PHYSICAL REVIEW B VOLUME 56, NUMBER 13 1 OCTOBER 1997-I Strong biquadratic coupling and antiferromagnetic-ferromagnetic crossover in NiFe/Cu multilayers K. Pettit Department of Physics, University of Illinois at Urbana Champaign, 1110 W. Green Street, Urbana, Illinois 61801-3080 and IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, California 95120-6099 S. Gider and S. S. P. Parkin IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, California 95120-6099 M. B. Salamon Department of Physics, University of Illinois at Urbana Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080 and Center for Materials Science, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Received 4 November 1996; revised manuscript received 22 May 1997 We report clear manifestations of biquadratic exchange in the magnetoresistance MR of 110 single- crystal NiFe/Cu multilayers. Magnetoresistance curves show a low-field MR minimum which results from an asymmetric canting of the moments away from the applied magnetic field. The stability of these magnetic configurations indicates that the biquadratic coupling can be significantly stronger than the bilinear coupling. In samples with ferromagnetic F bilinear coupling the strength of both the bilinear and biquadratic coupling decays in the temperature range from 200 to 400 K. In samples that are coupled antiferromagnetically AF at room temperature, we observe a crossover from AF to F bilinear coupling as the temperature is lowered below 200 K. We attribute the strong biquadratic coupling and temperature dependence of the bilinear coupling to pinholes in the Cu spacer layers. S0163-1829 97 07437-7 In recent years, the coupling between ultrathin ( 10 Å magnetic spacer layers.15 This observation gives some clues transition-metal ferromagnetic films, separated by nonmag- as to the origin of the strong biquadratic coupling. netic spacer layers, has been studied intensely.1 It was gen- The multilayered samples used in this study are composed erally assumed and observed that the interaction between the of 20 20-Å layers of Permalloy Ni79Fe21) separated by Cu magnetic moments m spacers of varying thickness. The samples were grown by dc 1 mn 1 and m2 mn 2 was propor- tional to n magnetron sputtering from Permalloy and Cu targets. In or- 1*n 2. This is termed bilinear exchange and posi- tive bilinear exchange favors antiparallel alignment of the der to induce in-plane uniaxial magnetic anisotropy, the m samples were prepared on MgO 110 substrates, on which i . Interest in this subject has been spurred by the large Fe and Pt seed layers were first grown at a substrate tempera- changes in resistance that can occur when the antiparallel mi ture of 450 °C to ensure high quality fcc growth. The sub- align in a magnetic field, the giant magnetoresistance GMR sequent layers were deposited at 40 °C. The sample struc- effect.2 More recently, a second-order biquadratic interac- tures are MgO 110 /Fe 5 Å /Pt 45 Å /Cu(t tion, which favors orthogonal alignment of successive m Cu)/ Ni 71Fe 21 20 i , Å /Cu(t has been studied and observed.3­7 The effects of biquadratic Cu) 20/Pt 45 Å , where tCu is the thickness of the Cu spacer layer. The multilayers are single crystals and have the coupling on the magnetic phase diagram and the magnetore- 110 hard direction and 100 easy direction axes in the sistance have been treated theoretically, primarily in the sample plane. Resistivity data were obtained using a conven- presence of antiferromagnetic bilinear exchange and mag- tional four-contact ac lock-in method with the field along netic anisotropy.8­10 both easy and hard directions. Magnetization data were ob- In this paper, we report a reentrant magnetoresistive effect tained using a superconducting quantum interference device- that signifies the presence of dominant biquadratic coupling based magnetometer and a magneto-optic Kerr effect polar- and permits us to determine the biquadratic and bilinear cou- imeter. pling strengths. We use the well-documented oscillation of Figure 1 is a plot of the room-temperature magnetoresis- the bilinear coupling with spacer layer thickness and tune tance, R(H)/Rs , of four samples with tCu 9, 10, 11, and that coupling to be weakly ferromagnetic.1,2 In the presence 13 Å; Rs is the resistance at magnetic saturation. The inset of such weak, negative bilinear coupling, the magnetoresis- shows the Kerr rotation at low fields for three of the samples. tance shows a sharp minimum with respect to fields applied The field is applied along the hard 110 axis and the current along the hard direction. Such