagnetic Phases of Quasi-T

a r X i v :c o n d -m a t /0611747v 2 [c o n d -m a t .s t r -e l ] 6 J u l 2007

Antiferromagnetic Spin Fluctuations and the Pseudogap in the Paramagnetic Phases

of Quasi-Two-Dimensional Organic Superconductors

Eddy Yusuf,B.J.Powell,and Ross H.McKenzie

Department of Physics,University of Queensland,Brisbane,Queensland 4072,Australia

(Dated:February 6,2008)

The metallic states of a broad range of strongly correlated electron materials exhibit the subtle interplay between antiferromagnetic spin ?uctuations,a pseudogap in the excitation spectra,and non-Fermi liquid properties.In order to understand these issues better in the κ-(ET)2X family of organic charge transfer salts we give a quantitative analysis of the published results of nuclear magnetic resonance (NMR)experiments.The temperature dependence of the nuclear spin relaxation rate 1/T 1,the Knight shift K s ,and the Korringa ratio K ,are compared to the predictions of the phenomenological spin ?uctuation model of Moriya,and Millis,Monien and Pines (M-MMP),that has been used extensively to quantify antiferromagnetic spin ?uctuations in the cuprates.For temperatures above T NMR ?50K,the model gives a good quantitative description of the data for the paramagnetic metallic phase of several κ-(ET)2X materials,with an antiferromagnetic correlation length which increases with decreasing temperature;growing to several lattice constants by T NMR .It is shown that the fact that the dimensionless Korringa ratio is much larger than unity is inconsistent with a broad class of theoretical models (such as dynamical mean-?eld theory)which neglect spatial correlations and/or vertex corrections.For materials close to the Mott insulating phase the nuclear spin relaxation rate,the Knight shift and the Korringa ratio all decrease signi?cantly with decreasing temperature below T NMR .This cannot be described by the M-MMP model and the most natural explanation is that a pseudogap opens up in the density of states below T NMR ,as in,for example,the underdoped cuprate superconductors.An analysis of the Mott insulating phase of κ-(ET)2Cu 2(CN)3is somewhat more ambiguous;nevertheless it suggests that the antiferromagnetic correlation length is less than a lattice constant,consistent with a large frustration of antiferromagnetic interactions as is believed to occur in this material.We show that the NMR measurements reported for κ-(ET)2Cu 2(CN)3are qualitatively inconsistent with this material having a ground state with long range magnetic order.A pseudogap in the metallic state of organic superconductors is an important prediction of the resonating valence bond theory of superconductivity.Understanding the nature,origin,and momentum dependence of the pseudogap and its relationship to superconductivity are important outstanding problems.We propose speci?c new experiments on organic superconductors to elucidate these issues.Speci?cally,measurements should be performed to see if high magnetic ?elds or high pressures can be used to close the pseudogap.

I.

INTRODUCTION

In the past twenty years a diverse range of new strongly correlated electron materials with exotic electronic and magnetic properties have been synthesized.Examples in-clude high-temperature cuprate superconductors,1man-ganites with colossal magnetoresistance,2cerium ox-ide catalysts,3sodium cobaltates,4ruthenates,5,6heavy fermion materials,7and superconducting organic charge transfer salts.8Many of these materials exhibit a sub-tle competition between diverse phases:paramagnetic,superconducting,insulating,and the di?erent types of order associated with charge,spin,orbital,and lattice degrees of freedom.These di?erent phases can be ex-plored by varying experimental control parameters such as temperature,pressure,magnetic ?eld,and chemical composition.Although chemically and structurally di-verse the properties of these materials are determined by some common features;such as,strong interactions between the electrons,reduced dimensionality associated with a layered crystal structure,large quantum ?uctu-ations,and competing interactions.Many of these ma-

terials are characterized by large antiferromagnetic spin ?uctuations.Nuclear magnetic resonance spectroscopy has proven to be a powerful probe of local spin dynamics in many strongly correlated electron materials.9,10,11,12Longer range and faster spin dynamics have been studied with inelastic neutron scattering.One poorly understood property of the paramagnetic phases of many of these materials is the pseudogap present in large regions of the phase diagram.Although the pseudogap has received the most attention in the cuprates,13it is also present in quasi one-dimensional charge-density wave compounds,14manganites,15heavy fermion materials,11,in simple met-als with no signs of superconductivity,16and quite pos-sibly in organic charge transfer materials.12The focus of this paper is on understanding what information about antiferromagnetic spin ?uctuations and the pseudogap can be extracted from NMR experiments on the organic charge transfer salts.

The systems which are the subject of the current study are the organic charge transfer salts based on electron donor molecules BEDT-TTF (ET),in particu-lar the family κ-(ET)2X (where κindicates a particular

2

polymorph17).Remarkably similar physics occurs in the other dimerised polymorphs,such as theβ,β′,λ,andκphases.8These materials display a wide variety of uncon-ventional behaviours8including:antiferromagnetic and spin liquid insulating states,unconventional supercon-ductivity,and the paramagnetic metallic phases which we focus on in this paper.They also share highly anisotropic crystal and band structures.However,as for various so-ciological and historical reasons,theκsalts have been far more extensively studied,and because we intend,in this paper,to make detailed comparisons with experi-mental data,we limit our study toκphase salts.This of course begs the question do similar phenomena to those described below occur in theβ,β′,orλsalts?We would suggest that the answer is probably y es but this remains an inviting experimental question.

As well as their interesting phenomenology the organic charge transfer salts are important model systems and a deeper understanding of these materials may help address a number of important fundamental questions concerning strongly correlated systems.The(non-interacting)band structure of theκphase salts is well approximated by the half-?lled tight binding model on the anisotropic lattice.8 This model has two parameters t,the hopping integral between nearest neighbor(ET)2dimers,and t′,the hop-ping integral between next nearest neighbors across one diagonal only.In order to describe strongly correlated phases of these materials we must also include the e?ects of the Coulomb interaction between electrons.The sim-plest model which can include these strong correlations in the Hubbard model contains one additional parameter over the tight binding model:U,the Coulomb repulsion between two conduction electrons on the same dimer.In the Hubbard model picture the di?erentκ-(ET)2X salts and di?erent pressures correspond to di?erent values of t′/t and U/t,but all of theκphase salts are half?lled. Varying U/t allows us to tune the proximity to the Mott transition-understanding the Mott transition and its as-sociated phenomena remains one most important prob-lems in theoretical physics22,23and the organics have pro-vided a new window on this problem.8,24,25,26,27Varying t′/t allows one to tune the degree of frustration in the sys-tem.Understanding the e?ect of frustration in strongly correlated systems is of general importance.4,28,29For example there are strong analogies between the organ-ics and Na x CoO2,30and much recent interest has been sparked by the observation of possible spin liquid states in organic charge transfer salts.31,32,33

The paramagnetic metallic phases ofκ-(ET)2X are very di?erent from a conventional metallic phase.Many features of the paramagnetic metallic phases agree well with the predictions of dynamical mean?eld theory (DMFT)which describes crossover from‘bad metal’at high temperatures to a Fermi liquid as the tempera-ture is lowered.24,25,34,35This crossover from incoher-ent to coherent intralayer125transport has been ob-served in a number of experiments such as resistivity,25 thermopower,24,36and ultrasonic attenuation.37,38The existence of coherent quasiparticles is also apparent from

the observed magnetic quantum oscillations at low tem-peratures inκ-(ET)2X.39,40,41However,nuclear mag-

netic resonance experiments(reproduced in Figs.1and 2)on the paramagnetic metallic phases onκ-(ET)2X do

not?nd the well known properties of a Fermi liquid. The nuclear spin relaxation rate per unit temperature,

1/T1T,is larger than the Korringa form predicted from Fermi liquid theory.As the temperature is lowered

1/T1T reaches a maximum;we label this temperature T NMR(the exact value of T NMR varies with the anion

X,but typically,T NMR～50K,see Fig.6).1/T1T de-creases rapidly as the temperature is lowered below T NMR

[see Fig1].12,18,19The Knight shift also drops rapidly around T NMR[see Fig4].19This is clearly in contrast the

Korringa-like behavior one would expect for a Fermi liq-uid in which1/T1T and K s are constant for T?T F, the Fermi temperature.Similar non-Fermi liquid tem-perature dependences of1/T1T and K s are observed in the cuprates.42,43For the cuprates,it has been argued that the large enhancement of1/T1T is associated with the growth of antiferromagnetic spin?uctuation within the CuO2planes as the temperature is lowered.44,45The large decrease observed in1/T1T and K s is suggestive of a depletion of the density of states(DOS)at the Fermi level which might be expected if a pseudogap opens at T NMR.

A qualitative description of spin?uctuations in the

paramagnetic metallic phase ofκ-(ET)2X has not been performed previously.The importance of spin?uctua-tions inκ-(ET)2X below T c has been pointed out by several groups.8,46,47,48,49,50Since the nature of the para-magnetic metallic and superconducting phases are inti-mately intertwined(in most theories,including BCS,su-perconductivity arises from an instability of the metal-lic phase),it is important to understand whether the spin?uctuations may extend beyond the superconduct-ing region into the paramagnetic metallic phase and if so how strong they are.Another unresolved puzzle is whether there is a pseudogap in the paramagnetic metal-lic phase ofκ-(ET)2X which suppresses the density of states(DOS)at the Fermi level.A pseudogap has been suggested on the basis of the NMR data and heat ca-pacity measurement.51If there is a pseudogap then im-portant questions to answer include:(i)how similar is the pseudogap inκ-(ET)2X to the pseudogaps in the cuprates,manganites and heavy fermions?(ii)is the pseudogap inκ-(ET)2X related to superconductivity? and(iii)if so how?

A number of scenarios in which a pseudogap may arise have been proposed.One possible origin of a pseudogap, which a number of authors8,49,55,56,57have argued may be relevant to the organic charge transfer salts,is the resonating valence bond(RVB)picture(for a review see Refs.1and58).In this picture the electron spins form a linear superposition of spin singlet pairs.The singlet formation can naturally explain the appearance of a gap: a non-zero amount of energy is required to break the sin-

3

1/T 1T (s K )-1

T(K)

1/T 1T (s K )-1

T(K)

1/T 1T (s K )-1

T(K)

0 50

100 150 200 250 300

1/T 1T (s K )-1

T(K)

FIG.1:[Color online]Comparison of the measured nuclear spin relaxation rate per unit temperature,1/T 1T ,with the predic-tions of the spin ?uctuation model for various organic charge transfer salts.Panel (a)shows data for κ-(ET)2Cu[N(CN)2]Br mea-sured by Maya?re et al.18,panel (b)shows data for κ-(ET)2Cu[N(CN)2]Br measured by De Soto et al.19,panel (c)shows data for κ(d8)-(ET)2Cu[N(CN)2]Br measured by Miyagawa et al.20,and panel (d)shows data for a κ-(ET)2Cu(NCS)2powder sample measured by Kawamoto et al.21The 1/T 1T data are weakly temperature dependent at high temperatures,have a maximum at T NMR ～50K,and drop abruptly below T NMR ,contrary to what one would expect for a Fermi liquid in which 1/T 1T is constant.The remarkable similarities of these data results from the quantitative and qualitative similarity of the antiferromagnetic spin ?uctuations in the paramagnetic metallic phases of these materials.The parameters that produce the best ?ts (solid lines)to Eq.(13)are tabulated in Table I.The spin ?uctuation model gives a good ?t to the experimental data between T NMR ～50and room temperature which suggests strong spin ?uctuations in the paramagnetic metallic states of κ-(ET)2Cu[N(CN)2]Br,κ(d8)-(ET)2Cu[N(CN)2]Br,and κ-(ET)2Cu(NCS)2.However,below T NMR the spin ?uctuation model does not describe the data well.In section V we argue that this is because a pseudogap opens at T NMR .In each ?gure the solid line indicates the large T approximation of the spin ?uctuation model [Eq.(15b)].To check that this approximation is reasonable we also plot the full spin ?uctuation model [Eq.(13)]as a dashed line in panel (b).The full and dashed lines cannot be distinguished until well below T NMR and so we concluded that the high T approximation is excellent in the relevant regime.Note that the analysis on 1/T 1T cannot di?erentiate between antiferromagnetic and ferromagnetic spin ?uctuations (see section II A 2),but the Korringa ratio strongly di?erentiates between these two case and indicates that the ?uctuations are antiferromagnetic (see Fig.2).The nomenclature κ-Br,d8-Br,and κ-NCS is used as shorthand for κ-(ET)2Cu[N(CN)2]Br,κ(d8)-(ET)2Cu[N(CN)2]Br,and κ-(ET)2Cu(NCS)2respectively in the ?gure keys.

glet pairs.For weakly frustrated lattices,such as the anisotropic triangular lattice in the parameter range ap-propriate for κ-(ET)2Cu[N(CN)2]Br,κ-(ET)2Cu(NCS)2,and κ-(ET)2Cu[N(CN)2]Cl,the RVB theory predicts ‘d -wave’superconductivity.8,49,50,55,56,57This is the symme-try most consistent with a range of experiments on these κ-(ET)2X salts.12,59,60,61However,as the frustration is increased changes in the nature of the spin ?uctuations drive changes in the symmetry of the superconducting state.57,61For example,for the isotropic triangular lat-tice t =t ′[t ～t ′is thought to be appropriate for κ-(ET)2Cu 2(CN)3]RVB theory predicts that the super-

conducting order parameter has ‘d +id ’symmetry.57,61RVB theory also predicts that a pseudogap with the same symmetry as the superconducting state exists in the paramagnetic phase at temperatures above the su-perconducting critical temperature,T c .This pseudogap results from the formation of short range singlets above T c ;only at T c do these singlets acquire o?-diagonal long-range order.There are two energy scales (?and ?

in the notation of,e.g.,Refs.49and 56)in the RVB the-ory.In the simplest reading of the theory,58,62the ratio ?/ ?

