VOLUME 80, NUMBER 19 P H Y S I C A L R E V I E W L E T T E R S 11 MAY 1998 Origin of Giant Magnetoresistance: Bulk or Interface Scattering P. Zahn, J. Binder, and I. Mertig Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany R. Zeller and P. H. Dederichs Institut für Festkörperforschung, Forschungszentrum Jülich, D-52425 Jülich, Germany (Received 12 September 1997) Calculations of giant magnetoresistance (GMR) of Co Cu (001) multilayers are presented. Starting from density functional theory the electronic structure of the multilayer is described by means of a new Green's function method. Scattering of superlattice wave functions at d-like scatterers is considered. It will be shown that due to the existence of quantum well and interface states in multilayers GMR is strongly affected by scattering centers at the interface. Results for a multilayer with a Cu thickness corresponding to the first antiferromagnetic maximum of the interlayer exchange coupling are discussed in detail. [S0031-9007(98)06042-6] PACS numbers: 75.70.Pa, 71.20.­b, 72.15.Gd, 75.70.Cn The discovery of giant magnetoresistance (GMR) in All calculations are performed within the framework of magnetic multilayer systems [1,2] initiated a variety of density functional theory in local spin density approxima- experimental and theoretical investigations to elucidate the tion using a new Green's function method, the so-called microscopic origin of the phenomenon. It was shown by TB KKR (tight binding Korringa-Kohn-Rostoker) [19,20]. several authors [3­6] that GMR in magnetic multilayers The method is extremely advantageous for calculating the is strongly influenced by the electronic structure of the electronic structure of magnetic multilayers due to linear system as a function of the magnetic configuration and it scaling of the numerical effort with the number N of atoms is the difference in Fermi velocities of the multilayers for in the supercell. Furthermore, by using this method we are parallel or antiparallel alignment of magnetic moments in in position to calculate IEC and GMR on the same footing. adjacent magnetic layers that establishes GMR by them- Since GMR occurs for systems with a magnetic ground selves. Since this effect is a result of Bragg reflection state characterized by antiparallel orientation of the mag- in ideal multilayers it might be less important in dirty netic moments in adjacent magnetic layers the IEC was samples which still have a remarkable GMR amplitude. calculated by comparing the total energies of the system Consequently, spin-dependent scattering [7­12] is as- for parallel (P) and antiparallel (AP) configuration of the sumed to play a crucial role for GMR. Although this fact layer moments. Accordingly, we have chosen a multi- was accepted generally the question is still open if bulk layer geometry in the so-called first antiferromagnetic or interface scattering dominates the effect. Experiments maximum of IEC consisting of 9 monolayers (ML) of Co [13] and theoretical calculations [14] tended to favor separated by 7 ML of Cu in the (001) direction, denoted interface scattering. But a microscopic explanation is as Co9Cu7. The calculated antiferromagnetic maximum missing. In this paper we present a systematic analysis of 7 ML Cu is in excellent agreement with experimental of impurity scattering cross sections focusing on the results [21­23] and other calculations [24]. peculiarities of superlattice wave functions. It will be GMR is defined to be shown that the cross sections and consequently GMR sP depend strongly on the position of the scatterer. To the GMR 2 1 (1) sAP best of our knowledge, the importance of interface states with conductivities calculated within a relaxation time ap- in magnetic multilayers was not realized previously. proximation of the transport equation for the antiferro- Magnetic multilayers which display GMR are charac- magnetic ground state in a zero magnetic field terized by a strong potential mismatch in one spin channel X which leads to the formation of quantum well and inter- sAP 2e2 d eAP face states. The importance of selected quantum well k 2 EF tAP k vAP k ± vAP k (2) k states for interlayer exchange coupling (IEC) was dis- and for parallel alignment of the magnetic moments cussed already by several authors [15,16]. Moreover, it reached by a finite external magnetic field was shown [17,18] that quantum well states play a role X X for GMR. In this paper we demonstrate that quantum sP e2 d esk 2 EF tskvsk ± vsk . (3) well states and especially the formation of interface states s k in magnetic multilayers give rise to strong interface scat- Here k is a shorthand notation for the wave vector tering which leads to large