behavior cannot result from along the easy 100 axis. Measurements at other angles con- bilinear exchange alone; rather, it is a result of biquadratic firmed that there is a single hard axis in the film plane. The coupling in cooperation with magnetic anisotropy.9 The bi- saturation field and hence coupling strength is largest for tCu quadratic coupling strength in these samples is significantly 11 Å; however, the maximum MR occurs at tCu 13 Å stronger than both intrinsic6,11,12 and extrinsic7,13,14 models where the parabolic MR curve and zero remanent magneti- of biquadratic coupling predict. We also observe a crossover zation are characteristic of complete antiparallel alignment of from antiferromagnetic to ferromagnetic bilinear coupling, adjacent magnetic moments at zero field.8 We will show that previously unseen in transition-metal multilayers with non- the cusped MR curve of the tCu 11 Å sample, and espe- 0163-1829/97/56 13 /7819 4 /$10.00 56 7819 © 1997 The American Physical Society 7820 BRIEF REPORTS 56 FIG. 2. The magnetoresistance vs applied magnetic-field plots FIG. 1. The magnetoresistance vs applied magnetic field for for the NiFe/Cu multilayer with tCu 10 Å. The magnetic field was four NiFe/Cu multilayers of different Cu spacer-layer thickness. applied along both the easy and hard directions of magnetization. The inset shows the Kerr magnetization loops for three of the The solid lines are results of a numerical simulation described in the samples. The field is applied along the hard axis. text. The arrows indicate the direction of magnetization in alternate layers. Dark arrows are for the field along the hard axis, light ar- cially the reentrant MR shape of the tCu 10 Å are indica- rows are for the field along the easy axis. tive of biquadratic coupling. We have observed the latter effect in these and other multilayers only in a narrow range of spacer-layer thicknesses close to the points at which the 2Hcos /2 cos , 2 bilinear exchange changes sign. The t where is the angle between the two magnetic moments and Cu 9 Å sample is fer- romagnetic and its MR is characteristic of the individual and are the angles the net magnetization and applied permalloy layers. magnetic field make with respect to the easy axis.8 The mag- The complex magnetoresistive behavior of the t netocrystalline, bilinear, and biquadratic coupling constants Cu 10 Å sample occurs only for fields applied along the hard axis, as are given by demonstrated in Fig. 2. There is little hysteresis ( 30 Oe when the field is applied in either direction. Note the hard- 2K 2 J 2 J H u 1 2 k axis MR maximum is nearly double the easy-axis MR maxi- m , H1 t m , and H2 t m , 3 mum. where magnetocrystalline anisotropy Ku is assumed to be In the simplest picture of the GMR effect, the MR de- uniaxial, the bilinear coupling strength is given by J1, and pends only on the angle cos 1(n i*n i 1) between succes- the biquadratic coupling strength by J2. sive ferromagnetic moments.1,2 Since this angle may take on The usual conditions for an energy minimum determine an arbitrary value o at zero field, we write the MR as the equilibrium configuration and lead to coupled nonlinear differential equations that are easily solved in special cases, R for example at high field, at zero field, or if /2. The R Ro 1 sin2 /2 , 1 s Rs sin2 saturation fields along the hard axis H o/2 s,h and the easy axis Hs,e are given by where Ro R( o). The data for the tCu 10 Å sample in Fig. 2 suggest that is smaller at zero field than it is at higher Hs,h H1 2H2 Hk and Hs,e H1 2H2 Hk . 4 fields around 500 Oe when the field is applied along the The stable configurations at H 0, ( hard direction. 0 , 0), are given by To better understand the origin of this MR minimum, we consider the total energy of the system, the minimum of 0 , 0 arccos Hk H1 2H , 2 if 2H2 Hk H1, which determines the equilibrium configuration of the mag- 2 5a netic moments. Although in a real system domain nucleation, growth, and domain-wall motion complicate the magnetiza- tion process, we will assume that the moment of each ferro- 0 , 0 , /2 0 2H2 Hk H1 , 5b magnetic layer is rigid and confined to the sample plane, that and the magnetization process occurs by rotation of these layers, and that the system always evolves to the global energy ,0 or if 2H minimum. In a system of two identical ferromagnetic layers 0 , 0 arccos Hk H1 2H 2 Hk H1 , 2 of thickness t in a magnetic field H the ``reduced'' total 6a energy per unit volume 2E/m where E is the total en- ergy per unit volume can be expressed as 0 , 0 0,0 or if 0 2H2 Hk H1 . 