≈T ?/T c where T ?is the temperature at which the

4

2 4 6 8 10 12 14 0

50

100

150 200

250

300

K o r r i n g a r a t i o

T(K)

FIG.2:[Color online]Comparison of the Korringa ratio

K ∝1/T 1T K 2

s of κ-(ET)2Cu[N(CN)2]Br measured by De

Soto et al .19

with the prediction of the antiferromagnetic spin ?uctuation model.The best ?t to Eq.(16)is indicated by the solid line.The Korringa ratio is larger than 1which indi-cates that the spin ?uctuations are antiferromagnetic (K <1for ferromagnetic ?uctuations,see Section II A 2).The an-tiferromagnetic correlation length is found to be 3.5±2.5lattice spacings at 50K.Below 50K the Korringa ratio is suppressed,and in section V we argue that this is because a pseudogap opens at T NMR .In the key to this ?gure κ-(ET)2Cu[N(CN)2]Br is abbreviated as κ-Br.

pseudogap opens.For the appropriate model Hamilto-nian for the layered κ-(ET)2X salts ?/ ?

?5near the Mott transition 49which is remarkably similar to the ratio T NMR /T c in κ-(ET)2Cu[N(CN)2]Br.

We use the phenomenological antiferromagnetic spin ?uctuation model which was ?rst introduced by Moriya 44and then applied by Millis,Monien and Pines (MMP)45to cuprates,to examine the role of spin ?uctuations in the paramagnetic metallic phase of κ-(ET)2X .We investi-gate whether the anomalous temperature dependences of NMR data can be explained without invoking a pseudo-gap in the DOS.We ?t the spin ?uctuation model to the nuclear spin relaxation rate per unit temperature 1/T 1T ,Knight shift K s ,and Korringa ratio K data and ?nd that the large enhancements measured in 1/T 1T and K above T NMR are the result of large antiferromagnetic spin ?uc-tuations [see Figs.1and 2].The correlation of the anti-ferromagnetic spin ?uctuations increases as temperature decreases and the relevant correlation length is found to be 3.5±2.5lattice spacings at T =50K.The model produces reasonable agreement with experimental data down to T ～50K.Below 50K,1/T 1T is suppressed but never saturates to a constant expected for a Fermi liquid while the spin ?uctuation model produces a mono-tonically increasing 1/T 1T with decreasing temperature.We argue that this discrepancy between theory and ex-periment is due to the appearance of a pseudogap,not captured by the spin ?uctuation model,which suppresses

the DOS at the Fermi level.

Our results suggest the paramagnetic metallic phase of κ-(ET)2X is richer than a renormalized Fermi liquid as has been previously thought to describe the low tem-perature metallic state.An exotic regime similar to the pseudogap in the cuprates appears to be realized in the paramagnetic metallic phase of κ-(ET)2X .Thus we be-lieve the appropriate phase diagram of κ-(ET)2X looks like the one sketched in Fig.3.However,the pseudogap in κ-(ET)2X is rather peculiar.On one hand,it shows a coherent intralayer transport (apparent from the T 2re-sistivity and the observed quantum oscillations).On the other hand it also shows a loss of DOS apparent from 1/T 1T and K s .Therefore it is important to emphasize that the pseudogap phase proposed for κ-(ET)2X is dif-ferent from the pseudogap phase realized in the cuprates.Understanding these di?erences may well provide impor-tant insight into the physics of the pseudogaps in both classes of material.We will discuss this matter further in Section V.

We have also applied the spin ?uctuation formalism to the Mott insulating phase κ-(ET)2Cu 2(CN)3(which may have a spin liquid ground state).31While a rea-sonable agreement between the calculated and the ex-perimental data on 1/T 1T has been obtained,the re-sult for the Knight shift does not agree with the data.We believe that this discrepancy re?ects the failure of the assumption that the peak in the dynamic suscepti-bility dominates even the long wavelength physics im-plicit in the spin-?uctuation model.The failure of this assumption is consistent with the strong frustration in κ-(ET)2Cu 2(CN)3and the observed spin-liquid behavior of this material.8,31We show that there are qualitative as well as quantitative di?erence between the spin ?uc-tuations in κ-(ET)2Cu 2(CN)3and the spin ?uctuations in the other κ-phase salts discussed in this paper.

The structure of the paper is as follows.In Section II we introduce the temperature dependence of the nuclear spin relaxation rate,spin echo decay rate,Knight shift,and Korringa ratio and describe how they probe spin ?uctuations by probing the dynamical susceptibility.We calculate these properties in a number of approximations and contrast the results.In Section III we demonstrate that the spin ?uctuation model provides reasonable ?ts to the existing experimental results for κ-(ET)2X and dis-cuss its limitations when applied to those materials.Sec-tion IV deals with the application of the spin ?uctuation model to the spin liquid compound κ-(ET)2Cu 2(CN)3.We discuss the nature and extent of the pseudogap in Section V.Finally,in Section VI we suggest new experi-ments and give our conclusions.

5 T

FIG.3:[Color online]The schematic phase diagram forκ-(ET)2X as a function of temperature and pressure.Thin solid lines represent second order phase transitions,the thick solid line is the?rst order transition line which ends at a critical point shown as a?lled circle,and dashed lines indicate crossovers.The pseudogap phase is much more complicated than a renormalized Fermi liquid that has been previously thought to characterize the paramagnetic metallic phase at low temperatures:it shows a coherent transport character with long lived quasiparticles,marked by T2resistivity behavior25and magnetic quantum oscillations,39but at the same time it exhibits a loss of density of states which is clearly seen in the NMR data.There are not su?cient data at this moment to determine where the pseudogap phase boundary ends so this uncertainty is represented by the shaded area with the question mark.More detailed experimental and theoretical studies in the vicinity of this point will give important insight into how the pseudogap is related to superconductivity.The possibility of a quantum critical point somewhere in the vicinity of the point where the superconducting critical temperature goes to zero may have important consequences for the observation that the materials with the lowest superconducting critical temperatures have extremely small super?uid sti?nesses and are very di?erent from BCS superconductors.52,53,54

II.THE SPIN LATTICE RELAXATION RATE,

SPIN ECHO DECAY RATE,AND KNIGHT

SHIFT

The temperature dependence of the nuclear spin lattice

relaxation rate1/T1T,spin echo decay rate1/T2,Knight

shift K s,Korringa ratio K,and the real and imaginary

part of the dynamic susceptibility,χ′(q,ω)andχ′′(q,ω),

de?ned by

χ(q,ω)= d3r dte i(q·r?ωt)χ(r,t).(1)

are discussed in this section.The general expressions for

these quantities are63

1

γ2e 4 q|A(q)|2χ′′(q,ω)

T22

=

2f A

γeγN 2

,(2c)

and

K= γ

N

21

6

A.The Spin Fluctuation Model

The dynamic susceptibility in this model is written

as44,45

χ(q,ω)=χL W(ω)+χAF(q,ω),(3)

whereχL W(ω)is the dynamic susceptibility in the long

wavelength regime andχAF(q,ω)is a contribution to the

dynamic susceptibility which peaks at some wave vector

Q.These susceptibilities take the form

χL W(ω)=

ˉχ0(T)

1+ξ(T)2|q?Q|2?iω/ωSF(T)(4)

whereˉχ0(T)[χQ(T)]is the static spin susceptibility at

q=0[Q],Γ(T)[ωSF(T)]is the characteristic spin?uc-

tuation energy which represents damping in the system

near q=0[Q],andξ(T)is the temperature dependent

correlation length.Hence,the real and imaginary parts

of the dynamic susceptibility can then be written as

χ′(q,0)=ˉχ0(T) 1+χQ(T)(1+ξ(T)2|q?Q|2)2

χ′′(q,ω)=

ωˉχ0(T)

ˉχ0(T)ωSF(T)1

ξ0

2?η

ˉχ0

ωSF(T)= ξ0

β

[ξ(T)/a]2

Γ 1+β[ξ(T)/a]4

ˉχ0ωSF(T) a

T1T

=

2πk B|A|2ˉχ0

1+[?Qξ(T)]2

(9a)

1

πγ4e 6 1+β[ξ(T)/a]4

β

γeγN 2 1+ 1+[?Qξ(T)]2

(9c)

K= γ2e1+[?Qξ(T)]2

β[ξ(T)/a]2

7 where?Q is a cuto?from the momentum integration[c.f.

Eq.(2a)].Forξ(T)?a:1/T1T～ξ(T)2,1/T2～ξ(T),

and K s～constant which leads to the Korringa ra-

tio K?( γ2e/2Γˉχ0)[?Qξ(T)]2.In this model the Kor-

ringa ratio can only be equal to unity if the spin?uc-

tuations are completely suppressed(β=0).Hence,

one expects K>1if antiferromagnetic?uctuations are

dominant.67,68This indicates that there are signi?cant

vertex corrections when there large strong antiferromag-

netic?uctuations.

2.Ferromagnetic Spin Fluctuations

For ferromagnetic spin?uctuations,χ(q,ω)is peaked

at q=0.The NMR relaxation rate and spin echo decay

rate are exactly the same as those given in Eqs.(9a)

and(9b)because1/T1T and1/T2come from summing

the contributions form all wave vectors in the?rst Bril-

louin zone,which makes the location of the peak in q

space irrelevant.In contrast,the Knight shift will be dif-

ferent in the ferromagnetic and antiferromagnetic cases

because K s only measures the q=0part of the dynamic

susceptibility;it will be enhanced by the ferromagnetic

?uctuations.Thus,in the ferromagnetic spin?uctuation

description K s is given by

K s=|A|ˉχ0β(ξ/a)2 (10)

and

K= γ2e1+[?Qξ(T)]2

β(ξ/a)2 2(11) Forξ(T)?a:1/T1T～ξ(T)2,1/T2～ξ(T),and K s～ξ(T)2which leads to K?( γ2e/2Γˉχ0)[πξ(T)/a]?2. We can see that K<1in the presence of ferromagnetic ?uctuations.67,68So again vertex corrections are impor-tant if the system has strong ferromagnetic?uctuations. Recall that,in contrast,in the case of antiferromagnetic ?uctuations the Korringa ratio is larger than one.Thus analyzing the Korringa ratio allows one to straightfor-wardly distinguish between antiferromagnetic and ferro-magnetic spin?uctuations.

B.Dynamical Mean Field Theory

DMFT is an approach based on a mapping of the Hubbard model onto a self-consistently embedded An-derson impurity model.69,70,71DMFT predicts that the metallic phase of the Hubbard model has two regimes with a crossover from one to the other at a tempera-ture T0.For T

The predictions of DMFT correctly describe the prop-erties of a range of transport and thermodynamic exper-iments on the organic charge transfer salts.8,24,25This suggests that these systems undergo a crossover from a bad metal regime for T>T0to a renormalized Fermi liq-uid below T0.As we shall see in more detail later(see Fig.1)the nuclear spin relaxation rate is suppressed but never saturates below T NMR;this is not captured by DMFT.This suggests that the low-temperature regime ofκ-(ET)2X is more complicated than the renormalized Fermi liquid predicted by DMFT which until now,is widely believed to be the correct description of the low temperature paramagnetic metallic state in the organic charge transfer salts.We will discuss the reasons for and implications of the failure of DMFT to correctly describe NMR experiments on the organic charge salts in section V.

C.Quantum Critical Region of Frustrated2D

Antiferromagnets

The static uniform and dynamic susceptibilities of nearly-critical frustrated2D antiferromagnets has been studied by Chubukov et al.73They considered a long-wavelength action with an N component,unit-length, complex vector which has a SU(N)?O(2)symmetry and performed a1/N expansion.This gives susceptibili-ties which follow a universal scaling form.As one ap-proaches the quantum critical point,the spin sti?ness will vanish but the ratio between in-plane and out-of-plane sti?nesses remains?nite and approaches unity.In this regime,to order1/N,the quantities in Eq.(2)are given by73

1/T1～Tη;1/T2～Tη?1;K s～T;K～Tη?2.(12) III.SPIN FLUCTUATIONS INκ-(ET)2X The NMR relaxation rate per unit temperature, Knight shift,and Korringa ratio in the antiferromag-netic spin?uctuations model are given by Eqs.(9a), (9c),and(9d).Their temperature dependence comes through the antiferromagnetic correlation length.We adopt the form ofξ(T)from M-MMP44,45:ξ(T)/ξ(T x)=

T x represents a natural temperature scale andξ(T)is only weakly temperature dependent for T?T x.For this choice ofξ(T)/a we have

1

T1T 0 1+βC2

βC

(T/T x+1)2+2π2C(T/T x+1)

βC

a 2 ,

(1/T1T)0=

2πk B|A|2ˉχ0

γeγN 2

,

and K0= γ2

e

T1T?1+β

a

2 1? T

T1T?1+β

a

2 1

Material(1/T1T)0β[ξ(T x)/a]2

(s?1K?1)

Maya?re[18] 6.5±5.5

De Soto[19]20±10

Miyagawa[20] 6.2±3.5

Kawamoto[21]11±2.6

β/(2π2)) which is temperature independent.We use this temper-ature independent Knight shift to calculate the Korringa ratio K

K= γ

N

21

π2(T/T x+1)

1

β/(2π2)

2 where the

prefactor K0is given by Eq.(14).

