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A Simple Model of the Magnetoresistance Contribution to the Magnetoimpedance Effect in Thin

A Simple Model of the Magnetoresistance Contribution to the Magnetoimpedance Effect in Thin
A Simple Model of the Magnetoresistance Contribution to the Magnetoimpedance Effect in Thin

phys.stat.sol.(a)171,R3(1999)

Subject classification:75.70.Ak;75.70.Pa;S1.1;S1.2A Simple Model of the Magnetoresistance Contribution to the Magnetoimpedance Effect in Thin Films

J.M.Barandiara ?n (a),G.V.Kurlyandskaya 1)(a),M.Va ?zquez (b),J.Gutie ?rrez (a),D.Garcia (b),and J.L.Mun ?oz (a,b)

(a)Dpto de Electricidad y Electro ?nica,Facultad de Ciencias,Universidad del Pa??s Vasco/EHU,Apartado 644,48080Bilbao,Spain;e-mail:galina@we.lc.ehu.es

(b)Instituto de Magnetismo Aplicado UCM-RENFE and Instituto de Ciencia de Materiales CSIC,P .O.Box 155,28230Las Rozas (Madrid),Spain;e-mail:vazquezv@fenix.ima.csic.es

(Received November 16,1998;accepted December 4,1998)

Giant magnetotransport phenomena,as giant magnetoresistance (GMR)[1,2]and giant magnetoim-pedance (GMI)[3,4],have brought much interest in the basic physical understanding and their appli-cations as magnetic recording heads and in magnetic sensor technology.The origin of these phenom-ena is rather different:GMR is connected with spin dependent electron scattering in magnetically non-uniform systems for dc or low-frequency current.The magnetoimpedance effect (MI)consists in the change of the total impedance Z =R (w ,H )+iX (w ,H )(real and imaginary components)of a magnetic conductor under dc applied magnetic field,when a high-frequency ac current flows through it.The change of total impedance of the magnetic conductor has been attributed up to now only to the classical skin effect [5,6].This seems to be correct for the kind of materials used in technical GMI applications,which usually show negligible magnetoresistance (MR).Nevertheless,the basic under-standing of the MR influence on the total impedance Z (w ,H )is a very important task.A simple model can be developed as follows:let us suppose a thin film with no magnetic do-main structure and a high frequency ac current I I 0e i 3t flowing parallel to the Z -axis in the plane of the film.The sample has the thickness 2a in the X -axis direction,the Y -axis is in the plane of the sample and perpendicular to the current.The transverse permeability m Y is uniform.The total impedance Z =R +iX can be written as

Z R DC i 1a 2q coth i 1a 2q Y 1

where i =(±±1)1/2,R DC is the dc resistance [7,8],q 2is the normalized frequency q 2 a 2smw G r DC à1

and s is the conductivity,w is the circular frequency,r =s ±±1is the sample resistivity.For the low

1

Permanent address:Institute of Metal Physics,Ural Division,Russian Academy of Sciences,Kova-levskaya str.18,GSP-170,620219Ekaterinburg,Russia.Fig.1.Effect of a)perpendicular and b)parallel MR on the magnetoimpedance normalized to Z (0)in the low-frequency limit.The evolution of r DC (H )(line)has been taken arbitrarily and mH follows the same trend in accordance with experimental data [9].Z (m )(open symbols)is the magnetoimpedance in the ab-sence of MR.Z (m ,r )(full symbols)is the combined effect;here Z |Z |represents the impedance

modulus

frequency limit q 2<<1,we have:R %R DC 1 q 445

G r 1 A r à2 Y where A a 4m 2Y w 245Y X %R DC q 23G r à1Y 2 Z j j %R DC 1 790 q 4 G r 1 B r à2 Y where B 7a 4m 2Y w 290

X The condition of the low-frequency limit applies,for example,to Permalloy (Fe 19Ni 81)films show-ing anisotropic MR effect.If we suppose typical values of 2a %1m m,m Y %104m 0,s %107W ±±1m ±

±1and a frequency range of about 20to 30MHz,then q 2%0.02,i.e we are in the low frequency limit.The choosen conditions are quite reasonable and compare well with the experimental results in Permalloy [9].We define the change of the electrical resistivity (D r /r )||=[r (H )±±r (H max)]?100/r (H max )as a parallel MR and (D r /r )c [r (H )±±r (H max)]?100/r (H max )as a tranverse MR when the current flows parallel or perpendicular,respectively,to the applied dc field,H max is the maximum field,which saturates the sample and is applied along the Z -axis or Y -axes,respectively.The simulated behaviour for D r (H )/r 2%,D m /m (H ) 100/1,and q (H 0)%0.5has been analyzed,starting from eq.(2).The calculations show that the magnetoresistance contribution to the total impedance plays an important role both in parallel and perpendicular geometries,for the low-frequency limit (Fig.1).In this limit the change of skin depth due to the change in m Y is small and the magnetoim-pedance is of the same order as the magnetoresistance.Moreover,the MR contribution is additive,and largely enhances (transverse case)or almost supresses (parallel case)the MI effect (Fig.1).In the high frequency limit q 2)1,eq.(1)for the total impedance can be written as

Z j j %R DC q G r 1a 2X

3 The simulated behaviour for the parameters D r (H )/r 2%and D m /m (H ) 10/1shows no appre-ciable magnetoresistance contribution to the total magnetoimpedance (Fig.2).In the high-fre-quency limit the MR contribution to MI is reduced to about half the low-frequency contribution and the MI effect is much larger (about 300%in this case).In conclusion,the first calculations of the magnetoresistance contribution to the total impedance show that MR can play an important role in the low frequency limit but can be neglected for the high frequency limit.

Acknowledgements The research has been partially supported by The Basque Government under the project PI97/113and The Spanish CICYT project MAT95/0273.G.V .Kurlyandskaya would like to acknowledge a fellowship of the Basque Government.We thank V .O.Vaskovskiy and V .N.Lepalovskij for helpful discussion.

References

[1]N.F.Mott ,Proc.Roy.Soc.156,638(1936).[2]J.Kondo ,Progr.Teor.Phys.(Kyoto)27,772(1962).[3]R.S.Beach and Berkowitz ,J.Appl.Phys.76,6209(1994).[4]L.V.Panina,K.Mohri,K.Bushida ,and M.Noda ,J.Appl.Phys.76,6198(1994).[5]R.L.Sommer and C.L.Chien ,J.Appl.Phys.79,5139(1996).[6]G.V.Kurlyandskaya,J.M.Garc??a-Beneytez,M.Va ?zquez,J.P.Sinnecker,V.A.Lukshina ,and A.P.Po-tapov ,J.Appl.Phys.83,6581(1998).[7]https://www.doczj.com/doc/9f7010290.html,ndau and E.M.Lifshitz ,Electrodynamics of Continuous Media,Pergamon Press,Oxford 1975.[8]D.-X.Chen and J.L.Mun ?oz ,IEEE Trans.Magn.,submitted.[9]G.V.Kurlyandskaya,J.M.Barandiara ?n,J.Gutie ?rrez,V.O.Vaskovskiy,V.N.Lepalovskij,M.Va ?z-quez ,and D.Garc??a ,Appl.Phys.Lett.,submitted.

Fig.2.Effect of MR on the MI normalized to Z (0)in the high-frequency limit (see eq.(3)).Same symbols as in Fig.1.Only the perpendicular configuration is represented (here Z |Z |)

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