6b The configurations in Eq. 5 have a lower energy than those , Hk sin2 /2 cos2 cos2 /2 sin2 in Eq. 6 if the bilinear coupling is positive i.e., it favors H H 1 2 antiparallel alignment . Conversely, the configurations in Eq. 2 cos 2 cos2 6 are favored for negative ferromagnetic bilinear cou- 56 BRIEF REPORTS 7821 pling. In those configurations with 0 or , the net mo- ment lies along the easy axis and the magnetocrystalline an- isotropy acts to reduce 0, whereas in the /2 configurations, the anisotropy acts to increase 0. Conse- quently, the 0 or configurations can have a lower re- sistance than those with /2. This analysis is based on a model of two magnetic layers while our data were taken on a multilayer with 20 ferromag- netic layers. To the extent that a 20 bilayer multilayer ap- proximates an infinite multilayer,9,16 Eq. 2 still describes the system but H1 (4/t)(J1 /m), and H2 (4/t)(J2 /m). For a finite multilayer, the outermost magnetic moments are coupled more weakly than the moments of the inner layers. FIG. 3. The temperature dependence of the bilinear and biqua- Although this has a large effect on the spin-flop transition dratic coupling constants for the NiFe/Cu multilayer with tCu 10 when the field is applied along the easy axis,9 it is not im- Å. portant here and our data are well described by the model obtain the best fit between the data and the predicted mag- above. netization or MR curves.17 The method described here dif- The data in Fig. 2 for the tCu 10 Å sample suggest that fers from these techniques: we have identified the MR asso- at zero field the magnetic moments of successive magnetic ciated with the two zero-field states and solved uniquely for layers are alternately canted at 0/2 and 0/2 away from J1 and J2 without using adjustable parameters. the easy axis of magnetization with 0. The absence of a The solid line in Fig. 2 corresponds to the MR generated remnant magnetization for fields along the hard axis, seen in by numerically solving for the global energy minimum in the Kerr data of Fig. 1, support this interpretation. The mag- Eq. 2 using the above values of H netization process pictured in Fig. 2 consistent with both the 1 and H2. The data and simulation compare well, although the data are more MR and Kerr data is this: at zero field the net magnetization rounded, probably because of a range of H must lie along the easy axis with 1 and H2 values o /2; when the field is within the sample. The same process that leads to an MR increased along the hard axis the net magnetization moves to minimum at zero field has been observed via magneto-optic the hard axis as opens to an angle o ; finally, closes imaging in a Fe/Cr system with fourfold magnetocrystalline to 0 at the hard-axis saturation field, Hs,h . This is a re- anisotropy, for spacer-layer thicknesses very near the ferro- versible process. magnetic bilinear coupling regime3 and asymmetric states Several conclusions can be drawn from the MR data. similar to those described above have been observed in Fe/Cr Considering Eqs. 5 and 6 , it is clear that the observed MR as well18 and in NiFe/Ag.19 minimum is a signature of biquadratic coupling and that be- This experiment shows that the biquadratic coupling cause the MR is nonzero at zero field, 2H2 Hk H1. The strength can be relatively strong in contrast with theories that MR minimum also indicates that the bilinear coupling is predict the biquadratic coupling strength is smaller than the negative and favors the parallel alignment of adjacent mag- maximum in the bilinear coupling strength.6,11,12 It seems netic layers. difficult to reconcile these data with the fluctuation formal- One can estimate the values of H2 and H1 in the follow- ism as presented in Ref. 7 as well as the loose spin13 and ing way. Since the zero field angle is given by Eq. 6a , Eqs. dipole mechanisms of biquadratic coupling.14 In the Fe/Cr 1 , 4 , and 6a can be combined to give system, strong biquadratic coupling may arise from the prox- imity magnetism effect in the antiferromagnetic spacer H H s,e 2 1 layer.20 This is not likely in a system with Cu spacer layers 2 4 and H1 Hk Hs,e 2 , 7 suggesting that another mechanism-one common to sys- where tems with magnetic and nonmagnetic spacer layers-may produce strong biquadratic coupling. Using the technique described above we can measure the R 0 R 0 R , temperature dependence of the bilinear and biquadratic cou- s Rs pling strengths for the sample with tCu 10 Å. As shown in the ratio of the MR at the minimum to the maximum MR the Fig. 3 over the range of temperatures measured the bilinear