We?t Eq.(16)to the experimental Korringa data for κ-(ET)2Cu[N(CN)2]Br.19The result is plotted in Fig.2. In this expression we have three parameters,β[ξ(T x)/a]2, T x,and

√

β,which can then be determined unambiguously from the Korringa?t which yieldsβ=60±20.This value ofβimplies that the an-tiferromagnetic correlation lengthξ(T)=3.5±2.5a(a is the unit of one lattice constant)at T=50K.This value is in the same order of magnitude as the value of the correlation length estimated in the cuprates.65

The Korringa ratio data are well reproduced by the antiferromagnetic spin?uctuation model when T> T NMR.This is again consistent with our earlier con-clusion that the spin?uctuations have antiferromagnetic correlations.A large Korringa ratio74,75has previously been observed in the cuprates indicating similar anti-ferromagnetic?uctuations in these systems.The Ko-rringa ratio has also been measured in a number of heavy fermion compounds76,77,78Similar antiferromag-netic?uctuations,like those observed in the cuprates and organics,are present in CeCu2Si2and.The Kor-ringa ratio of this material has a value of4.6at100mK (Ref.[77]).In contrast,YbRh2Si276and CeRu2Si278, show strong ferromagnetic spin?uctuations as is evident from the Korringa ratio less than unity.In Sr2RuO479 the Korringa ratio is approximately1.5at1.4K.Upon doping with Ca to form Sr2?x Ca x2RuO4,the Korringa ratio becomes less than one which indicates that there is a subtle competition between antiferromagnetic and ferromagnetic?uctuations in these ruthenates.

C.The Antiferromagnetic Correlation Length

It is important to realize that the spin?uctuation for-malism can be used to extract quantitative information about the spin correlations from NMR data.For exam-ple,the?ts presented in Figs.1and2allow us to esti-mate the antiferromagnetic correlation length.From the ?t forκ-(ET)2Cu[N(CN)2]Br(Table I)we found that the antiferromagnetic correlation lengthξ(T)/a=3.5±2.5 at T=T NMR=50K.In order to understand the phys-ical signi?cance of this value ofξ(T)it is informative to compare this value with the correlation length for

10

the square 80and triangular 81lattice antiferromagnetic Heisenberg models.

It has been shown 80that,on the square lattice,the antiferromagnetic Heisenberg model has a correlation length of order ξ(T )/a ～1for T =J and of order ξ(T )/a ～30for T =0.3J .On the other hand for the antiferromagnetic Heisenberg model on the isotropic tri-angular lattice,the correlation length is only of order a lattice constant at T =0.3J .81Thus the correlation length,ξ(T )/a =3.5±2.5,obtained from the analysis of the data for κ-(ET)2Cu[N(CN)2]Br is reasonable and places the materials between the square and isotropic an-tiferromagnetic Heisenberg model as has been argued on the basis of electronic structure calculations.8,47,82

One of the best ways to measure antiferromagnetic cor-relation length is by inelastic neutron scattering experi-ments.To perform this experiment,one needs high qual-ity single crystal.Unfortunately,it is di?cult to grow su?ciently large single crystals for κ-(ET)2X ;however,recently some signi?cant progress has been made.83An-other way to probe the correlation length is through the spin echo experiment.The spin echo decay rate 1/T 2is proportional to the temperature dependence correlation length [see

Eq.(9)]so measurements of T 2would give us direct knowledge on the nature of the correlation length.To the authors’knowledge there is no spin echo decay rate measurement on the metallic phase of the layered organic materials at the present time thus it is very de-sirable to have experimental data on T 2measurement to compare with the value of ξ(T )we have extracted above.

D.The Knight Shift

As we pointed out in Section II the Knight shift K s will

generally have a weak temperature dependence through-out the whole temperature range and so,thus far,we have neglected its temperature dependence.However,it is apparent from Eq.(13)that for any choice of parame-ter values {β,ξ(T x )/a ,and T x },K s will always increase monotically as the temperature decreases.Therefore the temperature dependence of the Knight shift potentially provides an important check on the validity of the spin ?uctuation model.However,in the following discussion one should recall the caveats (discussed in section II A)on the validity of the calculation of the Knight shift stem-ming from the assumption that the dynamics of the long wavelength part of dynamical susceptibility relax in the same manner as a Fermi liquid.

In contrast to the prediction of the spin ?uctuation model the experimental data,e.g.,those measured 19on κ-(ET)2Cu[N(CN)2]Br (reproduced in Fig.4),show that K s decreases slowly with decreasing temperature which then undergoes a large suppression around T K s ～50K.It should be emphasized here that T K s is approximately the same as T NMR ,the temperature at which 1/T 1T is maximum.

Since it is not possible to explain any of the NMR

data below T NMR in terms of the spin ?uctuation model within the approximations discussed thus far we focus on the temperature range between 50K to 300K just as we did for the analysis of 1/T 1T .Even in this temperature range,there is a puzzling discrepancy between theory and experiment:the experimental data decreases slowly with decreasing temperature while the theoretical calculation predicts the opposite.We will argue below that this dis-crepancy arises because the data are obtained at con-stant pressure while the theoretical prediction assumes constant volume.Since the organic charge transfer salts are particularly soft,thermal expansion of the unit cell may produce a sizeable e?ect to the Knight shift and may not be neglected.

Following Wzietek et al.,84we attempt to make an estimate on the correction of the Knight shift for κ-(ET)2Cu[N(CN)2]Br due to thermal expansion.Let us de?ne χv s (T,V )as the constant volume spin susceptibil-ity as a function of temperature.The measured sus-ceptibility is then given by a constant pressure suscep-tibility χp s =χp s [T,V (T,P )]while the theoretical sus-ceptibility is given by a constant volume susceptibility

χv s =χv

s [T,V (T =0,P )].The correction to the spin susceptibility is then given by

?χ=χp s ?χv

s

(17)

= T

dT ′

?χp s

?V

T ′

?V

?P

T ′

V ?P

V ?T ′

P

,

where K p

s is the (experimentally obtained)isobaric

Knight shift,K v

s is the (calculated)constant volume Knight shift,(V ?P/?V )T is the isothermal compress-ibility,and (?V/V ?T )P is the linear thermal expansion.It is hard to obtain an accurate estimate for ?K s be-cause there are no complete sets of data for K p

s ,isother-mal compressibility,and thermal expansion as a function of temperature and pressure for the κ-(ET)2-X family.However a rough estimate for ?K s may be made using the available experimental data.In Appendix B we estimate that

?K p s

?V

T

～?105bar ,and

1?T

P

～10?4K ?1.

Combining these order of magnitude estimates we are able to obtain a rough estimate on ?K s which can be

11

120

140 160 180 200 220 240 260 0

50

100

150 200 250 300

K s (p p m )

T(K)

FIG.4:The temperature dependence of the (constant pressure)Knight shift as measured by κ-(ET)2Cu[N(CN)2]Br by De Soto et al .19(?lled squares)and the corrected Knight shift obtained by taking into account thermal expansion of the lattice (half-?lled diamonds),i.e.,the constant volume Knight shift.The temperature at which the Knight shift decreases rapidly is about the same temperature at which 1/T 1T is suppressed (see Fig.1),i.e.T K s ～T NMR .This suggests that 1/T 1T and K s are suppressed by the same physics.In the limit of large correlation lengths,the spin ?uctuation model,Eq.(13),predicts a slowly varying Knight shift which is almost temperature independent (solid line).The discrepancy between theory and experiment arises because the model calculates constant volume Knight shift while the experiment measures constant pressure Knight shift.84Since κ-(ET)2X is soft there will be a sizeable e?ect on K s due to the large thermal expansion.The correction to the experimental Knight shift,by taking into account these e?ects,was calculated by using Eq.(18)(half ?lled squares).However,we stress that the lack of compressive measurements of pressure and temperature dependence of the Knight shift,isothermal compressibility,and thermal expansion means that this correction is no better than an order of magnitude estimate.However,our estimate indicates that there correction is large enough that the data above T K s cannot be shown to be in disagreement with the spin ?uctuation model.Below T K s there is a clear disagreement between the theory and data,in section V we argue that this is because a pseudogap opens at T NMR .In the key to this ?gure κ-(ET)2Cu[N(CN)2]Br is abbreviated as κ-Br.

written as K v s ≈K p

s ?0.3T for T in Kelvin.The re-sult is plotted in Fig.4.It is clear from the ?gure that our rough estimate has already produced a non trivial correction to the Knight shift.The Knight shift changes from having a positive slope in the raw data to exhibit a rather small negative slope between T K s ～50K and room temperature when the corrections to account for the thermal expansion are included.The correction be-comes small below about 50K.The lattice expansion clearly has a signi?cant e?ect on the measured Knight shift.To remove this e?ect one would need to either measure the Knight shift at constant volume or pursue an experiment in which the pressure dependence of K s ,isothermal compressibility,and thermal expansion [c.f.Eq.(18)]are measured simultaneously to accurately de-termine ?K s .Given the large uncertainty in ?K s we take K s to be constant for temperatures above 50K in the rest of this paper.This is clearly the simplest as-sumption,it is not (yet)contradicted by experimental data,and,perhaps most important,any temperature de-pendence in the Knight shift is signi?cantly smaller than the temperature dependence of 1/T 1T .

Regardless of the valuse of ?K s ,the Knight shift cal-culated from the spin ?uctuation model is inconsistent with the experimental data below T K s ～50K (see Fig.4).The calculated K s shows a weakly increasing K s with decreasing temperature,while the measured K s is heavily

suppressed below 50K.One important point to empha-size here is that the temperature dependence of K s will not change even if one uses the fully q-dependent A (q )since K s [see Eq.(2c)]only probes the q =0compo-nent of the hyper?ne coupling and susceptibility.Thus,putting an appropriate q-dependent hyper?ne coupling will not change the result for K s (although it might give a better description for 1/T 1T ).This provides a com-pelling clue that some non-trivial mechanism is respon-sible to the suppression of 1/T 1T ,K s ,and K below 50K.

We have not addressed how the nuclear spin relaxation rate is modi?ed by the thermal expansion of the lattice.Since the organic compound is soft,it is interesting to ask if there is a sizeable e?ect to 1/T 1T .Wzietek et al.84have performed this analysis on quasi-1D organic compounds whose relaxation rate in found to scale like χ2s .One can straightforwardly derive the e?ect of volume changes from the Hubbard model.If one uses the relation 1/T 1T ～χ2s and assumes ?xed U and t ,then 1/T 1T ～

1/V 2

will follow.However,it is clear from the phase diagram of the organic charge transfer salts (Fig.3and Ref.8)that there is a rather large change in U and t for even small pressure variations.Therefore,there is no obvious relationship between 1/T 1T and χs for the quasi-2D organics and it is not clear how the imaginary part of the susceptibility χ′′(q ,ω),which enters 1/T 1T ,

12

is e?ected by thermal expansion and lattice isothermal compressibility.More detailed experiments are clearly

needed to determine the e?ect of thermal expansion of the lattice on the measured relaxation rate.

IV.SPIN FLUCTUATIONS IN THE MOTT

INSULATING PHASE OFκ-(ET)2CU2(CN)3 Recent experiments onκ-(ET)2Cu2(CN)3by Shimizu

and collaborators31,85,86,87have generated a lot of interest.8,57,61,88,89,90,91This is because the Mott insulat-

ing phase of this material appears to have a spin liquid ground state,that is a state which does not have mag-

netic ordering(or break any other symmetry of the nor-mal state)even though well-formed local moments exist.

This is very di?erent from the Mott insulating phases of the otherκsalts,such asκ-(ET)2Cu[N(CN)2]Cl,which

clearly shows antiferromagnetic ordering92at low tem-perature and ambient pressure.An elegant demonstra-

tion of these two di?erent ground states is provided by susceptibility measurements:31the susceptibility ofκ-

(ET)2Cu[N(CN)2]Cl exhibits an abrupt increase around 25K which marks the onset of N′e el ordering while the

susceptibility ofκ-(ET)2Cu2(CN)3shows no sign of a magnetic transition.The transition to a magnetically or-dered ground state realized inκ-(ET)2Cu[N(CN)2]Cl is

also demonstrated by the splitting of NMR spectra below the transition temperature.12The di?erence in

the ground states ofκ-(ET)2Cu[N(CN)2]Cl andκ-(ET)2Cu2(CN)3appears to be connected with the fact

that there is signi?cantly greater frustration inκ-(ET)2Cu2(CN)3(for which t′/t～1)than there is inκ-(ET)2Cu[N(CN)2]Cl(for which t′/t～0.7).Geometrical frustration alone is not su?cient to explain the absence

of magnetic order inκ-(ET)2Cu2(CN)3because a Heisen-berg model on an isotropic triangular lattice is known

to exhibit a magnetically ordered ground state,i.e.120?state.It may be that the proximity to the Mott transition

plays an important role in allowing the absence of mag-netic ordering at low temperatures inκ-(ET)2Cu2(CN)3. One possible explanation for the existence of a spin liq-uid ground state is there are ring exchange terms in the Hamiltonian arising from charge?uctuations which has been studied by several groups.89,90,91

The NMR relaxation rate inκ-(ET)2Cu2(CN)3(Ref.

