PHYSICAL REVIEW B VOLUME 58, NUMBER 22 1 DECEMBER 1998-II Conductance, magnetoresistance, and interlayer exchange coupling in magnetic tunnel junctions with nonmagnetic metallic spacers and finite thick ferromagnetic layers Wu-Shou Zhang and Bo-Zang Li Institute of Physics and Center for Condensed Matter Physics, Chinese Academy of Sciences, P.O. Box 603-99, Beijing 100080, China Yun Li Department of Physics, Peking University, Beijing 100871, China Received 20 March 1998 Based on the two-band model and free-electron approximation, magnetism and transport properties of magnetic tunnel junctions with nonmagnetic metallic NM spacers and finite thick ferromagnetic FM layers are studied. The mean conductance and tunnel magnetoresistance are oscillatory functions of NM and FM thicknesses, their period is determined by the Fermi-surface properties of the metals, and magnetoresistances ( 103%) much greater than those predicted by Julliere's model are obtained. The oscillation of interlayer exchange coupling with metal layer thickness that originates from the interference of electron waves at differ- ent energy levels is found in contrast with the situation in metallic magnetic multilayers. Our results indicate that giant tunnel magnetoresistances with weak antiferromagnetic coupling can be attained by controlling the metal layer thickness, and this has potential in designing spin-polarized tunneling devices. S0163-1829 98 03346-3 I. INTRODUCTION scribed in terms of the Ruderman-Kittel-Kasuya-Yosida theory,21 or quantum well theory.22 IEC also changes as a Since the discovery of the giant magnetoresistance function of FM thickness as predicted theoretically23,24 and GMR in metallic magnetic multilayers MMM's ,1 there later observed experimentally.25,26 As concerns theories has been a renewed interest in the phenomenon of the tunnel about IEC in MTJ's, two models have been proposed: One is magnetoresistance TMR in magnetic tunnel junctions the so-called free-electron model due to Slonczewski as men- MTJ's consisting of two ferromagnetic FM electrodes tioned above.10 It predicts antiferromagnetic AF coupling separated by a tunneling barrier insulator or semiconductor for low barrier height and ferromagnetic FM coupling for layer FM/I S /FM .2,3 More recently, large TMR's were high barrier height, and the strength of IEC decreases expo- achieved in FM/I/FM structures4­8 which render MTJ's more nentially with the barrier thickness; The other model is due promising than MMM's in the manufacture of magnetic-field to Bruno.27 By using the t-matrix formalism, the coupling is sensors and digital storage devices. Since the resistance and expressed in terms of the spin asymmetry of the reflection at field sensitivity of MTJ's are much higher than those of the I S /FM interfaces. It succeeds in obtaining an IEC cou- MMM's, the power consumed and magnetic field needed pling which increases with temperature, and it reduces to Slonczewski's results at zero temperature. will be much less. Recently, Vedyayev et al.28 and the present authors29 Julliere2 discussed the TMR effects using Tedrow and studied MTJ's with NM spacers between the FM's and bar- Meservey's analysis,9 and he showed that TMR is propor- rier, i.e., FM/NM/I S /FM and/or FM/NM/I S /NM/FM . tional to the spin-polarization factors of two FM's. The results showed that the presence of thin NM spacers can Slonczewski10 studied MTJ's based on the free-electron ap- lead to the formation of quantum well states that lead to proximation by analyzing the transmission of charge and oscillations of TMR and IEC in sign with NM thickness. spin current through a rectangular barrier separating two TMR values much greater than those in the conventional semi-infinite free-electron-like FM's. He predicted that the sandwiched MTJ's with low AF coupling can be obtained in tunnel conductance varies as the cosine of the relative angle the structure. of two FM's magnetizations and it was verified widely,4,5,11 Based on the previous results we study a more realistic and