PHYSICAL REVIEW B VOLUME 53, NUMBER 5 1 FEBRUARY 1996-I Polarized-neutron-reflectivity confirmation of 90° magnetic structure in Fe/Cr 001... superlattices S. Adenwalla, G. P. Felcher, Eric E. Fullerton, and S. D. Bader Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 Received 8 June 1995 Polarized-neutron reflectivity together with magnetization and magnetotransport measurements on a 001 - oriented Fe 14 Ć /Cr 74 Ć 20 superlattice confirms the existence of 90° alignment of adjacent Fe layers due to biquadratic interlayer coupling. Each Fe layer is in a single domain state and the magnetic structure is coherent throughout the layered stack. The biquadratic coupling, however, is suppressed below the Cr NeŽel temperature TN 187 K as the Fe layers uncouple. But by field cooling through TN it is possible to retain a metastable biquadratic arrangement. I. INTRODUCTION tion and magnetotransport to study the biquadratic coupling of an Fe 14 Ć /Cr 74 Ć 20 superlattice near TN of the Cr Ferromagnetic films separated by nonferromagnetic spac- spacer. The neutron results confirm both the 90° alignment of ers can exhibit an oscillatory exchange coupling between the the Fe layers for T TN , and that the sample is in a single- ferromagnetic layers as a function of spacer thickness.1,2 Two domain state over an area of order of a cm2. For T TN , the oscillatory periods have been observed in Fe/Cr samples:3,4 a biquadratic coupling is suppressed and the magnetic configu- ``long'' 18-Ć period which is independent of crystallographic ration of the Fe layers depends sensitively on the applied orientation of the spacer, and a ``short'' 2.1-monolayers ML field in which the sample is cooled through TN . period along the 100 which results from the nested feature The 001 -oriented Fe 14 Ć /Cr 74 Ć 20 was epitaxially of the Cr Fermi surface and which is responsible for the grown by dc magnetron sputtering onto a 2.5 2.5 cm2 spin-density-wave antiferromagnetism of Cr. The interlayer MgO 001 single-crystal substrate. A 100-Ć Cr 001 base coupling energy is of the form J layer was deposited at 600 °C onto the MgO prior to the 1m1*m2 , where J1 is the bilinear coupling constant and m superlattice growth, which occurred at 75 °C. The epitaxial 1 and m2 are the magnetiza- tions of two adjacent ferromagnetic layers. The coupling en- relationship is Fe/Cr 100 MgO 100 . At this thickness of ergy is minimized when m Cr the bilinear coupling constant is small5 and, as will be 1 and m2 are parallel or antiparal- lel to each other depending on whether J shown, the biquadratic coupling is dominant. Transport and 1 is positive or negative, respectively. It was discovered in Fe/Cr/Fe 001 magnetization measurements were made on a 3 10 mm2 trilayers that 90° alignment of the Fe layers occurs in narrow section cleaved from the substrate. Measurements were made transition regions, where J with the applied field H along either the Fe 100 easy axis or 1 is small, located between the dominant antiferromagnetic AFM and ferromagnetic FM the 110 hard axis. The magnetization measurements uti- coupled regions.6 An additional phenomenological term lized a superconducting quantum interference device J SQUID magnetometer at temperatures between 10 and 350 2 m1*m2 2 can be included to describe the 90° coupling, where J K. Transport was measured using a standard, four-terminal 2 is referred to as the biquadratic coupling constant. For J dc technique with a constant current source. The neutron 2 0 the energy is minimized for m1 perpendicular to m measurements were performed at the POSY1 beamline at 2 . Biquadratic coupling has since been observed in a num- ber of trilayer e.g., Fe/Cr/Fe,3,6 Fe/Al/Fe,7 Fe/Cu/Fe,8 Argonne's Intense Pulsed Neutron Source. Fe/Ag/Fe,8,9 and Fe/Au/Fe Ref. 10 and superlattice e.g., FeNi/Ag Ref. 11 and Fe/Cr Ref. 12 structures. Also, the II. RESULTS temperature dependence8­11 of J2, in general, has been shown experimentally to be stronger than that of J A. Measurement of TN 1 . The origin of the biquadratic coupling has been attributed Transport measurements are often used to identify the