85and Fig.5)shows a similar temperature dependence to that in,for example,κ-(ET)2Cu[N(CN)2]Br.1/T1T is enhanced over the Korringa-like behavior with a peak at T NMR～10K below which it exhibits a large decrease. However the Knight shift K s inκ-(ET)2Cu2(CN)3is quite di?erent to that inκ-(ET)2Cu[N(CN)2]Br(com-pare Figs.4and5).Inκ-(ET)2Cu2(CN)3,K s increases as the temperature is lowered from room temperature until it reaches a broad maximum around T K s～30?50 K below which it drops rapidly.In contrast,K s inκ-(ET)2Cu[N(CN)2]Br shows a weak temperature depen-dence down to T K s below which it undergoes a sharp de-crease(see Fig.4).Another di?erence is T NMR is consid-erably lower than T K s inκ-(ET)2Cu2(CN)3whereas they

are roughly the same inκ-(ET)2Cu[N(CN)2]Br.This suggests that whereas the suppression of1/T1T below

T NMR and K s below T K s inκ-(ET)2Cu[N(CN)2]Br prob-ably has a common origin;inκ-(ET)2Cu2(CN)3the ori-

gin of the suppression of1/T1T below T NMR is di?erent from the origin of the broad maximum in K s at T K s.

Note that the fact that K>1shows that the spin?uc-tuations are antiferromagnetic,this is rather interesting

given the importance of Nagaoka ferromagnetism on the triangular lattice.30

Given the reasonable agreement between the antiferro-magnetic spin?uctuation model with the NMR data on

κ-(ET)2Cu[N(CN)2]Br(down to T NMR～50K),we ap-ply the same formalism toκ-(ET)2Cu2(CN)3.A slight

modi?cation to the spin?uctuation model is necessary since,unlike the otherκsalts studied in this paper,κ-(ET)2Cu2(CN)3is an insulator.Therefore we clearly cannot use the Fermi liquid form ofχL W.The sim-plest approximation is that the dynamic susceptibility given in Eq.(3)will only consist ofχAF(q,ω).In the region whereξ(T)/a is large,χQ=α(ξ/a)2?ηand ωSF=α′(ξ/a)?z whereαandα′are temperature inde-pendent constants and a is the lattice spacing.Within these approximations the nuclear spin relaxation rate and Knight shift are given by

1

T1T 0(ξ/a)2+z?η

1+(Qa)2(ξ/a)2

(19)

with

1α

′γ2e 4

(K s)0=

α′|A|

2T x/(T+T x).

Following the same approximation scheme as before (outlined in Section II B),we assume a relaxational dy-namics of the spin?uctuations,which are described by a dynamic critical exponent z=2,and a mean?eld critical exponentη=0.Within these approximations ωSF=α(a/ξ)2andχQ=α′(ξ/a)2.The nuclear spin relaxation rate and Knight shift are then given by

1

(T/T x+1)2+(Qa)2C(T/T x+1)

K s=

(K s)0C

1/T 1T (s K )-1

T(K)

K s (p p m )

T(K)

K o r r i n g a r a t i o

T(K)

FIG.5:[Color online]Comparison of the spin ?uctuation theory with the measured 85temperature dependence of the nuclear spin relaxation rate per unit temperature,1/T 1T (left panel),Knight shift,K s (center panel),and Korringa ratio (right panel)of the Mott insulating phase of κ-(ET)2Cu 2(CN)3[abbreviated as κ-(CN)3in the keys to the ?gures].The spin ?uctuation model is in good agrement with the measured 1/T 1T ,but does not describe the Knight shift (and hence K )well.We have also checked that using the Fermi liquid for χLW does not improve the ?t to the K s data,and this ?t is shown as a dashed line.This ?t to the data is clearly worse than simply setting χLW =0.Also note that the peak in 1/T 1T ,T NMR ,is at a lower temperature than the maximum in the Knight shift,T K s .This behavior is qualitatively di?erent from that of the other κsalts where T NMR ～T K s (see Figs.1and 4).This suggests that in κ-(ET)2Cu 2(CN)3the origin of the 1/T 1T suppression is di?erent from physics that gives rise to the maximum in K s .The parameter values from the lines of best ?t shown in this ?gure are reported in Table II.The fact that the model gives a reasonably good ?t to 1/T 1T but not to the K s data suggests that the spin ?uctuation model fails to correctly account for the long wavelength physics,but suggests that the model correctly describes the physics around a peak in χ(q ,ω)which dominates the integral over the ?rst Brillouin zone and thus 1/T 1T [c.f.,Eq.(2a)].This is rather surprising as the correlation length is less than one lattice constant at T =50K.This result is clearly inconsistent with the initial assumption that the long wavelength susceptibility is dominated by a peak in the dynamic susceptibility at a ?nite wave vector.Finally we note that the fact that K >1shows that the spin ?uctuations are antiferromagnetic,this is rather interesting given the importance of Nagaoka ferromagnetism on the triangular lattice.30

ployed to obtain Eq.(15b).If the dynamic sus-ceptibility is strongly peaked at q =Q then the pa-rameter 2(Qa )2(ξ(T x )/a )2is much larger than 1so (Qa )2C (T/T x +1)is larger than (T/T x +1)2and we can just keep the term proportional to (Qa )2in the de-nominator which allows us to write 1/T 1T as

1

2ξ(T x )/a ]2

Fit results 220±11

(K s )0

40±4

ξ(T x )/a

(ET)2Cu2(CN)3are clearly inconsistent with a magnetic ordered ground state.For a two-dimensional quantum spin system with an ordered ground state,the low tem-perature properties are captured by the non-linear sigma model.The observed temperature dependence of1/T1 and the spin echo rate1/T2follow1/T1∝T7/2ξ(T), and1/T2∝T3ξ(T),where the correlation lengthξ(T)is given by73

ξ(T)

ρs 4πρs T (23)

where c is the spin wave velocity andρs is the spin sti?-ness.In the quantum critical regime,731/T1T～Tη?1

and1/T2～Tη?1[c.f.,Eq.(12)]whereηis the anoma-lous critical exponent associated with the spin-spin cor-

relation function whose value is generally less than1. Thus for a magnetically ordered state,which can be well described by O(N)non linear sigma model,both 1/T1T and1/T2should increase with decreasing tem-perature.Forκ-(ET)2Cu2(CN)3Shimizu et al.94found that1/T1T～T1/2and1/T2～constant from1K down to20mK which suggests the critical exponentη>1. The nuclear spin relaxation rate decreases with decreas-ing temperature.Such a large value of z is what occurs for decon?ned spinons.73

V.UNCONVENTIONAL COHERENT

TRANSPORT REGIME AND THE

κ-(ET)2X PHASE DIAGRAM

In Section II B,we discussed the DMFT description of the crossover from a bad metal to a Fermi liquid.DMFT successfully predicts the unconventional behaviors ob-served in a number of experiments on theκ-(ET)2X salts. These include the resistivity,thermopower,and ultra-sound velocity.The unconventional behaviors seen in these measurements are associated with the crossover from bad metallic regime to a renormalized Fermi liquid in the DMFT picture.While DMFT gives reliable pre-dictions for the transport properties,24,25,34,35it is not able to explain the loss of DOS observed in the nuclear spin relaxation rate and Knight shift.Thus the NMR data suggest that the coherent transport regime is not simply a Fermi liquid,contrary to what has previously been thought.

To illustrate the nature of the low temperature param-agnetic metallic state more qualitatively,it is instructive to study how the bad metal-coherent transport crossover is related to the loss of DOS.Therefore we have investi-gated the relationship between Tρ～T2,the temperature at which the resistivity deviates from T2behavior;T?v/v, the temperature at which a dip in the ultrasonic velocity is observed;and T NMR,the temperature at which1/T1T (and K s)is maximum which appears to mark the onset of a loss of DOS.In Figure6we plot Tρ～T2,T?v/v,and T NMR as measured by several di?erent groups for various salts against T c which serves well as a single parameter to Material Tρ～T2(P)T NMR(P) [38,95][38]

[37,96][37]

[98][37]

[86]-

T (K )T c (K)

Mott Insulator

FIG.6:[Color online]The relationship between di?erent temperature scales for a range of organic charge transfer salts.The superconducting transition temperature T c is used to parameterize the proximity of the material to the Mott transition (T c decreases as one moves further away from the Mott transition).A plot of T ρ～T 2,T ?v/v ,and T NMR against T c for several κ-(ET)2X salts shows that the peak in 1/T 1T ,T NMR ,occurs at the same temperature as the crossover form a bad metal to the coherent transport regime measured in transport (T ρ～T 2)and ultrasonic attenuation (T ?v/v )experiments.T ρ～T 2is the temperature at which the resistivity deviates from a T 2behavior,T ?v/v is the temperature at which a dip in the ultrasound velocity is observed.The left panel shows the data for the κ-(ET)2X family in the metallic phase {κ-(ET)2Cu[N(CN)2]Cl and κ-(ET)2Cu 2(CN)3under pressure,κ-(ET)2Cu[N(CN)2]Br and κ-(ET)2Cu(NCS)2}while the right panel shows the data for the κ-(ET)2X family in the insulating phase [κ-(ET)2Cu[N(CN)2]Cl and κ-(ET)2Cu 2(CN)3at ambient pressure].In the metallic phase we use T c as a single parameter to characterize the e?ect of chemical substitution and hydrostatic pressure.This works surprisingly well and the data for κ-(ET)2Cu[N(CN)2]Cl,κ-(ET)2Cu[N(CN)2]Br,and κ-(ET)2Cu(NCS)2is seen to collapse roughly onto a single trend,which suggests that the spin ?uctuations in the metallic phases are rather similar.In contrast,the data for κ-(ET)2Cu 2(CN)3fall onto a separate curve which suggests that there are important di?erences between the spin ?uctuations in this material and those in other κphase salts.This is perhaps not so surprising in light of the fact that κ-(ET)2Cu 2(CN)3has a spin liquid round state in its Mott insulating phase while the materials are close to at N′e el ordered Mott insulating phase.This plot suggests that the pseudogap opens at the same temperature as the crossover from bad metal to coherent transport regime.Whether this is because of a deep link between the crossover and the pseudogap or because the lack of coherence in the bad metal destroys the pseudogap remains to be seen.Collectively these data show that the coherent transport regime is not simply a renormalised Fermi liquid as has previously been thought.It should be emphasized that the large error bars are the result of our estimates of the systematic errors produced by equating pressures in di?erent experiments.The procedure to obtain the error bars presented in this plot is discussed in Appendix C.The symbols represent both the material and the experiment as follows:?lled symbols correspond to the data for κ-(ET)2Cu[N(CN)2]Cl,open symbols denote κ-(ET)2Cu[N(CN)2]Br,open symbols with black dots denote κ-(ET)2Cu(NCS)2,and half ?lled symbols denote κ-(ET)2Cu 2(CN)3.The square symbols represent T ρ～T 2vs T c ,circles represent T ?v/v vs T c ,and triangles represent T NMR vs T c .The references from which the data were collected are given in Table III.

On the basis of the above analysis we sketch the phase diagram of κ-(ET)2X ,shown in Fig.3.The pseudogap phase shows an interesting set of behaviors.On one hand it exhibits a loss of DOS as is evident from 1/T 1T and K s .On the other hand,it exhibits coherent intralayer transport as is shown by the T 2resistivity behavior 25;it also has long lived quasiparticles and a well de?ned Fermi surface clearly seen from de Haas-van Alphen and Shubnikov-de Haas oscillation experiments.39,40,41One framework in which it may be possible to understand both of these sets of behaviors is if there is a ?uctuat-ing superconducting gap.99This idea has been applied to the cuprates;100,101it would be interesting to see whether such an approach gives a good description of κ-(ET)2X .Another interesting observation is that the measurements which see the loss in the DOS probe the spin degrees of freedom whereas the evidence for well de?ned quasiparti-cles comes from probes of the charge degrees of freedom.This may be suggestive of a ‘spin gap’which could result from singlet formation as in the RVB picture.

16

To date there have been few experiments studying the pressure dependence of1/T1T or K s.Therefore it is not possible,at present,to determine with great accuracy where the pseudogap vanishes.The available NMR ex-periment under pressure18,102suggest that at su?ciently high pressures the pseudogap onset temperature is lower than the incoherent-coherent crossover temperature and pressure eventually suppresses the pseudogap altogether. We represent the current uncertainty over where the pseudogap is completely suppressed by pressure by draw-ing a shaded area with a question mark in the phase di-agram.It is plausible that the pseudogap vanishes very close,if not at the same pressure,to the point where the superconducting gap vanishes.This would be consistent with RVB calculations49,56which suggest that the pseu-dogap and superconducting gap are proportional to each other and so should vanish at about the same pressure. However,we should stress that there really is not yet su?cient data to determine exactly where the pseudogap vanishes and admit that our choice is,perhaps,a little provocative.