GMR amplitudes. k and band index n. The superscript s indicates the 0031-9007 98 80(19) 4309(4)$15.00 © 1998 The American Physical Society 4309 VOLUME 80, NUMBER 19 P H Y S I C A L R E V I E W L E T T E R S 11 MAY 1998 spin direction. tsk and tAP k denote the relaxation times 3 Maj. a) characterizing the considered scattering processes for P and AP aligned moments, respectively; in general, the 2 relaxation time is state and spin dependent. vsk is the 1 ) group velocity of the one-particle eigenstates k, s . F 0 Because of tetragonal symmetry of the supercell the (r,E 15 Min. n conductivity in plane (CIP) is determined by the in-plane component s 10 xx or syy and the conductivity perpendicular to the plane (CPP) by szz. 5 An important ingredient to the microscopic understand- ing of the conductivity is the layerwise decomposed den- 0 sity of states (LDOS). These local densities of states are calculated from the diagonal part of the spin-dependent b) one-particle Green's function of the multilayer system 0.1 1 ns r, E 2 Im Gs r, r, E 0.0 p c) X j ± Cs 0.1 2 k r j2d E 2 es k . (4) k (r)| 0.0 By means of the spectral representation of the Green's | k d) function they can also be resolved into a superposition of 0.2 probability amplitudes of all eigenstates at energy E. The 0.0 eigenstates of a supercell calculation are all Bloch states e) ± 0.2 Csk r with a normalized probability amplitude Z 0.0 drj ± Csk r j2 1 . (5) Co Cu Since the conductivity is determined by electrons at the FIG. 1. Co9Cu7 in P configuration: Local density of states at Fermi level E E F our interest is focused on LDOS and F in (states spin Ry) (a). The different shaded areas corre- eigenstates at E spond to the weights of the four types of eigenstates. Proba- F . Consequently, the explicit energy de- pendence is dropped. The LDOS at E bility amplitudes of representative extended (majority) (b), Co F of the P configu- quantum well (minority) (c), Cu quantum well (minority) (d), ration is shown in Fig. 1(a). The local density of states in and interface (minority) states (e) for suitably chosen k values. the majority channel is nearly the same for all monolayers (about 2 states spin Ry). In contrast, the minority elec- trons are characterized by a very inhomogeneous profile. states are characterized by a high probability amplitude Because of the Co d states, the local density of states is at the Co interface layer. Some of these states are real much higher in Co layers (15 states spin Ry) than in Cu interface states with an exponential decay into Co and layers (2 states spin Ry). The largest values occur at Co Cu layers. But also quasilocalized states, i.e., resonances, interface layers. This is a general behavior independent of with a high probability amplitude at the Co interface and Co or Cu layer thicknesses that can be explained in terms finite but small probability amplitudes at the central layers of eigenfunctions and their localization in the superlattice. are found. For simplicity all states with a probability By means of a layerwise projection of the probability amplitude j ± Csk rCo,inter j2 . 2 N at the Co interface and amplitude j ± Cs small probability amplitudes at the central layer will k rlayer j2 within the supercell the electron confinement can be described. The analysis leads to four be called interface states. The interface states can be typical representatives of states [Figs. 1(b)­1(e)]. We understood in terms of resonance scattering and compare obtain extended or free electronlike states with nearly the to the virtual bound state of a Co impurity in a Cu matrix same probability amplitude in all layers j ± Cs [25]. The special shape of the probability amplitude of k rlayer j2 1 N [Fig. 1(b)]. Other representative states are so-called these states as calculated is a result of the multilayer quantum well states. We obtain states with a pronounced potential and could not be obtained in a Kronig-Penney electron confinement in Co layers. All states with an model calculation. averaged probability amplitude per Co layer larger than The spectral weight of these four types of eigenstates is indicated by the corresponding colors in Fig. 1(a). twice the Cu layer value [j ± Csk rCo j2 . 2j ±Csk rCu j2] will Although the classification of the eigenstates in Fig. 1(a) be considered as Co quantum well states [Fig. 1(c)]. For is arbitrary the picture is not drastically changed by Cu quantum well states the opposite condition has to modified classification conditions. Because of a smooth be fulfilled [j ± Csk rCu j2 . 