APPLIED PHYSICS LETTERS VOLUME 75, NUMBER 26 27 DECEMBER 1999 Magnetic configurations in exchange-biased double superlattices S. G. E. te Velthuis,a) G. P. Felcher, J. S. Jiang, A. Inomata, C. S. Nelson, A. Berger, and S. D. Bader Argonne National Laboratory, Argonne, Illinois 60439 Received 17 August 1999; accepted for publication 2 November 1999 The layer-by-layer magnetization of a ``double-superlattice'' Fe/Cr 211 exchange-bias junction was determined by polarized neutron reflectometry. An n-layered Fe/Cr n antiferromagnetic AF superlattice is coupled with an m-layered Fe/Cr m ferromagnetic F superlattice, to provide a controlled exchange bias. In low magnetic fields, the magnetizations of the two superlattices are collinear. The two magnetized states along or opposite to the bias field differ only in the relative orientation of the F and adjacent AF layer. At higher fields, the AF moments flop to the direction perpendicular to the applied field. The structure, thus determined, explains the magnitude of the bias field. © 1999 American Institute of Physics. S0003-6951 99 03052-1 Exchange bias was first discovered in 1956 by Meikle- polarized neutron reflectivity PNR study for which 18 Å is john and Bean in Co­CoO particle systems.1 It refers to the well within the instrumental resolution. occurrence of a unidirectional magnetic anisotropy that A prototype sample had a layer sequence manifests itself in shifted hysteresis loops for coupled ferro- Fe 50 Å /Cr 20 Å F AF 5/ Fe 14 Å /Cr 11 Å 20 see Table I . magnet F ­antiferromagnet AF systems cooled through tCr 20 Å between the F and AF superlattices, to provide a the Nee´l temperature in the presence of a magnetic field.1 ferromagnetic intersuperlattice coupling. A uniaxial anisot- Exchange bias is being utilized in applications such as mag- ropy was introduced by epitaxially growing the sample via netoresistive read heads,2 and is being studied extensively in dc magnetron sputtering onto single-crystal MgO 110 various AF/F systems,3­8 but its origin is still unclear.9 Typi- substrates.16 cally, the magnitude of the exchange-bias effect differs, with The magnetization of the sample, normalized to the satu- some exceptions,10 by 102 between experiment and theory. ration value, is presented in Fig. 1. The measurements were Initially, exchange biasing was interpreted as the result obtained with a superconducting quantum interference de- of the exchange interaction at AF/F interfaces: the magnitude vice magnetometer at room temperature and with the field H of the exchange-bias field is given by balancing the gain in applied along the easy axis. Above 15 kOe, the magnetic Zeeman energy with the energy cost of interfacial exchange moments of all layers in both superlattices are aligned with when the ferromagnet reverses its magnetization. In the ear- H. In decreasing H, the magnetization decreases as the Fe liest model,11 both F and AF spin structures were assumed to layers in the AF superlattice first enter a spin­flop state, as be a rigid sequence of ferromagnetic planes, with a sequence the AF coupling becomes comparable to the Zeeman energy or for the AF component; the AF/F inter- and then becomes AF aligned. Below 2 kOe, the magnetic face was taken to be atomically flat. Unfortunately, this pic- moments of all layers are along the easy axis and H. By ture overestimates the bias fields. Subsequent models12­14 cycling H well within 2 kOe, a minor hysteresis loop is attempted to address this by invoking roughness at the inter- measured Fig. 1, inset , which exhibits an exchange-bias face and/or magnetic domain formation in the AF structure. field of HE 39 Oe and a coercive field Hc 5 Oe. The bias It is impossible to control the interface between a conven- effect in the double superlattice is obtained simply by align- tional F­AF pair, and the magnetic configuration of a rough interface cannot be unambiguously defined experimentally. TABLE