Clearly a series of careful experiments are required to elucidate when T NMR tends to zero.Understanding where the pseudogap vanishes is an important consider-ation in light of the number of theories based on a hid-den pseudogap quantum critical point in the cuprates.103 Furthermore,the superconducting state in organic charge transfer salts far from the Mott transition are highly un-conventional.These low T c organic charge transfer salts have unexpectedly large penetration depths52,53and are not described by BCS theory.54The possibility that a quantum critical point is associated with the pressure where T c goes to zero invites comparison with the heavy fermion material CeCoIn5?x Sn x104in which a quantum critical point seems to be associated with the critical dop-ing to suppress superconductivity.Thus low T c organic charge transfer salts appear increasingly crucial for our understanding of the organic charge transfer salts.8

An important question to address theoretically is why T NMR might coincide with Tρ～T2and T?v/v.Of course, it may be that the two phenomena are intimately con-nected.However,another possibility suggests itself on the basis of DMFT and RVB calculations.DMFT correctly captures the local physics and it is this lo-cal physics that dominates the cross-over from a‘bad-metal’to coherent in-plane transport.On the other hand RVB does not capture this cross-over(because the Mott transition is only dealt with at the Brinkmann-Rice level105)but does capture some of the non-local physics which DMFT neglects.The pseudogap is predicted by RVB theory to increase in temperature when pressure is lowered.49,56This rise in the pseudogap temperature is predicted to continue until the pressure is lowered all the way to the Mott transition,in contrast with the observed behavior(c.f.,Figs3and6).However,we conjecture that the RVB physics is‘cut o?’by the loss of coherence at Tρ～T2and T?v/v thus preventing T NMR from exceeding Tρ～T2≈T?v/v.

VI.CONCLUSIONS

We have applied a spin?uctuation model to study the temperature dependences of the nuclear spin relaxation

rate and Knight shift in the paramagnetic metallic phases of several quasi two-dimensional organic charge transfer

salts.The large enhancement of1/T1T between T NMR {～50K inκ-(ET)2Cu[N(CN)2]Br}and room tempera-ture has been shown to be the result of strong antiferro-magnetic spin?uctuations.The antiferromagnetic corre-

lation length is estimated to be3.5±2.5lattice spacings inκ-(ET)2Cu[N(CN)2]Br at T=50K.The temperature dependence of1/T1T for T>T NMR from the spin?uctua-tion model is qualitatively similar with the predictions of DMFT.The spin?uctuations inκ-(ET)2Cu[N(CN)2]Cl,κ-(ET)2Cu[N(CN)2]Br,κ(d8)-(ET)2Cu[N(CN)2]Br,and κ-(ET)2Cu(NCS)2are found to be remarkably similar both qualitatively and quantitatively.Strong spin?uc-tuations seem to be manifested in materials close to Mott transition.Recent NMR experiments106onκ-(ET)2Ag(CN)2·H2O,which is situated further away from the Mott transition,suggests that the spin?uctuations in this materials are not as strong as those in the other κsalts studied here.

We have also applied the spin?uctuation formalism

to the strongly frustrated systemκ-(ET)2Cu2(CN)3.In this compound the measured1/T1T,which probes the entire Brillouin zone,agrees well with the predictions of the spin?uctuation model for T>T NMR～10K.In con-trast the measured Knight shift,which only depends on the long wavelength physics,is not well described by the spin?uctuation model.This suggests that at least one of the assumptions made in the spin?uctuation model: (i)z=2,η=0,or(ii)χ(q,ω)is strongly peaked at wave vector q=Q;is violated inκ-(ET)2Cu2(CN)3or that the model neglects some important long wavelength physics.In light of the recent evidence for a spin liq-uid ground state inκ-(ET)2Cu2(CN)3,in contrast to the antiferromagnetic or‘d-wave’superconducting grounds states inκ-(ET)2Cu[N(CN)2]Cl,κ-(ET)2Cu[N(CN)2]Br,κ(d8)-(ET)2Cu[N(CN)2]Br,andκ-(ET)2Cu(NCS)2,and the greater degree of frustration inκ-(ET)2Cu2(CN)3it is interesting that there are such important qualitative and quantitative di?erences between the spin?uctuations in κ-(ET)2Cu2(CN)3and those in the otherκphase salts. The peak of1/T1T and the suppression of K s are strongly dependent on pressure:they are systematically reduced and completely vanish at high pressure(>4 kbar);18at high pressure a Korringa-like temperature de-pendences of1/T1T and K s are recovered for all temper-atures.It is clear that high pressures will suppress both the antiferromagnetic spin?uctuations which are dom-inant above50K and the mechanism(presumably the pseudogap)which causes drops in1/T1T and K s below 50K at ambient pressure.

The large suppression of1/T1T and K s below T NMR observed in all theκsalts studied here cannot be ex-plained by the M-MMP spin?uctuation model.The

17

most plausible mechanism to account for this feature is the appearance of a pseudogap which causes the suppres-sion of the density of states at the Fermi energy.This is because at low temperature1/T1T and K s are propor-tional?ρ2(E F)and?ρ(E F),respectively[c.f.,Eq.(??)]. Independent evidence for the suppression of density of states at the Fermi level comes from the linear coe?cient of speci?c heatγ.42The electronic speci?c heat probes the density of excitations within k B T of the Fermi en-ergy.Any gap will suppress the density of states near the Fermi surface which results in the depression of the speci?c heat coe?cientγ.Kanoda51comparedγfor sev-eral of theκ-(ET)2X salts and found that in the region close to the Mott transition,γis indeed reduced.One possible interpretation of this behavior is a pseudogap which becomes bigger as one approaches the Mott tran-sition.However,other interpretations are also possible, in particular one needs to take care to account for the coexistence of metallic and insulating phases;this is ex-pected as the Mott transition is?rst order in the organic charge transfer salts.26,107The existence of a pseudogap has also been suggestedλ-(BEDT-TSF)2GaCl4108from microwave conductivity.The reduction of the real part of the conductivityσ1from the Drude conductivityσdc and the steep upturn in the imaginary part of the conduc-tivityσ2may be interpreted in term of preformed pairs leading to a pseudogap in this material.

The experimental evidence from measurements of 1/T1T,K s,and heat capacity all seem to point to the existence of a pseudogap below T NMR inκ-(ET)2Cu[N(CN)2]Br andκ-(ET)2Cu(NCS)2.Thus a phenomenological description which takes into account both the spin?uctuations which are important above T NMR and a pseudogap which dominates the physics be-low T NMR would seem to be a reasonable starting point to explain the NMR data for the entire temperature range(clearly superconductivity must also be included for T

Future experiments.There are a number of key ex-periments to study the pseudogap.The pressure and magnetic?eld dependences of the nuclear spin relaxation rate and Knight shift will be valuable in determining the pseudogap phase boundary,estimating the order of mag-nitude of the pseudogap,and addressing the issue how the pseudogap is related to superconductivity.In the cuprates,there have been several investigations of the magnetic?eld dependence of the pseudogap seen in NMR experiments.For Bi2Sr1.6La0.4CuO6the nuclear spin re-laxation rate does not change will?eld up to43T.109 However,since T?～200K,one may require a larger ?eld to reduce the pseudogap.Similar results were found in YBa2Cu4O8.110However,in YBa2Cu3O7?δ[see espe-cially Fig.6of Ref.111]a?eld of order10T is enough to start to close the pseudogap.Mitrovic et al.111interpret this observation in terms of the suppression of‘d-wave’superconducting?uctuations.

The interlayer magnetoresistance of the cuprates has proven to a sensitive probe of the pseudogap.112,113,114,115 Moreover,it is found that for the?eld perpendicular to the layers(which means that Zeeman e?ects will domi-nate orbital magnetoresistance e?ects)the pseudogap is closed at a?eld given by

H P G? k B T?

18 APPENDIX A:VERTEX CORRECTIONS AND

THE DYNAMIC SPIN SUSCEPTIBILITY FOR

STRONGLY CORRELATED ELECTRONS

We consider a strongly interacting electron system

and derive the real and imaginary parts of the dynamic

susceptibility.We show that under some quite general

(but speci?c)conditions that the Korringa ratio is unity.

Many de?nitions are simply stated in this appendix since

most are derived more fully in any number of textbooks

(for example Ref.118).The general expression for the

dynamic susceptibility in Matsubara formalism is given

by

χαβ(q,iωn)= β0dτe iωnτ Tτmα(q,τ)mβ(?q,0) ,(A1)

whereβ=1/k B T is the inverse temperature,τis the

imaginary time,ωn=(2n+1)πk B T/ is the Matsub-

ara frequency,mαis the component of magnetization in

theαdirection,and Tτis the(imaginary)time ordering

operator.In order to considerχ?+(q,ω)we de?ne the

operators:

m?(q,τ)= γe

2 p c?p+q,↓(τ)c p,↑(τ),(A2)

m+(q,τ)= γe

2 p c?p+q,↑(τ)c p,↓(τ).(A3)

Upon substituting(A2)and(A3)into(A1)and perform-ing the appropriate Wick contractions on the operators one?nds that

χ?+(q,iωn)=

2γ2e

1?G0(p,τ)Σ(p,τ)

,(A5)

G0(p,τ)is the non interacting Green’s function,and Σ(p,τ)is the self energy.Theτintegration can be evalu-ated by?rst transforming the integrand in Eq.(A4)into momentum space.This gives

χ?+(q,iωn)=

2γ2e

ip n?εp?Σ(p,ip n),(A7)whereεp is the dispersion of the non-interacting system. To evaluate the Matsubara summation,it is convenient to express the full interacting Green’s function using the spectral representation

G(p,ip n)= ∞?∞dE1ip n?E1,(A8) where A s(p,E1)is the spectral function given by

A s(p,E)=?2ImΣ(p,E)

2β p,m

∞

?∞

dE1

2π

×Γ(p+q,ip m;p,ip m+iωn)

×A s(p+q,E1)A s(p,E2)

2 p

∞

?∞

dE1

2π

A s(p+q,E1)

×A s(p,E2)n F(E1)?n F(E2)

ω

=

2γ2e

4π

A s(p+q,E)A s(p,E) ??n F T1T

=

k B|A|2

4π p

q A s(p,E)A s(p+q,E)×

??n F

19

where we have assumed a contact,i.e.momentum in-dependent,hyper?ne coupling.This expression can be written in the more intuitive form

1

∞

?∞dE ?E ,(A14)

where

?ρ(E )=

p

A s (p ,E )(A15)

is the full interacting density of states.At temperatures

small enough so that ?ρ(E )varies little with energy within k B T of the Fermi energy,E F ,the expression can be fur-ther simpli?ed to

1

4π

.

(A16)

Within the approximation of neglecting vertex correc-tions the real part of the dynamic susceptibility is given by

χ′

(q ,ω)=

2γ2e

2π

A s (p +q ,E 1)

×

∞

?∞

dE 2

ω+E 1?E 2

.

(A18)

To perform the integration over E 2,we ?rst make the change of variable x =ω+E 1?E 2and take the limit ω→0.Thus the integral over E 2becomes

∞

?∞

dx

2πA s (p ,E 1?x )n F (E 1)?n F (E 1?x )

dE 1

∞

?∞

dx

2π

A s (p ,y )=1,(A20)

χ′?+(q ,0)then becomes χ′?+(q ,0)=

2γ2

e

2π

p

A s (p +q ,E )

?

?n F

2γN

∞

?∞

dE

?E

.(A22)

At temperatures su?ciently low that ?ρ(E )varies lit-tle with energy within k B T near the Fermi energy,the

Knight shift is given by

K s ?

|A |γe ?ρ(E F )

4πk B γe

T 1T K 2s

=

γN

2

k B |A |2?ρ2(E F )

|A |γe ?ρ(E F )

2

=1.

(A24)

For non

interacting electrons,the self energy Σ(q ,ω)=0;expressions Eqs.(A14)and (A22)are still valid and one only need replace ?ρ(E )with the non interacting den-sity of states ρ(E ).On the temperature scale over which the density of states varies little with energy,the Kor-ringa ratio for free electron gas K free =1.By comparing Eqs.(A24)and K free =1we see that any deviation of the Korringa ratio from one must be caused by either vertex corrections or the q-dependence of the hyper?ne coupling.

APPENDIX B:ESTIMATION OF EFFECT OF THERMAL EXPANSION OF THE LATTICE ON

THE KNIGHT SHIFT

In this appendix we describe how we obtained our esti-mates of the isothermal compressibility the linear coe?-cient of thermal expansion and the pressure dependence of the Knight shift.By feeding these estimates into Eq.(18)we estimate the correction to the Knight shift re-quired because measurements are generally performed at constant pressure whereas calculations are most natu-rally performed at constant volume.The di?erence be-tween these two versions of the Knight shift can be quite signi?cant as can be seen in Fig.4.

First,let us discuss the ?rst term in the inte-grand in Eq.(18).We observed that K p

s can be

rewritten as K p

s =[ γ2e /(4πk B γ2N T 1T K )]1/2.

Us-ing Maya?re’s data,18

we extracted the pressure de-pendence of 1/T 1T at constant temperature and esti-mated that (1/T 1T )1/2is roughly linear with pressure:(1/T 1T )1/2～?3x10?5P for T 1in second,T in Kelvin,and P in bar.We then used this result and the Ko-rringa value for non interacting electron gas to cal-culate (?K p

s /?P )T for κ-(ET)2Cu[N(CN)2]Br which is found to be around ?3x10?8/bar.One can compare

the value obtained here with (?K p

s /?P )T obtained from the pressure dependence study on e?ective mass in κ-(ET)2Cu(NCS)2compound 98which is presumably more reliable.Since K s should be proportional to the e?ective

20

mass,the quantity of interest(?K p s/?P)

T can be esti-

mated from the pressure dependence of the e?ective mass data which yields a value around?6x10?8/bar.The two estimates agree to with a factor of two.