2j ±Csk rCo j2] [Fig. 1(d)]. The potential profile most of the eigenstates in the majority most surprising states are shown in Fig. 1(e). These band are extended or free electronlike. But also Co and 4310 VOLUME 80, NUMBER 19 P H Y S I C A L R E V I E W L E T T E R S 11 MAY 1998 Cu quantum well states and interface states appear. In impurity potential and assume a d scatterer with the same contrast, the minority electrons move in a strongly varying spin-dependent scattering strength ts at all lattice sites potential with a periodicity perpendicular to the layers (z direction). For this reason all states are confined in DVs ri tsd r 2 ri (9) the z direction but extended in plane. The LDOS is with a spin anisotropy ratio b t# t" 2. Consequently, dominated by Co quantum well states. As can be seen the spin-dependent relaxation time in Born approximation from the decomposition the high LDOS at the Co interface becomes layer is caused by Co quantum well states and interface ts states. These states, as will be shown later, are extremely k ri 21 2pcj ± Csk ri j2ns ri, EF ts2 1 t21. (10) important for GMR since they undergo a strong scattering To avoid short circuit effects due to states with a from defects at the interface. tiny probability amplitude at the impurity position a In the AP configuration both spin channels are domi- constant and spin-independent inverse relaxation time t21 nated by quantum well states. On average, these states is added. The amount of t21 is chosen to be on average are less extended than states in the majority band and less of the same order as the first term of Eq. (10). localized as in the minority band. The result of Eq. (10) can also be interpreted in terms The confinement of eigenstates is directly related to the of multiple scattering theory and would correspond to Fermi velocities and this shows up in the conductivities. a single site approximation neglecting all backscattering The analysis of realistic wave functions leads to the fol- effects. ts would then be the difference of single site lowing conclusions: In general, extended states behave transition matrices of impurity and host. free electronlike with nearly the same averaged velocities Since the relaxation time [Eq. (10)] is proportional to in plane and perpendicular to the plane. The averaged the spin dependent LDOS at the impurity site ns ri, EF in-plane velocity of quantum well and interface states is we expect a strong position dependence. Because of the also of the same order of magnitude as for extended states large enhancement of LDOS at the Co interface layer whereas the velocity perpendicular to the planes is dras- [Fig. 1(a)] impurities in this position will be the most tically reduced. Consequently, the quantum well states effective scatterers in comparison to all other positions. and interface states contribute mainly to CIP conductivity Furthermore, from the knowledge of spectral weights and and give a small contribution to CPP conductivity. Since probability amplitudes it is clear that at the interface extended states dominate for the majority channel in P position Co quantum well states and interface states are configuration, CIP and CPP conductivity are nearly of the strongly scattered. same order. The minority channel is dominated by quan- The influence of the position dependent impurity scat- tum well states which gives rise to a large CIP conductiv- tering cross sections to GMR is shown in Fig. 2. The case ity but a strongly reduced CPP conductivity. For the same of vanishing ts describes the scattering at homogenously reason CPP conductivity is reduced in the AP configura- distributed defects causing an averaged spin-independent tion since quantum well states prevent conduction. CIP relaxation time t [see Eq. (10)] which leads to straight conductivity in AP configuration is less influenced since lines at 30% for CIP-GMR and 125% for CPP-GMR. quantum well states have a considerable in-plane velocity. The triangles show GMR results for one impurity with Because of potential scattering the transition probability no spin anisotropy b 1 at all possible positions in the is given by supercell. As expected, the GMR amplitude is strongly Ps enhanced by defects at the Co interface layer and slightly kk0 ri 2pcjT s kk0 ri j2d es k 2 es k0 (6) in the case of low impurity concentration c. This expression describes the scattering probability caused by 3.0 an impurity at a lattice site ri with respect to the supercell. 2.5 The accompanying transition matrix Tskk0 ri is defined by Ts 2.0 kk0 ri ± CskjDVs ri jCsk0 . (7) DVs ri denotes the perturbation of the potential at 1.5 the impurity site. ± Cs GMR k and Cs k0 are the spin-dependent unperturbed and perturbed Bloch states of the system, 1.0 respectively. Since our calculations are performed at 0.5 T 0 spin-flip scattering is neglected. The relaxation time is then given by 0.0 X Co Cu tsk ri 21 Pskk0 ri . (8) Defect Position k0 FIG. 2. GMR of Co To focus on the influence of the superlattice wave 9Cu7: open symbols for CIP-GMR, closed symbols for CPP-GMR; ts 0, dashed and full lines; b functions to the relaxation time we neglect details of the 0.25, squares; b 1.0, triangles; b 4.0, circles. 