Cu multilayers

LETTER TO THE EDITOR

Journal of Magnetismand MagneticMaterials 136 (1994)L33-L37

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Electronic density of states at random interfaces and magnetoresistance in Co-Ni/Cu multilayers H. Itoh *, T. H o r i , J. I n o u e , S. M a e k a w a Departmentof Applied Physks, Nagoya University, Nagoya 464-01, Japan

Received13 May 1994

Abstract Local density of states of magnetic atoms dissolved in Cu layers near the interfaces of Co-Ni/Cu multilayers are calculated by using a realistic tight-binding model including s, p and d orbitals. By assuming that scattering of s electrons by the magnetic atoms dissolved in Cu layers due to s-d mixing is the main scattering mechanism, the spin dependent resistivity and magnetoresistance are estimated from the calculated results of the local densities of states at the Fermi level. It is shown that the large magnetoresistance in Co/Cu multilayers decreases with increasing Ni concentrations in agreement with the experimental results. This is because the asymmetry between up and down spin states decreases as the magnetization of the magnetic layer decreases.

The giant magnetoresistance (MR) in F e / C r and C o / C u multilayers [1-3] has attracted much attention as a novel magnetotransport possibility in magnetic materials. The giant MR has been observed also in multilayers where the magnetic layers are random alloys, e.g., C o / C u / N i F e / C u [4], FeC o / C u [5,6], Co-Ni/Cu [7,8], Fe-Co-Ni/Cu [9] multilayers. The giant MR is different from the conventional anisotropic MR because the decrease of the resistivity in the giant MR of multilayers is independent of the direction of the applied magnetic field. The electrical resistivity decreases with the reorientation of the magnetization of the magnetic layers from an antiparallel (antiferromagnetic) alignment to a parallel (ferromagnetic) alignment by the magnetic field. The fact that the resistivity depends on the direction of the magnetization of the magnetic layers indicates that the spin dependent resistivity is responsible for the giant MR. To clarify the origin of

* Correspondingauthor. Fax: + 81-52-789-3724.

the spin dependent scattering is crucial to elucidate the mechanism of the giant MR. In our previous works [10,11], we have attributed the origin of the spin dependent scattering to the randomness of the exchange and atomic potentials caused by interfacial roughness, and have successfully explained the material dependence of the giant MR by calculating the electronic structures near the interfaces for transition-metal/transition-metal type multilayers [12]. In T M / C u type multilayers (TM = Fe, Co and Ni), there exist magnetic atoms dissolved in Cu layers because of the interracial roughness. The currents may be carried mainly by s electrons of Cu layers and the s electrons are scattered by these magnetic atoms dissolved in Cu layers. In order to study the MR in T M / C u type multilayers, we adopted the Anderson model, where the magnetic atoms in Cu layers are treated as impurities in Cu matrix [13]. Despite of the simplified model, the qualitative tendency of the material dependence of MR observed in T M / C u type multilayers has been successfully explained. The physical picture of the giant MR in T M / C u type multilayers can be ex-

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plained in terms of the so-called virtual bound states (VBS) as follows. The TM atoms dissolved in Cu layers (see Fig. l(a)) are magnetic because of the adjacent magnetized layer. The VBS of these atoms are schematically shown in Fig. l(b) and (c) for antiferromagnetic (AF) and ferromagnetic (F) alignment of the magnetization of the magnetic layers, respectively. As the s electron.,; are scattered via s - d mixing, the resistivity becomes large when the VBS is located at the Fermi level (EF). In the AF alignment, either up or down spin VBS's of TM atoms dissolved near the interfaces is located at E F. Therefore, both up and down spin resistivities become large. In F alignment, on the other hand, only down spin VBS is located at E~ and the up spin s electrons are much more weakly scattered than down spin electrons. Then the total resistivity is much reduced when the F alignment is changed to the AF one. The spin dependent scattering at the interfaces is supported also by experiments where the MR depends on the roughness of the interfaces [14] and MR changes dramatically when thin layers of a third element are inserted at the interfaces [15-17]. A shortcoming of the previous work, however, is that the MR observed in N i / C u multilayers can not be explained because Ni impurities are nonmagnetic in Cu matrix. The discrepancy can be removed by introducing the existence of the magnetic layers into the formalism. It has been shown that the Ni impurities in Cu layers at the interfac.es can be magnetized because of the internal magnetic field from the magnetic layers [18]. The purpose of the present work is to extend the previous calculation done for N i / C u multilayers to Co-Ni/Cu multilayers by using a more efficient method and study the concentration dependence of the giant MR in Co-Ni/Cu multilayers. We use the realistic tight-binding model including s, p and d orbitals and calculate local densities of states of magnetic atoms dissolved in Cu layers taking into .account the effects of the magnetized layers. We also examine the validity of the concept of the virtual bound states used in the simplified model. We adopt the real space method to calculate the density of states (DOS), i.e., the recursion method [19]. We prepare a cluster with fcc structure made of magnetic TM and Cu atoms ,(about 10000 atoms) with one interface which forms the (001) plane. The