TMR depends not only on the spin-polarization factors MTJ with NM spacers and finite thick FM layers in this of FM's as that of Julliere but also on the barrier height. work. It is found that the mean conductance and TMR oscil- MacLaren et al.12 verified that Slonczewski's model pro- late with the NM and FM thicknesses, but the oscillation of vides a good approximation to the exact expressions for free IEC with these thicknesses exhibits multiple periods which electrons in the limit of thick barrier. Besides these two mod- are similar to those in MMM's but have different physical els, there were other theories had been applied to the origins. system.13­18 The plan of the paper is as follows. In Sec. II, the model Another extensively studied subject in MMM's and Hamiltonian is established and the corresponding Schro¨- MTJ's is the interlayer exchange coupling IEC . It is found dinger equation is solved, then we give the analytical and that IEC oscillates in sign with the nonmagnetic metallic numerical results of conductance and TMR in Sec. III, IEC NM thickness in MMM's,19,20 and this effect can be de- in Sec. IV. At last, we discuss the related topics about this 0163-1829/98/58 22 /14959 7 /$15.00 PRB 58 14 959 ©1998 The American Physical Society 14 960 WU-SHOU ZHANG, BO-ZANG LI, AND YUN LI PRB 58 where mi* (i 1­7 is the electron effective mass in region i. In practice, mi* may differ from the mass of free electron, for simplicity, we assume all electrons have the same mass m as that of the free electron. U(x) is the potential which is uniform in each layer, h(x)* is the internal exchange energy with h(x) denoting the molecular field and being the conventional Pauli spin operator. Although transverse momentum k is omitted from the above notations, the ef- fects of summation over k will be accounted for in our re- sults. Corresponding to the Hamiltonian in Eq. 1 , all compo- nents of eigenspinors of H with eigenenergy E are of the plane-wave form, the wave vector or virtual wave vector in each region is 1k n 2mE, forNM, 1 k 2m E Uf h , for FM, 2 1 i 2m E U0 , for barrier, FIG. 1. Schematic potential for NM/FM/NM/I S /NM/FM/NM where the subscript n indicates the NM layer; 1 corre- junction. Uf and U0 are the crystalline potentials in the FM and spond to , the majority- and minority-spin electrons ; barrier layers, respectively; h is the molecular field of the FM's; Uf and U0 are the crystalline potentials in the FM's and is the angle between magnetization of two FM's; a, b, and d are the barrier relative to NM, respectively; h is the amplitude of thicknesses of the FM, NM, and barrier layers, respectively. h(x) in the FM's and is constant; the directions of h, hence model Sec. V and conclude the paper with a summary the corresponding spin quantization axes, differ by the angle Sec. VI . between the two FM layers see Fig. 1 . Consider a spin-up incident plane wave having unit par- II. MODEL ticle flux in region 1 NM electrode, x x1,2 in Fig. 1 , the Consider two single-domain transition FM's separated by eigenfunction of H in each region is two flat plane NM's plus a flat plane tunneling barrier and 1/2eikn x x1,2 R covered on both sides by two semi-infinite NM cap layers as 1 kn 1 e ikn x x1,2 , lead wires see Fig. 1 . For simplicity, we assume that the FM's are made of the same metal and have the same thick- 1 R1 e ikn x x1,2 , ness a, the NM spacers and cap layers are made of the same material and the spacers have the same thickness b. This i Li eiki x xi 1,i Ri e iki x xi 1,i , i 2 6, assumption, however, can be released easily without chang- ing qualitatively the physical behavior of system. a,b and the 7 L7 eikn x x6,7 , 3 barrier thickness d, are much smaller than their in-plane di- where L mensions so that the system may be considered as homoge- i and Ri (i 1 7, , ) are coefficients to be determined, the index i denotes region i, k neous in the yz plane parallel to the interfaces and inho- i is a wave vector given in Eq. 2 , x mogeneous only in the x direction growth direction . Within i 1,i is the coordinate of boundary between region i 1 and i. each layer, the electrons are described as a free-electron To complete the solution of the Schro¨dinger equation, one gas.10,12,28­32 Between layers, they experience potential must find the 24 unknowns by matching steps. The latter are spin dependent at the FM/NM interfaces and d /dx at the interfaces x x (x x i 1,i , (i 2 5,7). The change in quan- 1,2 , x2,3 , x5,6 , and x6,7) due to the exchange splitting of tization axis at x x the d band in the FM's. In contrast, the height of the energy 5,6 requires the spinor transformation barrier is spin independent at the NM/I S interfaces (x x 3,4 and x4,5). In the present model, no diffuse scattering is 5 6 cos 6 sin , introduced at the interfaces and in each layer. The profile of 2 2 energy seen by the conduction electrons can be represented as drawn in Fig. 1. By assumption of small external voltage, , 4 the longitudinal along the x direction part of the effective 5 6 cos 2 6 sin 2 one-electron Hamiltonian takes the following form: and similarly for their derivatives. 2 d2 Some algebra produces the approximate solution for Li H U x h x * , 1 and R 2m i that is accurate to leading order in e d. For sim- i* dx2 plicity, we give only L7 PRB 58 CONDUCTANCE, MAGNETORESISTANCE, AND . . . 14 961 L 2 5/2 7 4D e dkn cos 2 , L 5/2 7 4D D e dkn sin 2 5 with k D k cos iknsin for E U 2 k2 f h, n 1/2 f 1/2f 6 FIG. 2. The mean tunnel conductance G ¯ as a function of the f 2 2 reduced FM thickness, k ,Fa/ and NM thickness, kn,Fb/ . G¯ x knsin2x k cos2x, 7 has been normalized to 1 by division G ¯ 0 e2exp( 2 d)/ d2. The k parameters: kn,F k ,F 0.4 k ,F , F k ,F , Fd 3. nb arctan /kn , 8 and e2 3k6 G ¯ n e 2 d D , 13 2 d 2 D 2 2 E EF k a arctan k kcot . 9 n and the TMR ratio is defined as The expression of other coefficients is tedious so we omitted G 2 1 X 2 it here and it can be obtained by the continuity conditions at R G TMR , 14 the boundaries. G 1 2X E EF In the following two sections, we will evaluate the tunnel where conductance, TMR, and IEC within the barrier region (x3,4 x x 2 4,5) where h 0. In addition, we will consider only the k f f case of the two-band model for the density of states and zero X D 2 15 2 temperature as done in Refs. 10 and 29­31. D k f f with f (x), , and being the same as those in Eqs. III. CONDUCTANCE AND TUNNEL 7 ­ 9 . Figures 2 and 3 show G ¯ and R MAGNETORESISTANCE TMR as functions of a and b, the FM and NM thicknesses. We find they oscillate The particle transmissivity of majority-spin incident elec- with a and b, and the period is determined by the Fermi wave trons is vectors. Another remarkable feature is that RTMR can be much greater than that observed in past experiments and d predicted by conventional theories.2,10 Based on Julliere's T Im * and Slonczewski's models, R dx . 10 TMR 2 P2/(1 P2) (k ,F k ,F)2/2k ,Fk ,F 45% (P is spin-polarization The particle transmissivity of minority-spin incident elec- factor of FM's for parameters given in Fig. 2 (k ,F trons, T is given by the same expression with k and k 0.4k ,F), but the present MTJ's exhibit the maximum interchanged. The summation of e(T T )/2 over occu- RTMR up to 220%. This means that we can obtain an en- pied states gives the total charge current (Ie) per unit flowing hanced TMR ratio using the present structure. from region 1 to 7. The differential tunnel conductance G is The results in Figs. 2 and 3 show a special case, i.e., defined as G dIe /dV. The detailed procedure for calculat- kn,F k ,F (Uf h0 , e.g., Fe/Cr . The minority electrons ing G can be found in Ref. 33. are free in regions of FM and NM, f 2 (x) kn in Eq. 7 so At zero temperature and small applied voltage, for nearly the oscillatory period, TFM /k ,F . Another special case is normal incidence, electrons with Ex near EF should carry kn,F k ,F (Uf h0 , e.g., Co/Cu , in which TFM /k ,F . most of the current, so that we can replace Ex with EF in calculating the conductance due to tunneling. By summing the charge transmission over Ex and k for occupied states in the usual manner,10,12,28­31,33 one finds the conventional ex- pression e2 G T . 