Next we need to obtain a value for lattice isother-mal compressibility.We use the analytical expression obtained from DMFT34

(K v)?1=B0

v0

2

χel,(B1)

where K is the inverse isothermal compressibility (v?P/?v)?1,v0is the reference unit-cell volume,v is the unit-cell volume under pressure,B0is a reference bulk elastic modulus,D0is a reference bandwidth,νis a parameter that characterizes the change in the band-width under pressure,andχel is the electronic suscep-tibility.We estimated that forκ-(ET)2Cu[N(CN)2]Cl, v0=1700?A3,B0=122kbar,D0=0.13eV,and D0χel～1.Putting everything together,the order of magnitude of the lattice isothermal compressibility for κ-(ET)2Cu[N(CN)2]Cl is around?105bar.Although we are not aware of any measurements of the isothermal compressibility ofκ-(ET)2Cu[N(CN)2]Cl systematic ax-ial pressure studies119onα-(BEDT-TTF)NH4Hg(NCS)4 found that the isothermal compressibility is of order?105 bar,a value which is very close to our crude estimate for κ-(ET)2Cu[N(CN)2]Cl.

The temperature dependence of the thermal expan-sion at constant pressure has been measured by M¨u ller et al.120They found thatκ-(ET)2Cu[N(CN)2]Cl,κ-(ET)2Cu(NCS)2,and undeuterated and fully deuterated κ-(ET)2Cu[N(CN)2]Br all have a relatively temperature independent thermal expansion above about80K while complicated features are observed below80K associated with glassy transitions and the many-body behavior of these materials.Since we are only interested in getting an order of magnitude,we neglect the complicated tem-perature dependence observed inκ-(ET)2-X and approx-imate the thermal expansion as a constant.The value extracted from M¨u ller et al.’s data is around10?4K?1.

APPENDIX C:ESTIMATION OF ERRORS IN

FIGURE6

In this appendix we outline the procedure use to esti-mate the errors on the data presented in Fig6.Let us consider a given set of data,for example T c(P).To a rea-sonable degree of accuracy,T c forκ-(ET)2X decreases linearly with increasing pressure,i.e.T c=aP+b where a and b are the coe?cients obtained from?tting the ex-pression to the data.In a typical pressure measurement, there will be some uncertainties in the pressure(?P) which may be caused by systematic errors due to the un-certainties in the pressure calibration.The size of?P will depend on a speci?c apparatus used in the experi-ment.For example,a helium gas pressure system would have uncertainties as large as0.1kbar while a clamped pressure cell which uses oil pressure medium may have uncertainties as large as1kbar.121,122Knowing?P,we can estimate the uncertainty in T c when it is compared with another data set from a di?erent experiment taken by a di?erent group,say Tρ～T2(P).This is done by cal-culating the following:

?T c=

dT c(P)

太阳的话读后感

太阳的话读后感 本文是关于读后感的，仅供参考，如果觉得很不错，欢迎点评和分享。 太阳的话读后感（一） 四年级的一篇诗歌《太阳的话》，文章比较简单明了，这节课严老师在指导小组合作的方法切实可行，如在小组读文的时候，老师强调：你给他提的建议要让他马上能得到提高。我想我们在教学生时就是要具体告诉他怎样做到最好，说话要到位。本节课学生在仿说诗歌和仿写诗歌时，学生们展示了较高的运用语言能力。严老师自己说讲完课后，知道自己在讲课时出现了诸多语病，如不能说“ 读出你的感受和感情” 。可以说“ 读出你的感受” 或者“ 有感情的读一读” 。总体来说，这是一节成功的课。 解读一篇文章，是探讨生活；用动听的语言引导别人，是一种艺术。 太阳的话读后感（二） 在《太阳的话》这首诗中，诗人以拟人的手法，赋予太阳人的语言与思想，展示了太阳渴望走进小屋，打开人们关闭的心灵，让人们享受亮光、温暖、花束、香气和露水，享受太阳带来的欢乐和美好。召唤人们敞开心扉迎接光明，促使人们树立起积极乐观的信念。 生活，一个普普通通的词，热爱生活，一个最简单的道理，但是谁也没有真正理解过这个词，生活是由几千几万个小事构成的，做好事是生活，受批评是生活，同情一个人还是生活，生活不一定要干出

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《太阳》读后感

《太阳》读后感 下面是带来的《太阳》读后感，让我们共同来了解太阳的重要性。 通过学习《太阳》这篇课文，我深深地感受到它对我们的重要性。 首先，从课文中我知道了太阳离我们有亿里远，如果我们日夜不停地走，还要3500年呢!而太阳又是那么的大，130万个地球才能抵得上一个太阳。太阳会发光、发热，是个大火球，它表面温度有6000摄氏度，中心温度是表面温度的2500倍，就是钢铁碰到它，也会变成气。正因为太阳这么大，温度这么高，距离我们又这么远，才能给地球送来光明和温暖。 地球上一切的生物都和太阳有着密切的关系。万物的生长需要太阳，有了太阳，地球上的树木、花草、动物才能生存、繁殖。如果没有太阳，地球上不会有植物、也不会有动物。我们人类的吃、穿、住、行也都离不开太阳。没有太阳，我们人类就不能在地球上生存。可见太阳对人类是多么的重要啊! 因为有了太阳的热量，才形成了空气中的水蒸气、云、风、雨、雪······这些自然现象。太阳还有杀菌的作用，我们利用它来预防疾病。我们生活中用的太阳能热水器，就是利用太阳的热能来工作的。在其他的科学技术中，也用到

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太阳读后感100字三篇

太阳读后感100字三篇 太阳读后感（一） 通过学习《太阳》这篇课文，我深深地感受到它对我们的重要性。 首先，从课文中我知道了太阳离我们有1.5亿里远，如果我们日夜不停地走，还要3500年呢！而太阳又是那么的大，130万个地球才能抵得上一个太阳。太阳会发光、发热，是个大火球，它表面温度有6000摄氏度，中心温度是表面温度的2500倍，就是钢铁碰到它，也会变成气。正因为太阳这么大，温度这么高，距离我们又这么远，才能给地球送来光明和温暖。 地球上一切的生物都和太阳有着密切的关系。万物的生长需要太阳，有了太阳，地球上的树木、花草、动物才能生存、繁殖。如果没有太阳，地球上不会有植物、也不会有动物。我们人类的吃、穿、住、行也都离不开太阳。没有太阳，我们人类就不能在地球上生存。可见太阳对人类是多么的重要啊！ 因为有了太阳的热量，才形成了空气中的水蒸气、云、风、雨、雪……这些自然现象。太阳还有杀菌的作用，我们利用它来预防疾病。我们生活中用的太阳能热水器，就是利用太阳的热能来工作的。在其他的科学技术中，也用到了很多有关太阳的能量…… 地球上的一切光明和温暖，都是太阳送来的，如果没有太阳，地球上将到处是黑暗。我们生活的世界这么美丽，太阳有多么神

奇的力量啊！ 太阳读后感（二） 今天我们学习了《太阳》这篇课文，它让我了解到太阳离我们有1.5亿公里远，如果步行到太阳去要走3500年，就是坐飞机，也要飞二十几年。太阳很大，130万个地球才能抵得上一个太阳。因为太阳离地球太远了，所以我们看到的太阳只有一个盘子那么大。太阳光有杀菌的能力。我们可以利用他来预防和治疗疾病。 地球上的光明和温暖，都是太阳送来的。有了太阳才有了我们这个美丽可爱的世界！ 太阳读后感（三） 语文书上的第二十一课《太阳》主要内容是： 有这么一个传说，古时候，天上有10个太阳，后来用箭射死9个太阳。其实，太阳离我们有1.5亿公里远，到太阳上去，如果步行，日夜不停地走，差不多要走3500年，就是坐飞机也要走20多年。 我们看到太阳，觉得它并不大，实际上太阳特别的大，130万个地球才能抵得上一个太阳。因为，太阳离地球太远了，所以我们看起太阳来只是一个盘子一样大。 太阳会发光，会发热，是个大火球。太阳的温度很高，表面温度有6000摄氏度。就是什么东西碰到太阳，就会变样子或非常的很烫。 所以地球上的太阳给我们了很多很多帮助，我们一定要珍惜每一分时间，太阳没有，我们的世界也不会这么美好这么可爱！ 词语理解：1、凝成：凝聚在一起

五大销售技巧和话术

五大销售技巧和话术 要想成为一名出色的推销员，掌握一些推销技巧是必不可少的，那么，有效实用的推销技巧有哪些?下文就介绍了推销高手们总结的五大推销技巧，可供参考! 步骤/方法 1.推销技巧一：厉兵秣马 兵法说，不打无准备之仗。做为销售来讲，道理也是一样的。很多刚出道的促销员通常都有一个误区，以为销售就是要能说会道，其实根本就不是那么一回事。记得那时候我们培训了将近一个月，从产品知识到故障分析，从企业历史到销售技巧，每一个环节都反复练习，直至倒背如流。那时候我们同事之间经常互相打趣说咱都成了机器人了。我记得当时为了调试出一个最佳音乐效果，一没有顾客在场，我就专心致志地一个键一个键的反复试验，持续了将近一个星期，终于得到了自己满意的效果。 每次轮到自己休息，我总喜欢到各个卖场去转转：一来调查一下市场，做到心中有数。现在的顾客总喜欢讹促销员，哪里哪里有多么便宜，哪里哪里又打多少折了，如果你不能清楚了解这些情况，面对顾客时将会非常被动。二来可以学习一下别的促销员的技巧，只有博采各家之长，你才能炼就不败金身! 2.推销技巧二：关注细节 现在有很多介绍促销技巧的书，里面基本都会讲到促销员待客要主动热情。但在现实中，很多促销员不能领会到其中的精髓，以为热情就是要满面笑容，要言语主动。 其实这也是错误的，什么事情都要有个度，过分的热情反而会产生消极的影响。 热情不是简单地通过外部表情就能表达出来的，关键还是要用心去做。所谓精诚所至，金石为开!随风潜入夜，润物细无声，真正的诚就是想顾客所想，用企业的产品满足他们的需求，使他们得到利益。 3.推销技巧三：借力打力 销售就是一个整合资源的过程，如何合理利用各种资源，对销售业绩的帮助不可小视。作为站在销售第一线的促销员，这点同样重要。 我们经常在街头碰到骗子实施诈骗，其中一般都有一个角色—就是俗称的托，他的重要作用就是烘托气氛。当然，我们不能做违法的事，但是，我们是不是可以从中得到些启发呢?我在做促销员的时候，经常使用一个方法，非常有效，那就是和同事一起演双簧。特别是对一些非常有意向购买的顾客，当我们在价格或者其他什么问题上卡住的时候，我常常会请出店长来帮忙。一来表明我们确实很重视他，领导都出面了，二来谈判起来比较方便，只要领导再给他一点小实惠，顾客一般都会买单，屡试不爽!当然，如果领导不在，随便一个人也可以临时客串一下领导。关键是要满足顾客的虚荣心和爱贪小便宜的坏毛病。

【销售技巧】SPIN销售四大模式-方法和技巧

SPIN销售四大模式-方法和技巧 SPIN技法由四种类型的提问构成，每一种提问都有不同的目的。以销售一个自动仓储设备系统为例（能解决买方可能存在的仓储能力不足、出错机率高、服务不及时等问题），卖方可用以下的问题组合来发掘和引导潜在客户（如一个物流中心）的需求和购买决定： 一、有关现状的提问(Situation Questions)。了解有关客户组织与现状的背景信息，如：现在货物仓储采用什么作业方式？共存储多少不同种类的货物？高峰期最多有多少产品需要仓储？ 二、有关问题的提问(Problem Questions)。发现和理解客户的问题、困难和不满，如：目前的仓储能力您是否满意？货物存储品种太多，差错率高吗?高峰期的仓储服务跟得上吗？ 三、有关影响之提问(Implication Questions)。发掘问题不解决将给客户带来的不利后果，如：仓储能力有限对成本控制和业务增长有何影响？仓储差错会不会影响到营运效率和客户满意度？高峰时货 物不能及时处置会有什么不利？ 四、有关需求与回报之提问(Need-Payoff Questions)。取得客户对于解决问题后的回报与效益的看法，将讨论推进到行动和承诺阶段，如：如果仓储能力得以充分利用，可增加多少收入？您考虑过用更先进的自动仓储系统来消除差错吗？高峰时的及时服务能为您带来什 么正面影响？

我们还可以从下面这样一段销售对话案例中进一步了解SPIN技法： 卖方：你们现在的复印机使用得如何？有什么不满意的地方？ 买方：没什么不满意，用得挺好。 卖方：影印效果是不是令人满意呢？ 买方：就是有时复印图像时黑黑的。 卖方：你们经常复印有图像的文件吗？ 买方：是的，尤其在投标中，70%的文件都有图像。 卖方：用这些黑黑的图像会对你们的投标有什么影响吗？ 买方：当然，这种复印质量很影响我们中标的。 卖方：如果单单因为图像质量差而失了标，你觉得这意味着什么？ 买方：我们从来不敢去这样想。 卖方：你们现在有什么解决办法来解决这个问题呢？ 买方：关键的投标我们都拿出去印。 卖方：那这样做在时间上来得及吗？ 买方：一般还可以。