either to intrinsic properties of the spacer layer13 or to extrin- NeŽel transition in Cr and Cr alloys.18,19 The resistivity is sic factors such as i dipolar fields resulting from rough enhanced above its extrapolated value as T decreases interfaces,14 ii superparamagnetic impurities within the through TN . This increase in is the result of energy gaps spacer ``loose spins'' ,15 or iii fluctuations in the spacer opening on the nested parts of the Fermi surface and is high- thickness which average out the short-period oscillations.15,16 est when the current is parallel to the nesting vector Q.18 Recent experiments on Fe/Cr 001 superlattices identified Shown in Fig. 1 is vs T measured at 1 kOe. In this field, the the NeŽel transition for Cr spacers 42 Ć thick.17 It was also Fe layers are aligned parallel to H and there are no additional reported that the magnetic properties of superlattices with magnetoresistance MR contributions to due to misalign- such relatively thick Cr spacers are dramatically altered at ment of the Fe layers. An anomaly in appears in Fig. 1 as the NeŽel temperature (TN). For T TN , the magnetic prop- an increase above its expected linear behavior shown by the erties are consistent with 90° coupling of adjacent Fe layers, dashed-line extrapolation. The 10% enhancement of at while for T TN the layers uncouple. In the present paper we TN is consistent with values reported for bulk Cr and Cr use polarized-neutron reflection combined with magnetiza- films. The resistive transition is, however, considerably 0163-1829/96/53 5 /2474 7 /$06.00 53 2474 © 1996 The American Physical Society 53 POLARIZED-NEUTRON-REFLECTIVITY CONFIRMATION OF . . . 2475 FIG. 1. Resistance measurements on the Fe 14 Ć /Cr 74 Ć 20 superlattice showing the NeŽel transition of the Cr. T FIG. 3. Magnetoresistance with H applied along easy and hard N is defined as the point of inflection of the d /dT curve. axes. broader than that of single-crystal Cr in which a singularity saturation value Ms . As H decreases, the hard-axis magne- in is observed at T tization gradually decreases to its remanent value N . For such broad transitions, TN is often defined as the point of inflection in the -vs-T curve Mr 0.7MS for all temperatures. This behavior is consistent which can be identified as a minimum in d /dT. Using this with coherent rotation of the Fe layers toward the easy axis criterion, T and as expected M N for the present sample is 187 5 K. r 1/& M s . For T TN , the easy-axis magnetization decreases sharply at low fields to M B. Magnetization and magnetoresistance r 0.54M s . This suggests biquadratic coupling of the Fe layers in which alternate layers are sequentially magnetized Magnetization and magnetotransport measurements are parallel or perpendicular to the field. The slightly higher Mr shown in Figs. 2 and 3, respectively, with H in-plane along value from the expected 0.5Ms is due to the coercivity of the both the Fe 100 easy and 110 hard axes. The figures show Fe layers. The 90° alignment of the Fe layers at low fields the first-quadrant hysteresis loops in decreasing field. At high gives the expected enhanced MR as seen in Fig. 3. The shape fields, the magnetic moments are aligned with the field at the of both the magnetization and magnetoresistance are consis- tent with a combination of biquadratic coupling and cubic anisotropy. Below TN , there is a dramatic change in the mag- netization loops, as reported previously.17 Mr increases along the easy axis, and the saturation field along the hard axis decreases, which both suggest that the biquadratic coupling is suppressed. The temperature dependence of the saturation MR value denoted / and the saturation field Hs are shown in Fig. 4. Hs is defined as the field at which the sharp drop in the easy-axis magnetization see arrows in Fig. 2 and rise in the MR occur. Both / and Hs are strongly temperature de- pendent and show anomalies at the measured value of TN consistent with previous measurements. Hs exhibits a maxi- mum at 205 K and goes to zero just below TN . The MR exhibits an anomaly at TN consistent with the