11 8 2 d T E EF Some algebra produces the area conductance as G G ¯ 1 cos , 12 FIG. 3. TMR as a function of k ,Fa/ and kn,Fb/ . The pa- where the mean conductance is rameters are the same as those in Fig. 2. 14 962 WU-SHOU ZHANG, BO-ZANG LI, AND YUN LI PRB 58 but if k ,F kn,F , it has no effect on RTMR,max . For fixed k ,F /k ,F , if k ,F kn,F k ,F , RTMR,max does not change with kn,F /k ,F ; Otherwise, RTMR,max decreases with kn,F /k ,F when kn,F k ,F but increases when kn,F k ,F . This means we can choose a suitable NM material to en- hance RTMR regardless the type of FM. But in the conven- tional MTJ's, only a FM with great polarization factor e.g., Fe will give greater RTMR than that with lower one e.g., Ni .Another special case is for k ,F/k ,F 1/2, there is 2 k2 2 n k , k k2 2k2 n,F 1 3 4 k ,F , X k n , 17 k2 2 /kn , 1 34k ,F kn,F that corresponds to RTMR,max as shown in Fig. 4, too. Equa- tions 14 , 16 , 17 , and the related Fig. 4 give the upper limit of TMR ratios which are much greater than those in conventional structures. FIG. 4. Maximum TMR vs kn,F /k ,F for different values of IV. INTERLAYER EXCHANGE COUPLING k ,F /k ,F as shown beside each curve. Slonczewski introduced and employed a method for cal- Other situations are complex with TFM determined by the culating exchange coupling from torque produced by rotation lowest common multiple of period for majority and minority of the magnetization of one FM to that of the other.10 This electrons, i.e., TFM /k ,F , /k ,F . Suppose the FM's in method was further elaborated by Erickson et al.,34 Edwards Figs. 2 and 3 are Fe, we have k ,F 1.09 Å 1 Ref. 32 and et al.35 and Drchal et al.36 This method of calculating the TFM 2.88 Å. The lattice constant for -Fe is 2.86 Å, veri- torque involves the construction of a spin-flip or exchange fying that TFM is about the interatomic spacing and this case current, which is a measure of the probability that an incident is similar to the aliasing effect in the oscillatory coupling electron will undergo a change of spin state on transmission through NM spacers in MMM's. It can lead to a measured through the NM spacers and barrier layer. The spin-flip cur- period that is significantly longer than the theoretical one. rent due to a majority-spin electron of energy E incident The effective period can be expressed as: from the left electrode, j e is expressed as TFM,eff 2/ 1/TFM 2n/c where c is the monolayer thickness of FM, n is chosen such that T FM,eff 2c.21 The oscillatory period with b determined by k je n,F as 2mRe * * . 18 shown in Figs. 2, 3 and the previous results.28,29 The aliasing effect is similar to the above discussion. Similarly, one obtains the current due to a minority-spin In contrast to that of the conventional sandwiched MTJ's, electron incident from the left electrode, je by applying this we find the height of barrier has no effect on the amplitude equation with k and k interchanged. The net current of except the phase of R majority- and minority-spin electrons j TMR vs a and b as indicated by Eqs. T is calculated by 7 ­ 9 , 14 , and 15 . We assume that m summing both j and j over allowed states up to the Fermi i* in Eq. 1 is the e e same as the free-electron mass m. Although m* may be dif- energy, then multiplying by a factor of 2 to account for elec- ferent from m obviously so in an insulator and it affects trons incident from the right NM electrode, which contribute TMR in conventional MTJ's,13 it has little effect in the equally to the total spin current present model. This is because the influence of effective mass can transfer to the effective barrier height. j j j . 19 Because R T 2 e e TMR is the oscillatory function of a and b, it is 0 E EF interesting to obtain the maximum RTMR , RTMR,max for given parameters. We find if k The coupling strength J of the Heisenberg term (J 0 is for ,F /k ,F 1/2, when FM coupling is given by 2/k2 , kn,F k ,F , J j min2 k kn T/2 sin . 