如何提高销售技巧和话术

怎样提高销售成交?反客为主,用提问引导你的客户。用提问引导你的客户 所谓用提问引导你的客户，就是先陈述一个事实，然后再针对这个事实发问，让对方给出相应信息。确实，以提问的方式引导客户可以起到让对方易于接受的作用。 那么，销售人员如何用提问的方式引导客户呢？下面我们介绍几种方法： 一、肯定性诱导提问 肯定性诱导提问法是对肯定性说法、诱导性说法以及提问的说话方法三种方式的同时运用。首先是肯定性说法，即使用正面性用语——“很受人欢迎的”。其次是诱导性说法——“这种产品有大小两种，不知您愿选择哪一种，不过我想是不是大的比较好呢？”最后是提问的方法——“这位先生，您要如何使用呢？” 二、与类似问题相比较 简单地说，就是利用客户的随身物品作为一个实际的例子来说服客户。 比如，小陈是学习软件的推销员。有一次，一位客户在看了产品简介之后，还想要看看所要购买软件的内容：“我应根据所要买的产品内容是 否适合我来确定买不买，对不对？” 小陈：“您说得没错，可是出版这本书的出版社非常有名，我希望您能相信一流的出版社。先生，可以问一下您的笔记本电脑是什么品牌吗？” 客户：“是国产产品。” 小陈：“哦！您买这台电脑的时候是否先把它拆开看一下里面的部件呢？” 客户：“没有。” 小陈：“我想你在看过电脑后，即便认为电脑质量没问题，也是因为相信这家公司的信誉和服务才买下它的。同样，买汽车的时候你也不能把 车子拆开看一下引擎吧？还有买药品的时候你无法从100元一盒的药品中，挑选其中一颗拿起来品尝，试试其功效后，才决定购买与否。虽然不同品牌的产品，也有可能有许多的价

格差异，但若是你分不出品质的好坏，我认为你应该依据厂商的信誉来购买。买这部学习软件也是一样，您应信任出版商的声誉。” 三、拆分问题引导 在推销价格昂贵的产品时，这个方法十分有效。一位销售人员经常在推销一套价格不菲的家具时，多次利用拆分问题来说服客户客户：“这件家具太贵了。” 销售人员：“您认为贵了多少？” 客户：“贵了1000多元。” 销售人员：“那么现在就假设贵了1000元整。”这时销售人员拿出了随身带的笔记本，在上面写下1000元给目标客户看。 销售人员：“先生，你想这套家具你肯定至少打算能够用10年再换吧？” 客户：“是的。” 销售人员：“那么，依照你所想的也就是每年多花了100元，您指的是不是就是这样？” 客户：“对，我就是这样认为的。” 销售人员：“1年100元，每个月该是多少钱？” 客户：“哦！每个月大概就是8块多点吧！” 销售人员：“好，就算是8.5元吧。你每天至少要用两次吧，早上和晚上。” 客户：“有时更多。” 销售人员：“我们保守估计为l天2次，那也就是说1个月你将用60次。所以，假如这套家具每月多花了8.5元，那每次就多花了不到0. 15元。” 客户：“是的。” 销售人员：“那么每天不到1毛5分，却能让你的家变得利落和整洁，让你不再为东西没合适地方放而苦恼、发愁，而且还起到装饰作用，你不觉得很划算吗？”

《小太阳》读后感600字

《小太阳》读后感600字 导读：读书笔记《小太阳》读后感600字，仅供参考，如果觉得很不错，欢迎点评和分享。 《小太阳》读后感600字： 家像海上的灯塔，等待远航的船只归来；家像黎明前的启明星，照亮旅人前进的道路；家像沙漠里的一汪清泉，滋润着忙碌奔波的人们的心灵......在这个寒冷的冬日，我却从《小太阳》中感受到了家的温暖。 这本书是林良爷爷以“丈夫”、“父亲”的角度来记叙了：一对父母、三个女儿和一只小狗组成了一个平凡的家庭。林良爷爷用他温暖的笔触，书写了一部有趣而并不“传奇”的“家庭史”。从第一篇到最后一篇，首尾相隔了14年，是一本散文集，更是一本散文体小说。 其中，让我印象最深刻的一篇是《打架教育》,讲了琪琪和樱樱两人打架，“我”及时宣布家庭里的“政治制度”，目的就是要维护樱樱在家庭宪法里的合法地位——父母不在家的时候，由于“宪法”赐予她的职责和权力，琪琪必须对她服从。俗话说得好，君子动口不动手。一个人如果不能奋发向上，受人重视，她的谦和不谦和，根本毫无意义。但是，一个具有值得重视的美质的人，如果不懂得谦和，她的美质也就变得格外不重要了。人类社会所能接受的，事实上只有一种人：谦虚的杰出人物。只有在这种人面前，她们才肯献出人性中

的“稀有情愫”——敬爱。 有时候，为了形容家的美好，我们试图用一些华丽的、带着刺眼光芒的词语去修饰它，但这样，其实只是走远了它。只要一家人在一起，这就是家的样子，朴实且真切。林爷爷笔下的家，就是平凡的。三个小孩就是三个太阳。樱樱、琪琪和玮玮，虽然经常调皮，不免惹是生非，可一次平息的怒火，就是一片的温暖光芒。供稿：六（3）班郑雯欣 感谢阅读，希望能帮助您！

销售技巧和话术培训

销售技巧和话术培训 销售员是企业销售的主力军之一，为企业的发展进步做出巨大贡献，好的销售员能成功树立商品的形象，并且能销售出商品，形成二次顾客。所以，良好的销售员技巧培训是企业明智的选择。 徐清祥老师的销售技巧和话术培训能深入的讲解销售的技巧，并与实际相结合，让促销员受益匪浅，为企业形成良好销售回路。 主讲老师：徐清祥 课程时间：2天 课程背景： 在竞争激烈的销售市场上，精确掌握销售循环前、中、后的销售技巧与全方位的客户服务，是赢得最佳商机的关键。从销售的基本理论方法、实战技巧到销售的十大步骤、销售人员的自我管理，为销售人员专业技能训练提供了一整套的解决方案。如果你要掌握销售人员应具备的正确与基础的技巧，并吸收专家和成功者的经验与智慧，以资借鉴，减少自己摸索的时间、精力和犯错的机会，那就快走近我们的课程，唯有行动才能解决问题。 课程预定: 0371- 课程提纲： 第一部分：自我管理与规划能力 一、准备: 1、精神状态的准备： 静坐; 良好的睡眠.

2、体力的准备: 饮食; 运动. 3、专业知识的准备: 商品名称; 商品内容; 使用方法; 商品特征; 售后服务; 交货期与交货方式; 价格与付款方式; 研究同行业竞争中的商品; 材料来源与生产过程; 相关商品. 4、广泛知识的准备: 心理学; 管理学; 人际关系学; 行销学; 国学; 公众演说. 5、对顾客的准备.

使自己达到巅峰状态: 改变自己的动作: 1)自我确认; 2)自我放松. 二、改变自己的心态: 学习的心态; 积极的心态; 老板的心态; 感恩的心态; 付出的心态; 持之以恒的心态; 平衡的心态; 自律的心态; 宽容的心态; 拒绝找借口的心态. 三、问自己一些好的问题: 发生这些事对自己有什么好处? 自己学到了什么? 自己现在可以做什么? 第二部分：塑造良好的职业形象能力。 一、拥有良好的形象:

《太阳照常升起》读后感五篇

《太阳照常升起》读后感五篇 《太阳照常升起》是美国作家海明威创作的一部长篇小说，小说最主要的便是讲述了在战争中“迷惘的一代”的人物的生活与思想变化。有看过一次，似乎还没有全领悟其中的内涵呢。以下是的有关《太阳照常升起》的读后感，一起来看看吧！ 一直觉得海明威是个硬汉型的文人，也许和他的经历有关，参加一战，在欧洲当战地记者，喜欢看斗牛，打猎，航海，游历欧洲等等，没想到看完此部小说，才了解他并不是天生的硬汉，在自己生活的年代中的遭遇与经历造就了他后来的性格，也注定了他用饮弹这种方式来结束自己的生命…… 这样性格的文人不多，我很是敬仰与钦佩…… 与其苟且活着，不如自己了结，生命由自己主宰…… 《太阳照常升起》是海明威的第一部长篇小说，作者藉此成为“迷惘的一代”的代言人。小说中的主人公杰克。巴恩斯的经历，正是海明威在参加一战后的那段经历的缩影，他借此来表达战争给人类带来的创伤，主要是心灵上的创伤，这些创伤是永远无法愈合的。那个年代的这批受战争创伤的年轻人，心灵空虚，病态，桀骜不驯，没有明确的理想与目标，无精神支柱，所以称他们为“迷惘的一代”。 “你们都是迷惘的一代” “一代过去，一代又来，地却永远长存。日头出来，日头落下，急归所出之地。风往南刮，又向北转，不住的旋转，而且返回转行原

道。江河都往海里流，海却不满。江河从何处流，仍归还何处。”—《传道书》 我们都是迷惘的一代…… 1926年，还藉藉无名的海明威推出了首部长篇《太阳照常升起》，个人以为是他最好的长篇之一，虽然在当时算不上石破天惊。之前，他也有过一系列短篇投石问路，纵然水波不兴，也成为长篇准备中的练笔，使长篇处女作丝毫没有生涩的痕迹。当然这也有巴黎的良好催化作用在其中——饥饿与贫穷的磨练，良师斯坦因小姐的指点，与第一任妻子哈德莉恩恩爱爱、相濡以沫…… 可惜的是，这样的天时地利人和的因素在其成名后就一一分解。窃以为，吃得太饱，钞票与老婆太多，往往与才华的枯竭程度成正比。这是后话。 起初并不明白科恩在《太阳照常升起》中所起的作用。他显然不是一个应该被忽略的人物，开首就是一篇科恩小传，将其人交代清楚：就读于老牌名校——普林斯顿大学，曾是大学拳击冠军——身强体壮，出身富有的犹太家庭——身家清白，为人厚道，对女人尤其心软——要么被女人抛弃，要么被女人捏在手心。看起来并无不妥，中产阶级的普通一员，却无值得大书特书之处。看到后来发现苗头不对，他与书中正派的主人公及其寓公朋友总是格格不入，就象牛栏里那头想与公牛处好却被孤立的犍牛。后来我恍然大悟，科恩是作为一个未曾受过创伤的参照物而存在。所谓受过创伤，就是吃过战争的苦头，象巴恩斯被战争阉了就是一个直接的象征。

SPIN销售技巧课程概览

SPIN?销售技巧概览

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朝着太阳走读后感

朝着太阳走读后感 本文是关于读后感的，仅供参考，如果觉得很不错，欢迎点评和分享。 朝着太阳走读后感 看了张安阳的长篇文学传记《朝着太阳走》，颇受教益，感慨万端。因为本书的主人公是我们丹东曙光集团的缔造者李进巅，所以，倍感亲切。 《朝着太阳走》不仅描述了李进巅在创办曙光之前的风雨人生之路，而且透过生动的描述，从哲理的层面上解读李进巅的风雨人生，深层开掘他的性格，塑造他的形象。不言放弃，这是李进巅风雨人生最重要的经验，也是他最基本的性格。他从童年时代起，经历困顿的生活，到作为“双突干部”被逐出市委，政治生活上遭受重大挫折，以及在曙光创业路上的举步维艰，经历许多曲折，但他在每次受挫之后，都从不轻言放弃，而是迎着风雨前行；而且他还善于从失败中总结经验和教训，他总是认为，“失败给了我最宝贵的经验和财富”。这一点，不仅凸显他宁折不弯永不满足、永远奋斗的坚韧的性格，也是他冒着风雨前行的重要人生经验，给我们留下了深刻的印象，也给我们以人生的启迪讲信誉是一个成功企业家最重要的经验，也是李进巅的人生信条。他认为，“信誉是金，金子有价，而信誉则千金难求。”因此，他在为人和创业中，坚持以诚信为本。他是一个重信誉的企业家。亲民思想、平民姿态，这是李进巅成功后难得的表现。因为他有这种亲民思想和平民姿态，所以他平易近人，乐于助人、了解员工的

困苦，理解和体恤员工的需求。他说：“以心换心，才能赢得人心。领导者被员工拥戴，成为员工的依赖，这个企业才能被视为‘职工之家’。”曙光经历风风雨雨，不断壮大，同李进巅这种亲民思想和种种关心职工的举措是分不开的。重视企业文化建设，也是李进巅作为一位成功企业家的重要经验，同时也是他儒雅性格的一种表现。他提出的“创造效益、造福社会”的企业文化理念，创造的“把信带给加西亚”的企业精神以及所谓“鲶鱼效应”的选人用人原则，都为曙光的成长创造奇迹、成为比百亿产值更加可贵的一种无形的精神财富。 读过《朝着太阳走》这部书，我认为，这是一部很好的人生教科书，从书中我们领略了李进巅的人生经历，领略了他的创业史，也让我们学到了许多做人的道理。为此，我们要以李进巅为榜样，爱岗敬业，勇于进取，奋力拼搏，努力做自己的本职工作，以回报企业，以回报社会。 感谢阅读，希望能帮助您！