suppression of the biquadratic coupling. C. Neutron reflectivity measurements The neutron reflectivity was measured at 300, 205, 160, and 20 K. We focus primarily on the 205- and 160-K results because they straddle TN . At 205 K, the biquadratic coupling is strongest as evidenced from the magnetization measure- ments and measurements taken at two applied fields, 6 and 40 Oe, both show evidence of a 90° coupling; in addition we see the effect of the Zeeman energy term as the moments cant towards the applied field. The arrangement of POSY1 permits the reflectivity to be measured with and without po- FIG. 2. Upper quadrant of the magnetization along the easy larization analysis. A polarized beam of neutrons passes 100 orientation and hard 110 orientations. Arrows indicate easy- through a flipper which is turned on at every alternate pulse. axis saturation fields Hs . This allows us to measure the reflectivity of the sample for 2476 ADENWALLA, FELCHER, FULLERTON, AND BADER 53 FIG. 4. a Saturation magnetoresistance / and b saturation field Hs measured as a function of temperature. initial polarizations of the beam either parallel or antiparallel to H as given by R and R , respectively. An analyzer placed in the path of the reflected neutron beam reflects neu- trons of only one polarization . Using this analyzer we can measure the non-spin-flip NSF reflectivity R and the spin-flip SF reflectivity R . The relation between these quantities is given by R R R , R R R , FIG. 5. Neutron reflectivity measured with R and R and without R and R polarization analysis along the easy 100 axis and at H 40 Oe and T 205 K. The lines are the fit to the data for the spin structure shown in the inset. R R . The NSF reflectivities R and R depend upon both the Fig. 5 consists of two Bragg peaks and higher-frequency nuclear scattering potential bN and the component of the Kiessig oscillations resulting from the finite size of the su- magnetization parallel or antiparallel to the neutron spin. perlattice. The peak at high k, the ferromagnetic FM peak, Hence, the NSF reflectivity is nonzero even in the absence of corresponds to the superlattice periodicity and results from magnetization, and the difference between R and R is a both the nuclear scattering from the layers and components measure of the component of the sample magnetization par- of the Fe-layer magnetization ferromagnetically aligned with allel to H. In contrast the SF contribution arises solely from H. The peak at low k, the antiferromagnetic AFM peak, the perpendicular component of the magnetization and is results from the noncollinear alignment of the Fe layers and zero if this component is not present. Neutron reflectivity corresponds to a doubling of the magnetic unit cell. Both with polarization analysis is hence an ideal probe for study- peaks are present for all four reflectivity curves: R , R , ing the magnetization profile of a multilayer system. R , and R . Shown in Fig. 5 are reflectivity results measured at 205 K There are a number of striking features in the data. The with H 40 Oe along the easy axis. The measurements were presence of an AFM peak in the SF reflectivity indicates that taken over a range of momenta k 2 sin / where is the there is a perpendicular component of magnetization with a angle of incidence of the neutrons on the surface, and is the repeat distance of twice the superlattice spacing; this is a neutron wavelength from the region of total external reflec- signature of the presence of interlayer coupling. The width of tion through the first superlattice Bragg reflection at k 0.037 the AFM peak indicates that the magnetic structure is coher- Ć 1. To check on the magnetic-history dependence of the ent throughout the thickness of the superlattice. The R and sample, data were taken while cooling the sample from room R AFM peaks are shifted with respect to each other, the R temperature in either the full field 3.5 kOe or in low field 6 peak being shifted to lower k as can be seen more clearly in Oe . The results for T TN were identical. The spectrum in Fig. 6 . We fitted the reflectivity data in the conventional 53 POLARIZED-NEUTRON-REFLECTIVITY CONFIRMATION OF . . . 