sample would attain if 0 . This is easily applied to the coupling favors parallel alignment and is about half as strong sample with tCu 10 Å because the MR and magnetization as the biquadratic coupling. At high tempertures both J1 and data suggest that the sample with tCu 13 Å is fully antifer- J2 decrease with increasing temperature as expected; how- romagnetically aligned at zero field. Neglecting the very ever, they have similar temperature dependences in contrast small short circuiting effect of the extra Cu layers, this sets with measurements in a NiFe/Ag system.21 the MR scale for the sample with tCu 10 Å so that 0.22 In the temperature range shown in Fig. 3 the sample with and 0 56°. In this sample Hs,h and Hs,e combine to give tCu 13 Å attained the fully antiparallel orientation and, as H2 1.08 kOe and H1 0.49 kOe or J2 0.046 ergs/cm2 mentioned above, served as the MR reference allowing us to and J1 0.021 ergs/cm2. For comparison, the sample with determine J1 and J2 for the sample with tCu 10 Å. However tCu 13 Å has J1 0.047 ergs/cm2. Other researchers have below 200 K the sample with tCu 13 Å no longer attains modeled magnetoresistance curves in a similar fashion and the fully antiparallel configuration. In fact, at low tempera- extracted the coupling strengths by adjusting J1 and J2 to tures the MR curve for the sample with tCu 13 Å develops 7822 BRIEF REPORTS 56 namely indirect interlayer exchange coupling then the sign of the bilinear coupling should be independent of tempera- ture. Observation of a change of sign of the bilinear coupling term implies that the coupling mechanisms are different for the F and AF regions. We propose that the ferromagnetically coupled regions arise from pinholes in the Cu spacer layer. The pinhole re- gions provide strong ferromagnetic coupling which when combined with regions of antiferromagnetic interlayer ex- change coupling and strong intralayer coupling can lead to dominant biquadratic coupling.20,22 The regions of ferromag- FIG. 4. Magnetoresistance curves for the NiFe/Cu sample with netic coupling also contribute to the measured bilinear cou- tCu 13 Å when the field is applied along the hard axis. At room pling. The observed crossover from antiferromagnetic to fer- temperature the moments are coupled antiferromagnetically, as the romagnetic bilinear coupling as the temperature is reduced is shape of the room-temperature MR curve indicates. In contrast the a result of the increased stiffness of the ferromagnetic pin- MR minimum at low temperatures is indicative of strong biqua- holes which are believed to be more temperature dependent dratic coupling and ferromagnetic bilinear coupling. The asymme- than the bulk material23 . try in the MR curve at low temperatures results from the slight Our work clearly demonstrates that the reentrant magne- misalignment of the applied magnetic field relative to the sample's toresistance results from biquadratic coupling and that, with hard axis. few assumptions, the biquadratic and bilinear coupling a low-field minimum as shown in Fig. 4. This indicates not strengths can be determined by resistance measurements only that the sample with t alone. We have shown that systems with noble-metal spacer Cu 13 Å develops a strong bi- quadratic coupling term at low temperatures but also that the layers may have very strong biquadratic coupling, stronger bilinear coupling changes sign from antiferromagnetic to fer- than predicted by several existing theories. A crossover at romagnetic as the temperature is lowered below about 200 low temperatures from antiferromagnetic to ferromagnetic K. To our knowledge this is the first evidence for such a bilinear coupling has been observed. This suggests that the change of sign in the bilinear coupling term in transition- ferromagnetic coupling, which in a frustration model is es- metal multilayers with nonmagnetic spacer layers. sential for biquadratic coupling, does not arise from inter- Such a change of sign in the bilinear coupling term layer exchange coupling. We propose that pinholes in the strongly suggests that the observed biquadratic does not re- spacer layer are responsible for the ferromagnetic coupling. sult from fluctuation mechanism. In the fluctuation model The authors thank Kevin Roche and Arley Marley for indirect interlayer exchange coupling is responsible for both their technical assistance. M.B.S. gratefully acknowledges the ferromagnetically F and antiferromagnetically AF support from Los Alamos National Laboratory. This work coupled regions. 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