I. The layer sequence of the double superlattice. The layer thick- In view of these unresolved issues, an artificial magnetic ness, rms interface roughness, and x-ray scattering length density are ob- system where the effect can be examined with minimal tained from the fit of the x-ray reflectivity data. The x-ray scattering length density consists of real and imaginary terms. The neutron scattering length materials-related complexities was proposed.15 This system density used in the calculations are given. The neutron scattering length is a double superlattice consisting of one F superlattice ob- density of Fe contains a nuclear a magnetic term. tained by an epitaxial sequence of Fe and Cr 211 layers, and one AF superlattice obtained similarly but with a different Cr Scattering length density thickness t (10 6 Å 2) Cr since the interlayer exchange coupling oscil- Thickness Roughness lates with t Layers Å Å X ray Neutron Cr . The coupling between the AF and F superlat- tices is governed by the value of tCr between the two super- 9.5 lattices. Since the interlayer coupling has an 18 Å period, the Cr Cap 49 53.2 5.44i 2.97 coupling between the AF and F superlattices in double- Fe 8.12 4.40 superlattice structures is relatively insensitive to atomic-scale Cr 5 F 54 17.8 6.3 58.3 7.53i 53.2 5.44i 2.97 thickness fluctuations. The layered structure is ideal for a Fe 8.12 4.68 Cr 20 AF 14.3 12.1 6.3 58.3 7.53i 53.2 5.44i 2.97 Cr Buffer 197 2.97 a Electronic mail: tevelthuis@anl.gov MgO 110 Substrate 2.8 53.2 5.44i 30.5 0.32i 5.97 0003-6951/99/75(26)/4174/3/$15.00 4174 © 1999 American Institute of Physics Downloaded 21 Mar 2001 to 148.6.169.65. Redistribution subject to AIP copyright, see http://ojps.aip.org/aplo/aplcr.jsp Appl. Phys. Lett., Vol. 75, No. 26, 27 December 1999 te Velthuis et al. 4175 FIG. 1. Partial magnetization curve measured with decreasing field. The arrows indicate the fields for the neutron reflectivity measurements. Inset: The minor hysteresis curve after alignment at 30 kOe. ing the magnetization of both F and AF superlattices in high field: this procedure breaks the symmetry between the two energetically degenerate AF states and is analogous to field cooling below TN for conventional AF­F systems. Given that the magnetic configuration of the AF superlattice is ``fixed'' and only the magnetization of the F superlattice is reversed FIG. 3. Measured and calculated polarized neutron reflectivity in H in the minor hysteresis loop, the magnitude of HE is equal to 166 Oe top and 72 Oe bottom . Neutrons with spin parallel to H are that expected on the basis of exchange between collinear indicated by filled symbols/full line (R ); those antiparallel to H by open superlattices.15 symbol/dashed line (R ). The first step in the depth profiling is to obtain the x-ray reflectivity with Cu K radiation from a rotating anode x-ray m(z), where n is a depth-dependent nuclear scattering am- source. The x-ray reflectivity was measured from below the plitude, and m is the depth-dependent magnetization. R is critical angle to above the first AF Bragg peak. The structural an optical transform of n(z) m(z). By alternatively mea- parameters were obtained via fitting the data to a Parratt suring with neutrons in either spin state, the magnitude and model17 modified to include interface roughness. To reduce direction of the layer-by-layer magnetization can be deter- the number of free parameters, all Fe and Cr layers within mined. each superlattice were assumed to have identical thicknesses. PNR experiments were performed at Argonne's Intense In addition, the rms interfacial roughness was assumed to be Pulsed Neutron Source. Initially, the sample was saturated in equal at each Fe/Cr interface. The x-ray data and fit are 30 kOe. Measurements were taken at two opposite magne- shown in Fig. 2 and the fit parameters are listed in Table I. tization states in the minor loop, at H 166 