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local Green's function g(z), z = E + i6, at Cu site where a magnetic TM atom is dissolved (see Fig. l(a)) is calculated by using the block tridiagonalized recursion method [20]. In this method g(z) is given by a nine by nine matrix. The coefficients of the continued fraction are calculated up to seventh level exactly and further coefficients are approximated in the usual way [20]. The effects of other interfaces on the g(z) are neglected. The random potentials in magnetic layers are averaged over, that is, the virtual crystal approximation is used for the magnetic layers. The local Green's function of a atom ( a = Ni or Co) dissolved at the Cu site where g(z) is calculated is given by G,~(z) = g ( z ) [1 - (v~,~ - Vcu)g ( z)] -1,

H. Itoh et al. /Journal of Magnetism and Magnetic Materials 136 (1994) L33-L37

where o" denotes spins (1', $) and Vcu and v,,,~ are the potentials of Cu and a atoms, respectively. The DOS of the dissolved atom is given by D~,,~= - I m Tr G,~(z)/~'. The hopping parameters between nearest neighbor sites are assumed to be independent of materials. The values of the parameters of Ni up spin state are used in the calculations [21]. It is also assumed that v,~,~ and Vcu are diagonal and the matrix elements are independent of orbitals. These values are determined by uniform shifts of the DOS of Ni up spin state to give the correct number of electrons of Co $, Co ~., Ni $ and Cu. Calculated results of the up and down spin DOS of Co atom dissolved in the Cu layer are shown in Fig. 2. Each DOS has a large sharp peak, which is of Lorentzian shape. There is mixing between d bands of Co and those of Cu atoms around E = 0.2-0.5 Ry, and then the tails of the DOS become asymmetric. The asymmetry is larger in the up spin state than in the down spin state because the mixing is larger in the up spin state. The calculated results of the DOS are consistent with those of Ni atoms in Cu layer calculated previously [18], where the DOS was calculated directly by using the recursion method. The results are also consistent with the DOS of TM atoms in Cu matrix calculated by the more sophisticated KKR method [22]. In C O l _ x N i x / C U multilayers, both Co and Ni atoms are dissolved in Cu layers. We assume that the concentrations of Co and Ni atoms in Cu layers are

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Fig. 3. Calculated results of the averaged DOS of Co and Ni atoms dissolved in Cu layers. The vertical line show the Fermi energy.

the same. The averaged DOS of the dissolved atoms are shown in Fig. 3. The up spin DOS are almost independent of x because VCor ~ VNir" Therefore, only the DOS for x = 0 is shown in Fig. 3. At finite concentrations, each down spin DOS has double peak structure, where the higher peak is due to Co atoms in Cu and the other is due to Ni atoms. We can see the rigid band picture is not realized. The virtual bound state picture, however, still holds because the peak structure of the DOS originates from the virtual bound states of Co and Ni atoms in Cu layers. The existence of the magnetized layer near the Co and Ni atoms in Cu layers does not affect so much the shape of the DOS calculated, but the exchange splitting of the DOS. The calculated values of the magnetic moments of Co atoms, mco, and Ni atoms, mNi , in Cu layer are about 1.0 and 0.22 /xB/atom, respectively, independently of the concentration. Because of the existence of the magnetized layer, mNi is not zero. The charge neutrality, however, is not satisfied in this case, that is, the number of electrons of Co and Ni atoms are n c o = 9.7 and nNi = 10.5 per atom, respectively. They are larger than the number of electrons in pure