4311 VOLUME 80, NUMBER 19 P H Y S I C A L R E V I E W L E T T E R S 11 MAY 1998 enhanced by bulk defects in Co. Defects in Cu are [5] W. H. Butler, J. M. MacLaren, and X.-G. Zhang, Mater. absolutely ineffective for GMR which is related to the Res. Soc. Symp. Proc. 313, 59 (1993). small LDOS in Cu [see Fig. 1(a)]. [6] P. Zahn, I. Mertig, M. Richter, and H. Eschrig, Phys. Rev. With spin-dependent scattering b . 1, that is, stronger Lett. 75, 2996 (1995). scattering of minority than majority electrons, the existing [7] R. E. Camley and J. Barnas, Phys. Rev. Lett. 63, 664 spin anisotropy of LDOS is amplified and leads to an (1989). even stronger enhancement of the GMR amplitudes. For [8] P. M. Levy, S. Zhang, and A. Fert, Phys. Rev. Lett. 65, opposite spin anisotropy b , 1 the spin anisotropy of 1643 (1990). [9] J. Inoue, A. Oguri, and S. Maekawa, J. Phys. Soc. Jpn. 60, LDOS and scattering potential compensate each other and 376 (1991). GMR is reduced in comparison to the spin-independent [10] R. Q. Hood and L. M. Falicov, Phys. Rev. B 46, 8287 case. The above discussed position dependence is, of (1992). course, reflected in both cases. It is well known from [11] T. Valet and A. Fert, Phys. Rev. B 48, 7099 (1993). residual resistivities of dilute alloys [27] that, depending [12] P. M. Levy, Solid State Phys. 47, 367 (1994). on the valence difference between impurity atom and [13] S. S. P. Parkin, Phys. Rev. Lett. 71, 1641 (1993). host, spin anisotropies b smaller or larger than 1 can be [14] K. M. Schep and G. E. W. Bauer, Phys. Rev. Lett. 78, 3015 obtained for one and the same host. In particular, Cu (1997). impurities in bulk Co or Ni have anisotropies b 1.85 [15] C. Carbone, E. Vescovo, O. Rader, W. Gudat, and [26] and b 3.7 [27], respectively. W. Eberhardt, Phys. Rev. Lett. 71, 2805 (1993). In conclusion, we have shown using wave functions [16] L. Nordström, P. Lang, R. Zeller, and P. H. Dederichs, Europhys. Lett. 29, 395 (1995). of a periodic multilayer that quantum well and interface [17] S. Zhang and P. M. Levy, Mater. Res. Soc. Symp. Proc. states give large contributions mainly to CIP conductivity 313, 53 (1993). whereas CPP conductivity is caused by extended states. [18] W. H. Butler, X.-G. Zhang, D. M. C. Nicholson, T. C. Furthermore, our results demonstrate that, due to quantum Schulthess, and J. M. MacLaren, Phys. Rev. Lett. 76, 3216 well and interface states, the GMR amplitude depends (1996). strongly on the position of the scatterers and favors [19] R. Zeller, P. H. Dederichs, B. Újfalussy, L. Szunyogh, and interface scattering in agreement with experiments [13]. P. Weinberger, Phys. Rev. B 52, 8807 (1995). The calculations suggest that smooth interfaces with [20] P. Zahn, I. Mertig, R. Zeller, and P. H. Dederichs, Mater. impurities in the Co layer and with large b values (b . Res. Soc. Symp. Proc. 475, 525 (1997). 1) lead to high GMR amplitudes in Co Cu multilayers. [21] M. T. Johnson, S. T. Purcell, N. W. E. McGee, R. Coe- One of us (I. M.) thanks P. M. Levy and A. Fert for hoorn, J. aan de Stegge, and W. Hoving, Phys. Rev. Lett. 68, 2688 (1992). helpful discussions. This work was partly supported by [22] Z. Q. Qiu, J. Pearson, and S. D. Bader, Phys. Rev. B 46, the BMBF Contract No. 05 621 ODA 7 and NATO Grant 8659 (1992). No. CRG 960340. [23] P. J. H. Bloemen, M. T. Johnson, M. T. H. van de Vorst, R. Coehoorn, J. J. de Vries, R. Jungblut, J. aan de Stegge, A. Reinders, and W. J. M. de Jonge, Phys. Rev. Lett. 72, 764 (1994). [24] P. Lang, thesis, RWTH Aachen, 1995; L. Nordström, P. Lang, R. Zeller, and P. H. Dederichs, Phys. Rev. B 50, [1] M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, 13 058 (1994). F. Petroff, P. Etienne, G. Creuzet, A. Friederich, and [25] P. H. Dederichs and R. Zeller, in Festkörperprobleme, J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988). Advances in Solid States Physics Vol. XXI (Vieweg, [2] G. Binash, P. Grünberg, F. Saurenbach, and W. Zinn, Braunschweig, 1981), pp. 243­269. Phys. Rev. B 39, 4828 (1989). [26] J. Binder (private communication). [3] T. Oguchi, J. Magn. Magn. Mater. 126, 519 (1993). [27] I. A. Campbell and A. Fert, in Ferromagnetic Materials, [4] K. M. Schep, P. J. Kelly, and G. E. W. Bauer, Phys. Rev. edited by E. P. Wohlfarth (North-Holland, Amsterdam, Lett. 74, 586 (1995). New York, Oxford, 1976), Vol. 3, p. 747. 4312