20 X n ,k k2/k2 , k max2 16 k ,F kn,F k ,F , After some algebra, we have n ,k k2 2 /kn , k ,F kn,F , 2m EF 6 there will be R J k 2exp 2 d D 2Im D D* TMR,max as shown in Fig. 4. For fixed 2 2 n 0 kn,F /k ,F , if k ,F kn,F , a lower k ,F /k ,F higher spin- polarization factor results in a higher RTMR,max as expected, EF E dE 21 PRB 58 CONDUCTANCE, MAGNETORESISTANCE, AND . . . 14 963 2m E 2 F k k6 2exp 2 d D D , 23 2 2 n 2 D 2 Im D D * 2 0 2 k2n f f EF E dE 22 with and k Im D nk k k k sin k k sin D * 24 2 2 k2n f f 1/2f f for E Uf h, where f (x), , and are the same as with metal layer thickness in MMM's that originate from the those in Eqs. 7 ­ 9 . IEC consists of two components, one specific shape of Fermi surface21,38 but they are not an effect including D 2 is for the majority-spin flip current and the of the total energy. counter one is for the minority-spin flip current. For simplicity, we discuss two special situations: One is Numerical results of IEC are shown in Figs. 5­8, changes kn,F k ,F(Uf h0 , e.g., Fe/Cr as illustrated in Figs. 5 of J with a and b have features of decaying oscillations as and 6. Figure 5 shows J as a function of a while b is fixed, it those in MMM's but the amplitude is smaller by a factor exhibits multiple periods as discussed above. Because exp( 2 2 2 2 Fd) than the latter.10,29 Another interesting feature is f (x) kn and D 2 1/kn( 2 kn), the oscillatory part the multiple period of oscillation. From Eqs. 21 ­ 24 , we mainly comes from the majority-spin flip current, while the find that different E results in different k and kn , hence minority-spin flip current has a small contribution to it. The there is different period of oscillation with a and b. Because oscillatory behavior of J vs b appears clearly in Fig. 6. The electron waves with different energy levels all contribute to striking difference with the oscillation of J vs a is that the J, summation of different period oscillations results in mul- oscillations are not necessarily around zero; instead, J may tiple period. This is in contrast to IEC in MMM's where oscillate around a positive, zero, or negative value, depend- different energy states contribute to oscillation of different ing on the choice of a. This is an important consequence for periods, but most of them cancel each other out and only the the experimental observation the oscillatory behavior of J vs states near the Fermi level have the most contribution. IEC in b. If one uses a technique that is sensitive only to the sign of MMM's embodies properties of the Fermi surface such as coupling, then it is necessary to choose properly the FM GMR, and transport and magnetic properties are correlated thickness, so that the oscillations do actually yield a change with each other.37 There are also multiple periods of IEC of sign of J. This property can be understood from Eqs. FIG. 5. IEC as a function of k ,Fa/ for kn,Fb/ 5. J has FIG. 6. IEC as a function of kn,Fb/ for various values of been normalized to 1 by division J 2 0 2mEFexp( 2 d)/ 2 2. The k ,F /k ,F as shown beside each curve. The parameters are the same other parameters are the same as those in Fig. 2. as those in Fig. 5. 14 964 WU-SHOU ZHANG, BO-ZANG LI, AND YUN LI PRB 58 spin flip current gives most of the contribution to IEC. Figure 7 shows J vs b for a fixed, and illustrates that the sharp peaks come from the electrons which satisfy the resonant condi- tion, n . As b increases, the number of energy levels which satisfy the resonant condition increases and the peaks widen correspondingly. Figure 7 shows the AF coupling and it can also exhibit the FM coupling if other values of a are chosen. Figure 8 illustrates J vs a with fixed b and it also manifests the multiple periods as discussed above. In realistic MTJ's, kn,F is not necessarily equal to k ,F or k ,F , but according to the above discussion we conclude that 1 the electrons with energy Uf h E EF all give their contribution to IEC, and the summation of different states gives the multiple periods of oscillation of