销售技巧与话术

酒店销售技巧与话术 酒店在日常经营过程中，是最需要客流量的一种行业之一，对于酒店来说，如果客流量断了，那么将会给整个企业带来巨大的损失，而酒店销售技巧和话术是维持客户不销售，形成二次甚至多次消费的重要条件。 一、酒店客房销售技巧和话术 1. 把握客人的特点 不同的客人有不同的特点，对酒店也有不同的要求。总台人员要注意客人的衣着打扮、言谈举止以及随行人数等方面把握客人的特点(年龄、性别、职业、国籍、旅游动机等)，进而根据其需求特点和心理，做好有针对性的销售。 (1)商务客人通常是因公出差，对房价不太计较，但要求客房安静，光线明亮(有床头灯)，办公桌宽大，服务周到、效率高，酒店及房内办公设备齐全[如安装有宽带网和直拨电话以及电脑、传真机等现代化设备]，有娱乐项目。 (2)旅游客人要求房间外景色优美，房间内干净卫生，但经济承受能力有限，比较在乎房间价格。 (3)度蜜月的客人喜欢安静、不受干扰且配有一张大床的双人房。 (4)知名人士、高薪阶层及带小孩的父母喜欢住套房。 (5)年老的和有残疾的客人喜欢住在靠近电梯和餐厅的房间。 (6)朋友多的喜欢住多床房 2. 熟悉客房 总台员工在销售客房时应明确自己是在销售客房，而非销售价格。因此总台员工应熟悉客房，在销售时，应多做客房的具体描述，而尽量少提及价格。具体如下： (1)总台人员在销售客房时，必须对客房做适当的描述，以减弱客房价格的分量，突出客房能够满足客人需要的特点。 (2)比如，不能只说：“一间198的客房，您要不要?”而应说，“一间刚装修过的、宽敞的房间”“一间舒适、安静、能看到临街景色的客房”“一间具有有民族特色的、装修豪华的07客房”，等等。这类形容词是无穷无尽的，只有这样容易为客人所接受。 (3)要准确地描述客房，必须首先了解客房的特点。这是对总台员工的最基本要求之一，比如带他们参观客房，并由专人讲解客房的特点，以加深印象。 3. 从高到低报价 在总台销售服务过程中，不可避免要谈到房价，向客人报房价也需要一定的技巧，即要从高到底报价。 (1)总台人员可根据客人的特点，向他推荐两中乃至三种不同价格的、可供比较的客房，让客人自己选择。 (2)如果是推荐一种客房，就会使客人失去比较的机会，推出价格范围，应考虑到客人的特点。 (3)一般来说，报房价由高价格退到较底价格比较适宜。例如：可以说“配备先进麻将机和电脑设备，装修宽敞的是208元”“靠近绿色菜圃，麻将房隔音效果极佳的客房是188元”“进出

《渔夫的太阳》读后感

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销售技巧和话术经典语

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四个太阳 听后感

《四个太阳》听后感 莱西市香港路小学张娟 《四个太阳》是一篇极富想象力和创造力的文章，作者通过画四种不同颜色的太阳来表达自己善良的心地和美好的愿望。课文语言优美，读起让人感到亲切、惬意。在这节课中，李老师用音乐给学生一种优美的气氛。而且，李老师指导的朗读，令我受益匪浅。李老师那亲切的语言和时时的鼓励话语，让学生积极的投入到文章中。 李老师借助课件展示的一幅幅美丽的画面与课程内容的有机结合，给孩子强烈的视觉冲击——变成真真切切的感受。而且，在这期间，李老师加了优美的音乐，给孩子们一种美的感受。教师同样利用多媒体课件，把学生带入万紫千红的季节。这个环节精妙之处在于，教师没有让学生停留在对春天欣赏的感性层次上，而是结合优美的旋律和画面，让学生用学过的词语来赞美春天，语文的工具性与人文性密切的结合。通过对比——冬天，北风呼啸，雪花纷飞，冻僵了孩子的小手，多想温暖一下呀！红色是温暖的，所以就画红色的太阳。学生对夏天有亲身的感受，那么，让学生说一说夏天的感觉，注重了学生的多元体验，尊重了个性。这样学生广开思路，发表对四季的独特感悟，在教学秋天时，教师利用课件渲染秋天的景色。并选择了具有代表性的事物——落叶，作为情境创设。小朋友说得津津有味。周老师引领学生画一个自己心中的太阳，准备送给谁，再写一段话。使学生学习更进一步升华情感，使学生不留痕迹地理解了课文内容。板书设计体现了课文的主要内容，起到了提纲挈领的作用，不同的太阳送给不同的季节，总之都是为了别人。教师在设计每个环节时，都以激发兴趣为主，良好的兴趣是获取知识最重要的因素，学生在老师的引导下，认真观察，用心思考。 在这堂课中，李老师亲切的话语，循循善诱的目光，笑容可掬的面容，值得我不断地学习，还有课件设计实在很精美，起到了很好的辅助手段。 李老师的的课真可谓精彩之极，老教师身上所展现的魅力让我折服。我作为一个年轻教师需要多像李老师学习，争取进步的快一些。

销售技巧和话术经典

1.销售技巧和话术经典语句一： 2.推销前的准备、计划工作，决不可疏忽轻视，有备而来才能胜券在握。准备好推 销工具、开场白，该问的问题、该说的话，以及可能的回答。 3.对与公司有关的资料、说明书、广告等，均必须努力研讨、熟记。同时要收集竞 争对手的广告、宣传资料、说明书等加以研讨、分析，以便做到知己知彼，采取相应对策。 4.强烈的第一印象的重要规则，是帮助别人感到自己的重要。准时赴约，迟到意味 着：我不尊重你的时间，迟到是没有任何借口的。假使无法避免迟到的发生，你必须在约定时间之前打通电话过去道歉，再继续未完成的推销工作。 5.每个销售人员都应当认识到，只有目不转睛地注视着你的客户，销售才能成功。 6.有计划且自然的接近客户，并使客户觉得有益处，而能顺利进行商洽，是销售人 员必须事前努力准备的工作与策略 7.销售人员不可能与他拜访的每一位客户达成交易，他应当努力去拜访更多的客户 来提高成交百分比。 8.要了解你的客户，因为他们决定着你的业绩。 9.相信你的产品是销售人员的必要条件，这份信心会传给你的客户，如果你对自己 的商品没有信心，你的客户对他自然也没有信心，客户与其说是因为你说话的逻辑水平高而被说服，倒不如说他是被你的深刻信心所说服的。业绩好的销售人员经得起失败，部分原因是他们对于自己和所推销的产品有不折不扣地信心。

10.对于销售人员而言，最有价值的东西莫过于时间，了解和选择客户，是让销售人 员把时间和力量放在最有可能购买的人身上，而不是浪费在不能购买你的产品的人身上。 11.客户没有高低之分，却有等级之分，依客户等级确定拜访的次数、时间，可以使 销售人员的时间发挥出最大的效能。 12.接近客户一定不可千篇一律公式化，必须事先有充分准备，针对各类型的客户， 采取最合适的方式及开场白。 13.推销的机会往往是稍纵即逝，必须迅速、准确地判断，细心留意，以免错失良 机，更应努力创造机会。 14.把精力集中在正确的目标，正确的使用时间及正确的客户，你将拥有推销的老虎 之眼。 15.推销的黄金准则是你喜欢别人怎样对你，你就怎样对待别人，推销的白金准则是 按人们喜欢的方式待人。 16.让客户谈论自己，让一个人谈论自己，可以给你大好的良机去挖掘共同点，建立 好感并增加完成推销的机会 17.推销必须有耐心，不断的拜访，以免操之过急，亦不可掉以轻心，必须从容不 迫，察言观色，并在适当的时机促成交易。. 18.客户拒绝推销，切勿泄气，要进一步说服顾客并设法找出顾客拒绝的原因。再对 症下药。 19.为帮助顾客而销售，而不是为了提成而销售

太阳读后感

太阳读后感 本文是关于读后感的，仅供参考，如果觉得很不错，欢迎点评和分享。 太阳读后感（一） 通过学习《太阳》这篇课文，我深深地感受到它对我们的重要性。 首先，从课文中我知道了太阳离我们有1.5亿里远，如果我们日夜不停地走，还要3500年呢！而太阳又是那么的大，130万个地球才能抵得上一个太阳。太阳会发光、发热，是个大火球，它表面温度有6000摄氏度，中心温度是表面温度的2500倍，就是钢铁碰到它，也会变成气。正因为太阳这么大，温度这么高，距离我们又这么远，才能给地球送来光明和温暖。 地球上一切的生物都和太阳有着密切的关系。万物的生长需要太阳，有了太阳，地球上的树木、花草、动物才能生存、繁殖。如果没有太阳，地球上不会有植物、也不会有动物。我们人类的吃、穿、住、行也都离不开太阳。没有太阳，我们人类就不能在地球上生存。可见太阳对人类是多么的重要啊！ 因为有了太阳的热量，才形成了空气中的水蒸气、云、风、雨、雪……这些自然现象。太阳还有杀菌的作用，我们利用它来预防疾病。我们生活中用的太阳能热水器，就是利用太阳的热能来工作的。在其他的科学技术中，也用到了很多有关太阳的能量…… 地球上的一切光明和温暖，都是太阳送来的，如果没有太阳，地球上将到处是黑暗。我们生活的世界这么美丽，太阳有多么神奇的力

量啊！ 太阳读后感（二） 今天我们学习了《太阳》这篇课文，它让我了解到太阳离我们有1.5亿公里远，如果步行到太阳去要走3500年，就是坐飞机，也要飞二十几年。太阳很大，130万个地球才能抵得上一个太阳。因为太阳离地球太远了，所以我们看到的太阳只有一个盘子那么大。太阳光有杀菌的能力。我们可以利用他来预防和治疗疾病。 地球上的光明和温暖，都是太阳送来的。有了太阳才有了我们这个美丽可爱的世界！ 太阳读后感（三） 语文书上的第二十一课《太阳》主要内容是： 有这么一个传说，古时候，天上有10个太阳，后来用箭射死9个太阳。其实，太阳离我们有1.5亿公里远，到太阳上去，如果步行，日夜不停地走，差不多要走3500年，就是坐飞机也要走20多年。 我们看到太阳，觉得它并不大，实际上太阳特别的大，130万个地球才能抵得上一个太阳。因为，太阳离地球太远了，所以我们看起太阳来只是一个盘子一样大。 太阳会发光，会发热，是个大火球。太阳的温度很高，表面温度有6000摄氏度。就是什么东西碰到太阳，就会变样子或非常的很烫。 所以地球上的太阳给我们了很多很多帮助，我们一定要珍惜每一分时间，太阳没有，我们的世界也不会这么美好这么可爱！ 词语理解：1、凝成：凝聚在一起。

八大销售技巧和话术

直入人心的八大销售技巧和话术 推销话术其实就是说服技巧，推销员通过信息传递，让对方改变观点的过程。怎样才能让对方改变态度呢？最有效的方法是抓住对方的心理需求，利用心理需求来制定说服策略，从而改变他的态度。关于人的需求和需求层次，可以参看《马斯洛需求层次论》。 销售话术的任务实际上是推销一种象征性满足人的心理的方式，这种需求往往是隐含的潜意识。高明的销售话术就是瞄准说服对象的潜意识，将潜意识转化为一种动力。这样就知道了卖啤酒其实卖的是文化，卖可口可乐其实卖的是活力和正宗，卖彩券、保险是卖的未来期望。消费者行为学认为，消费者行为在很大程度上取决于隐藏在它们内心的心理需要，而将销售话术与这些心理需要结合起来，就会打动他们，让他们改变态度。 第一大销售话术：安全感 人总是趋利避害的，内心的安全感是最基本的心理需求，用安全感来说服客户是最常用的销售话术。这种说服随处可见，比如保险销售话术中基本都是从安全保障为出发点来说服的。汽车销售话术中，说这种汽车的安全系统对于保证出行中的家庭很有效，对于买车的人肯定是一个有力的论点。比如卖房子，对客户说物价上涨、房价上涨，资金缩水，不如投资房屋来得安全。再比如卖设备说，购买这台设备，可以让客户的体验更好，吸引更多的客户，而如果不买，你的竞争对手就会买，会把你的客户抢走。 安全感的反面是恐惧感，如果安全感打动不了客户，那你不妨用恐惧感吓唬他一下。卖儿童智力玩具的说，不要让孩子输在起跑线上，就是一种吓唬；让客户观察皮肤里面的螨虫来推销化妆品，也是一种吓唬；日本一个保险公司推销员用录音机模拟死人到阴间和阎王的对话，讲述由于没有给家人购买保险，而受到惩罚的事情，更是吓唬。吓唬可能是最有效的推销话术。 第二大销售话术：价值感 每个人都希望自己的个人价值得到认可。汶川大地震中，有乞丐主动为灾区捐款，除了是善心之外，恐怕也有一份希望得到社会认可的潜意识。抓住价值感，也是的一个重点。劝说买保险，你可以说：“给家人买保险就是买平安，这是作为父亲和丈夫的职责。”、“这台设备用上以后，公司的工作效率会大大提高，这说明你这个设备部主任的慧眼识货。”。推销烤肉机“当丈夫拖着疲惫的身子回来，他多么渴望吃一顿美味可口的饭菜，当妻子将美味的烤肉端上来的时候，丈夫的心该有多幸福？”呵呵，如果你小嘴这样会说，那妻子如果不买，我都想鄙视她一下。 第三大销售话术：自我满足感