Oe and H The spin-dependent neutron reflectivity gives informa- 72 Oe, and at room temperature. The results are shown tion about the magnetic and structural profile perpendicular as a function of momentum transfer (qz) in Fig. 3. to the surface. R and R denote reflectivities for neutrons The large difference in reflectivity for the two spin states polarized parallel and antiparallel to H, respectively. The indicates that there is a significant magnetization parallel to analysis of the data is simple if the magnetization of all lay- H. In the low qz region, the reflectivity becomes unitary at ers is collinear with H. R is an optical transform of n(z) the critical value of the MgO substrate. At higher qz there are two Bragg reflections due to the periodic layer structure of the superlattices. The reflection at qz 0.09 Å 1 arises from interference between the Fe layers in the F superlattice. This is clearly a ferromagnetic Bragg reflection because it is ex- tremely spin dependent. The reflection at 0.12 Å 1 arises from the interference between the Fe layers within the AF superlattice, and corresponds to a periodicity twice that of the structural ordering. Since an equal number of Fe layers are magnetized parallel and antiparallel to H, the reflectivi- ties for the two spin states are approximately equal. The reflectivities for the two magnetic states also show some differences. These do not appear at the critical value which would mean that the net magnetization is identical in both states , but at larger values of qz . This shows that some of the Fourier components of the magnetization are indeed different for the two states. However, the problem of FIG. 2. X-ray reflectivity data symbols and fit curve . uniquely determining the two magnetic depth profiles might Downloaded 21 Mar 2001 to 148.6.169.65. Redistribution subject to AIP copyright, see http://ojps.aip.org/aplo/aplcr.jsp 4176 Appl. Phys. Lett., Vol. 75, No. 26, 27 December 1999 te Velthuis et al. but now perpendicular to H and to the F superlattice i.e., flopped . The finite ratio of R /R at 3.6 kOe is ame- nable to different interpretations. Assuming the system is homogeneous, R /R tan2 , where is the angle be- tween the antiparallel components of the AF sublattice mag- netization and H. Such an angle ( 70° from the easy axis is not expected for a uniaxial structure with H along the easy axis. A second interpretation is that the sample is made of lateral domains and at H 3.6 kOe a majority, but not all, have flopped. The third and more interesting cause is that the spin­flop transition is not homogeneous along the thickness of the AF superlattice, but is initiated at one end, for in- stance, at the F/AF interface. FIG. 4. Ratio between the reflectivity measured for neutrons with the inci- In conclusion, polarized neutron reflectivity demon- dent spin antiparallel and reflected spin parallel to the field (R ), and with the incident and reflected spin parallel to the field (R ), in 68 Oe open strates that in a double superlattice, engineered to provide a symbols and 3.6 kOe filled symbols . controllable exchange bias, the magnetic structure matches that inferred by magnetization measurements,15 providing a seem arduous. Rather than attempting to fit the data, we cal- direct link between the microscopic and macroscopic aspects culated the reflectivities from: i the values for the nuclear of the magnetism. The two states at either side of the biased scattering length densities for Fe, Cr, and MgO evaluated for hysteresis curve consist of collinear alignments of the Fe the bulk; ii structural parameters layer thicknesses taken magnetization within both superlattices. The difference be- from the best fit of the x-ray reflectivity data; and iii the tween the two states originates solely in the orientation par- magnetic scattering length density of Fe calculated using the allel or antiparallel of the F with respect to the AF