J with a and b; 2 if kn,F k ,F (Uf h), J approaches a constant as b in- creases; 3 if kn,F k ,F (Uf h), J exhibits sharp peaks at some thicknesses of FM and NM. V. DISCUSSION We point out that the electrons with momentum perpen- FIG. 7. IEC as a function of kn,Fb/ for k ,Fa/ 5.5. The dicular to the interface give the largest contribution to the parameters: kn,F k ,F , k ,F 0.4 k ,F , F k ,F , Fd 3. TMR due to the strong decrease of the factor exp( 2 d) with x. This one-dimensional character of transport through 21 ­ 24 , because f ( ) 0, J does not oscillate in sign the tunneling barrier leads to quite sharp resonances in con- with b but its asymptotic value is determined by a. ductivity. It is in contrast with MMM's in which quantum Another special case is kn,F k ,F (Uf h0 , e.g., Co/Cu size effects on the conductivity also exist but lead to much as shown in Figs. 7 and 8. When E Uf h the minority smoother oscillations due to the averaging of all incidences electrons face barriers at NM/FM interfaces, so there is an of conduction electrons. The predicted sharp resonance may exponential decaying factor exp( k a) in the factor be difficult to observe experimentally. Indeed, the roughness Im(D D *) in the integrand of Eq. 22 . It means that elec- of the layers leads to spatial fluctuations in the thickness of trons with energy E Uf h have no significant contribution the FM, NM, and barrier layers. If the roughness is smaller to J beyond a few FM monolayers. We need only pay atten- than the Fermi wavelength, it may be taken into account by tion to the energy region of Uf h E EF . When E is near averaging the currents over a distribution of thickness with U 2 f h, kn k , there is f (x) kn sin2x, i.e., D 2 an amplitude of one or several monolayers. Even in that csc2 csc2 2 2 while D 2 1/kn( 2 kn), so the minority- case, the averaged value of TMR in the present MTJ is larger than that for the ordinary MTJ of the sandwiched structure. The present results are appropriate only to the case a,b MPF mean free path of electrons , otherwise the elec- trons will be scattered in FM's and NM's and the quantum size effect will be destroyed. If a MPF, the effects of re- flection on the outer FM/NM interfaces (x1,2 ,x6,7) can be omitted and the present structure will be identical to the FM/NM/I S /NM/FM structure as discussed before.28,29 If b MPF, the electrons will lose the polarization memory and the present structure reduces to a normal tunnel junction. The preceding elementary model does not take into ac- count the generally important complications such as interfa- cial roughness, electron-electron correlations,14 bias5,15,16 and temperature14 dependence, and spin-flip tunneling.17 How- ever, it does provide a basis for initial appraisal of magnetic and transport effects on MTJ's arising from NM spacers and finite thick FM layers. Although not verified at present, our results indicate that we can alter TMR and IEC, and obtain giant TMR ratios with lower IEC in the MTJ's by controlling the FM and NM thicknesses. VI. SUMMARY FIG. 8. IEC as a function of k ,Fa/ for kn,Fb/ 9. The other We have studied the magnetism and transport properties parameters are the same as those in Fig. 7. of MTJ with NM spacers and finite thick FM layers. It is PRB 58 CONDUCTANCE, MAGNETORESISTANCE, AND . . . 14 965 found that the mean conductance and TMR are oscillatory ACKNOWLEDGMENTS functions of the FM and NM thicknesses, and the oscillation of IEC with these thicknesses exhibit multiple periods. Giant We would like to express sincere thanks to Professor Fu- TMR with weak AF coupling can be obtained in the mixed Cho Pu and Dr. Jun-Zhong Wang for helpful discussion. structure and it has potential in designing spin-polarized tun- This work was supported by the Natural Science Foundation neling sensors with a large TMR and field sensitivity. in China under Grants No. 19774076 and 59392800. 1 M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. 