H. ltoh et al. /Journal of Magnetism and Magnetic Materials 136 (1994) L33-L37

l+36

metals by 0.7 and 0.5 per atom for Co and Ni atoms, respectively. In order to satisfy the charge neutrality, the values of v,~,, are uniformly shifted by an amount of 0.0175 Ry. As a result, the magnetic moments increase to mco = 1.6 /xB/atom and mNi ---- 0.45 /z~/atom. These values of the magnetic moments are consistent with those calculated by the APW method where an ordered structure of Co and Ni is assumed at the interfaces [23] and with those of Co and Ni monolayer on Cu substrates [24]. As the picture of the virtual bound states is valid even for realistic electronic states in Co-Ni/Cu, the main mechanism of the resistivity is such that the s electrons are scattered via mixing with d states of magnetic atoms in Cu layers. Therefore, the resistivity may be proportional to the DOS at the Fermi energy E F as in the Anderson model, i.e., p,~ ot (D,~,,(EF)), where ( . . . ) denotes an average. MR ratio is defined by MR = ( PAY -- P F ) / P A v where PAF and PF are the resistivities in the antiferromagnetic and ferromagnetic alignments of the magnetic layers. The MR ratio can be approximated as [( p __ p ,[+) / / ( p I" ..[_ p $ )]2 in the two current model [10,13]. The calculated results of MR with and without the charge neutrality are shown in Fig. 4 by solid and open circles, respectively. The experimental re-

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suits are shown by open triangles. The dotted line is the theoretical result calculated previously [18]. The MR ratio is large in C o / C u and decreases with increasing x, because the asymmetry between up and down spin DOS at E F decreases, but remains finite at N i / C u multilayer. The tendency of the calculated results is the same as the experimental one for both cases with and without charge neutrality. The difference between MR's with and without the charge neutrality becomes large in N i / C u multilayer b e c a u s e mNi is rather sensitive to parameter values [18]. We can see that the previous results in the Anderson model have been improved quantitatively, but the qualitative feature is not altered. It should be noted that the theoretical values of MR are much larger than the experimental ones because no spin independent scattering is included. When the magnitude of the spin independent scattering has the same order as that of the spin dependent one, the observed MR ratio can be explained [13]. In conclusion, the local densities of states of random magnetic atoms dissolved in Cu layers have been calculated in the realistic tight-binding model including s, p and d orbitals for C o - N i / C u multilayers. By using the calculated results of the density of states at E F, the concentration dependence of the MR ratio is obtained. The MR ratio decreases with increasing Ni concentration in agreement with experiments. This is because the asymmetry between up and down spin states decreases as the magnetic moments become small with increasing Ni concentration.

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H. Itoh et al. /Journal of Magnetism and Magnetic Materials 136 (1994) L33-L37

[6] N. Kataoka, K. Saito and H. Fujimori, J. Magn. Magn. Mater. 121 (1993) 383. [7] H. Sakakima and M. Satomi, J. Magn. Magn. Mater. 121 (1993) 374. [8] H. Kubota, S. Ishio and T. Miyazaki, J. Magn. Magn. Mater. 126 (1993) 463. [9] M. Jimbo, T. Kanda, S. Goto, S. Tsunashima and S. Uchiyama, J. Magn. Magn. Mater. 126 (1993) 422. [10] J. Inoue, A. Oguri and S. Maekawa, J. Phys. Soc. Jpn. 60 (1991) 376; J. Magn. Magn. Mater. 104-107 (1992) 1883. [11] J. Inoue and S. Maekawa, Prog. Theor. Phys. Suppl. 106 (1991) 187. [12] H. Itho, J. Inoue and S. Maekawa, Phys. Rev. B47 (1993) 5809. [13] J. Inoue, H. Itho and S. Maekawa, J. Phys. Soc. Jpn. 61 (1992) 1149. [14] E.E. Fullerton, D.M. Kelly, J. Guimpell and I.K. Schuller, Phys. Rev. Lett. 68 (1992) 859.

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[15] P. Baumgart, B.A. Gumey, D.R. Wilhoit, T. Nguyen, B. Dieny and V.S. Speriosu, J. Appl. Phys. 69 (1991) 4792. [16] S.S.P. Parkin, Phys. Rev. Lett. 71 (1993) 1641. [17] V.S. Speriosu, J.P. Nozi~res, B.A. Gurney, B. Dieny, T.C. Huang and H. Lefakis, Phys. Rev. B47 (1993) 11579. [18] H. Itoh, J. Inoue and S. Maekawa, J. Magn. Magn. Mater. 126 (1993) 479. [19] R. Haydock, V. Heine and M.J. Kelly, Solid State Physics 35 (Academic Press, New York, 1980). [20] J. Inoue and Y. Ohta, J. Phys. C: Solid State Phys. 20 (1987) 1947. [21] D.A. Papaconstantopoulos, Handbook of the Band Structure of Elemental Solids (Plenum, New York, 1986). [22] R. Zeller and P.H. Dederichs, Phys. Rev. Lett. 42 (1979) 1713. [23] R. Coehoorn, J. Magn. Magn. Mater. 121 (1993) 432. [24] A.J. Freeman and R.-q. Wu, J. Magn. Magn. Mater. 100 (1991) 497.