superlat- measured magnetizations 1512 and 1609 emu/cm3 for the F tice. Furthermore, at high fields the AF superlattice becomes and AF superlattices, respectively . Collinear magnetization spin flopped with respect to H and the F superlattice. The was assumed for all layers, where the difference between the double superlattice is an exchange-bias system, unhampered two states is only in the orientation of the magnetization of by interfacial spin frustrations, yet where field alignment in- the F with respect to the AF superlattice. As illustrated in stead of field cooling initiates the bias effect, which exhibits Fig. 3, not only is there good agreement between experiment good agreement with theory based on coherent, collinear and calculation, but the features that distinguish the reflec- models. tivities of the two magnetization states are reproduced in the This work has been supported by U.S. DOE, BES­MS calculations. Contract No. W-31-109-ENG-38. In the case of noncollinear magnetizations, PNR can be discussed in a simple way only within the kinematic approxi- 1 W. H. Meiklejohn and C. P. Bean, Phys. Rev. 105, 904 1957 . mation. The intensity of the AF Bragg reflection is propor- 2 C. Tang, J. Appl. Phys. 55, 2226 1984 3 tional to R 2 2 2 2 J. S. Kouvel, J. Phys. Chem. Solids 16, 132 1960 AF RAF RAF (nAFmAF, n m ) and AF AF, 4 A. E. Berkowitz and J. H. Greiner, J. Appl. Phys. 36, 3330 1965 . R 5 AF RAF RAF RAF . nAF is the number of AF layers. R. Jungblut, R. Coehoorn, M. T. Johnson, C. Sauer, P. J. van der Zaag, A. m R. Ball, T. G. S. M. Rijks, J. aan de Stegge, and A. Reinders, J. Magn. AF is the AF scattering amplitude per layer that originates from the antiparallel components of the sublattice magneti- Magn. Mater. 148, 300 1995 . 6 T. J. Moran, J. M. Gallego, and I. K. Schuller, J. Appl. Phys. 78, 1887 zation and mAF, and mAF, are, respectively, its components 1995 . parallel and perpendicular to H. Experimentally, they can be 7 J. Nogue´s, D. Lederman, T. J. Moran, I. K. Schuller, and K. V. Rao, Appl. separated by analyzing the polarization of the reflected neu- Phys. Lett. 68, 3186 1996 . 8 trons: R R n2 2 N. J. Go¨kemeijer, T. Ambrose, and C. L. Chien, Phys. Rev. Lett. 79, 4270 AFmAF, while R R 1997 . n2 2 AFmAF, . In Fig. 4 the ratio R /R is shown for H 9 J. Nogue´s and I. K. Schuller, J. Magn. Magn. Mater. 192, 203 1999 . 68 Oe and 3.6 kOe. At H 68 Oe, R /R 0 at 10 P. J. van der Zaag, A. R. Ball, L. F. Feiner, R. W. Wolf, and P. A. A. van the AF Bragg reflection, indicating a collinear alignment der Heijden, J. Appl. Phys. 79, 5103 1996 . 11 along H. Similarly, no spin­flip reflectivity was observed for W. H. Meiklejohn, J. Appl. Phys. 33, 1328 1962 . 12 D. Mauri, H. C. Siegmann, P. S. Bagus, and E. Kay, J. Appl. Phys. 62, a field of 2 kOe. Therefore, there is no evidence of a do- 3047 1987 . main wall in the AF as is predicted by the Mauri12 and 13 A. P. Malozemoff, Phys. Rev. B 35, 3679 1987 . Malozemoff13 models. For this system, which is insensitive 14 N. C. Koon, Phys. Rev. Lett. 78, 4865 1997 ; T. C. Schulthess and W. H. to interfacial spin frustration, there is a good agreement with Bulter, ibid. 81, 4516 1998 ; M. D. Stiles and R. D. McMichael, Phys. Rev. B 59, 3722 1999 . the classical Meiklejohn­Bean model.11 Similar results 15 J. S. Jiang, G. P. Felcher, A. Inomata, R. Goyette, C. Nelson, and S. D. might be obtained for a conventional F­AF pair without in- Bader unpublished . terface roughness. 16 E. E. Fullerton, M. J. Conover, J. E. Mattson, C. H. Sowers, and S. D. At high fields, 3.6 kOe, R /R 9.7, indicating Bader, Phys. Rev. B 48, 15755 1993 ; J. Appl. Phys. 75, 6461 1994 . 17 L. G. Parratt, Phys. Rev. 95, 359 1954 ; L. Nevot and P. Croce, Rev. that the Fe layers in the AF superlattice are still AF ordered, Phys. Appl. 15, 761 1980 . Downloaded 21 Mar 2001 to 148.6.169.65. Redistribution subject to AIP copyright, see http://ojps.aip.org/aplo/aplcr.jsp