19 P. Gru¨nberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sow- Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas, ers, Phys. Rev. Lett. 57, 2442 1986 ; J. Appl. Phys. 63, 3473 Phys. Rev. Lett. 61, 2472 1988 . 1988 . 2 M. Julliere, Phys. Lett. 54A, 225 1975 . 20 S. S. P. Parkin, N. More, and K. P. Roche, Phys. Rev. Lett. 64, 3 S. Maekawa and U. Ga¨fvert, IEEE Trans. Magn. 18, 707 1982 . 2304 1990 . 4 T. Miyazaki and N. Tezuka, J. Magn. Magn. Mater. 139, L231 21 P. Bruno and C. Chappert, Phys. Rev. Lett. 67, 1602 1991 ; 67, 1995 ; 151, 403 1995 ; J. Magn. Soc. Jpn. in Japanese 21, 2592 E ; Phys. Rev. B 46, 261 1992 . 22 493 1997 ; J. Appl. Phys. 79, 6262 1996 . D. M. Edwards and J. Mathon, J. Magn. Magn. Mater. 93, 85 5 J. S. Moodera, L. R. Kinder, T. M. Wong, and R. Meservey, 1991 ; D. M. Edwards et al., Phys. Rev. Lett. 67, 493 1991 ; J. Phys. Rev. Lett. 74, 3273 1995 ; J. S. Moodera, L. R. Kinder, J. Phys.: Condens. Matter 3, 4941 1991 . 23 Nowak, P. LeClair, and R. Meservey, Appl. Phys. Lett. 69, 708 J. Barna s, J. Magn. Magn. Mater. 111, L215 1992 . 24 1996 ; J. S. Moodera and L. R. Kinder, J. Appl. Phys. 79, 4724 R. P. Bruno, Europhys. Lett. 23, 615 1993 . 25 S. N. Okuno and K. Inomata, Phys. Rev. Lett. 72, 1553 1994 ; 1996 ; 81, 5515 1997 ; J. S. Moodera, E. F Gallagher, K. Phys. Rev. B 51, 6139 1995 ; K. Inomata et al., J. Magn. Robinson, and J. Nowak, Appl. Phys. Lett. 70, 3050 1997 . 6 Magn. Mater. 156, 219 1996 . C. L. Platt, B. Dieny, and A. E. Berkowitz, Appl. Phys. Lett. 69, 26 P. J. H. Bloemen, M. T. Johnson, M. T. H. van de Vorst, R. 2291 1996 ; J. Appl. Phys. 81, 5523 1997 . Coehoorn, J. J. de Vries, R. Jungblut, J. aan de Stegge, A. Re- 7 C. Kwon, Q. X. Jia, Y. Fan, M. F. Hundley, D. W. Reagor, J. Y. inders, and W. J. M. de Jonge, Phys. Rev. Lett. 72, 764 1994 . Coulter, and D. E. Peterson, Appl. Phys. Lett. 72, 486 1998 . 27 P. Bruno, J. Magn. Magn. Mater. 121, 248 1993 ; Phys. Rev. B 8 C. H. Shang, G. P. Berera, and J. S. Moodera, Appl. Phys. Lett. 49, 13 231 1994 ; 52, 411 1995 . 72, 605 1998 . 28 A. Vedyayev, N. Ryzhanova, C. Lacroix, L. Giacomoni, and B. 9 R. Meservey and P. M. Tedrow, Phys. Rep. 238, 174 1994 ; P. Diny, Europhys. Lett. 39, 219 1997 . Fulde, Adv. Phys. 22, 667 1973 ; Phys. Rev. B 7, 318 1973 ; 29 W.-S. Zhang and B.-Z. Li, Chin. Phys. Lett. 15, 296 1998 ; J. 16, 4907 1977 . Appl. Phys. 83, 5332 1998 . 10 J. C. Slonczewski, J. Phys. Paris , Colloq. 49, C8-1629 1988 ; 30 Y. Li, B.-Z. Li, W.-S. Zhang, and D.-S. Dai, Phys. Rev. B 57, Phys. Rev. B 39, 6995 1989 ; Symposium On Magnetism and 1079 1998 ; Chin. Phys. Lett. 15, 210 1998 . Magnetic Materials, edited by H. L. Huang and P. C. Kuo 31 X. Zhang, B.-Z. Li, W.-S. Zhang, and F.-C. Pu, Phys. Rev. B 57, World Scientific, Singapore, 1990 , pp. 285. 1090 1998 . 11 T. Yaoi, S. Ishio, and T. Miyazaki, J. Magn. Soc. Jpn. 16, 303 32 M. B. Stearns, J. Magn. Magn. Mater. 5, 167 1977 . 1992 . 33 C. B. Duke, Tunneling in Solids Academic, New York, 1969 ; in 12 J. M. MacLaren, X.-G. Zhang, and W. H. Butler, Phys. Rev. B Tunneling Phenomena in Solids, edited by E. Burstein and S. 56, 11 827 1997 . Lundquist Plenum, New York, 1969 , pp. 31. 13 A. M. Bratkovsky, Phys. Rev. B 56, 2344 1997 . 34 R. P. Erickson, K. B. Hathaway, and J. R. Cullen, Phys. Rev. B 14 S. Maekawa, J. Inoue, and H. Itoh, J. Appl. Phys. 79, 4730 47, 2626 1993 ; J. Magn. Magn. Mater. 104-107, 1840 1992 . 1996 ; J. Inoue and S. Maekawa, Phys. Rev. B 53, R11 927 35 D. M. Edwards, J. M. Ward, and J. Mathon, J. Magn. Magn. 1996 . Mater. 126, 380 1993 ; D. M. Edwards et al., ibid. 140-144, 15 S. T. Chui, Phys. Rev. B 55, 5600 1997 . 517 1995 . 16 N. F. Schwabe, R. J. Elliott, and N. S. Wingreen, Phys. Rev. B 36 V. Drchal, J. Kudrnovsky, I. Turek, and P. Weinberger, Phys. 54, 12 953 1996 . Rev. B 53, 15 036 1996 . 17 R. Y. Gu, D. Y. Xing, and J. M. Dong, J. Appl. Phys. 80, 7163 37 J. Barna s and Y. Bruynseraede, Phys. Rev. B 53, R2956 1996 . 1996 . 38 D. Li, J. Pearson, S. D. Bader, E. Vescovo, D.-J. Huang, P. D. 18 J. Mathon, Phys. Rev. B 56, 11 810 1997 . Johnson, and B. Heinrich, Phys. Rev. Lett. 78, 1154 1997 .