2477 TABLE I. Normalized intensities of the ferromagnetic and anti- ferromagnetic peaks for the various reflectivities shown in Fig. 5. I I I I AFM 1.213 1.103 0.408 0.802 FM 7.45 0.915 6.87 0.582 An alternative method for a generalized fitting of the re- flectivity data is to analyze the peak intensity within the framework of the conventional kinematic theory, as is often done in large-angle diffraction. Any two-sublattice magnetic structure can be resolved into FM and AFM components: the FM component being along the magnetization axis and the AFM component lying perpendicular to it. A similar method was used to fit the FM peak in the experiments on NiFe/Ag multilayers by Rodmacq et al.11 For example, a bi- quadratic structure with spins exactly at 0° and 90° could be resolved into an FM component repeated every lattice spac- ing at 45° and an AFM component which alternates its direction at sequential layers, i.e., having a double repeat distance at 135° to H. In this case, both components have the same magnitude. In general, the intensities of the AFM and FM peaks for the SF and NSF reflectivities are propor- tional to I 2 2 FM n fp 2 f s , IFM n fp 2 f s, 1a I 2 FM n fp 2, IFM f s, 1b I 2 2 2 2 AFM ap as , IAFM ap as, 2a FIG. 6. Neutron reflectivity measured without polarization analysis along the easy 100 axis at H 6 Oe and T 205 K. The lines are the fit to the data for the spin structure shown in the inset. I 2 2 AFM ap, IAFM as, 2b a low-k data showing clearly the splitting of the AFM peak; b high-k data. where n is the nuclear scattering amplitude (bN)Fe manner by assigning a refractive index to each layer, match- (bN)Cr , f and a denote the FM and AFM components, ing boundary conditions and then calculating the total reflec- respectively, and the subscripts s and p refer to magnetiza- tivity. The only parameters in the fit were the direction of tion parallel and perpendicular to the neutron spin and H , magnetization in each layer; the thickness was known from respectively. The values for these intensities obtained from earlier x-ray measurements and the scattering-length density the data in Fig. 5 at 205 K and 40 Oe are given in Table I. was assumed to be that of the bulk. We assume a two- The values are in units of 10 8 Ć2/atom obtained after renor- sublattice model in which the angle of magnetization of each malizing the experimental intensities. sublattice with respect to H is a fitting parameter. The magnitude of the AFM and FM components, and the The solid lines in Fig. 5 represent fits to the data, and the angle they make with the magnetic field are calculated with resultant magnetic structures are shown in the inset. Note the aid of Eqs. 1 and 2 and presented in Table II. By that all magnetizations are in-plane: parallel and perpen- inserting the correct values for n in Eqs. 1 a and 1 b here dicular refer to in-plane directions with respect to H . The tilt n 5 10 6 Ć 1, from the bulk values for Fe and Cr we away from the 90° arrangement is due to the Zeeman energy, obtain the magnitude of the FM component. Fitting the AFM which makes it energetically favorable for the magnetization to cant towards the field direction. Measurements at lower fields show a substantial decrease in the tilt see Fig. 6 . The TABLE II. Amplitude and orientation of the ferromagnetic and separation of the AFM peak is successfully modeled assum- antiferromagnetic component with reference to the applied field 40 ing a single-domain sample; this results in the the reflectivity Oe . being slightly weighted in favor of the front face of the sample due to attenuation of the neutron beam as it traverses Angle the sample. This weighting effect would be obscured in a Magnitude B with respect to field multidomain sample. In the case shown, the shift of the AFM 0.85 55° AFM peak indicates that the top Fe layer is magnetized per- FM 1.72 35° pendicular to H. 2478 ADENWALLA, FELCHER, FULLERTON, AND BADER 53 TABLE III. Amplitude and orientation of the sublattice magne- tization in reference to the applied field 40 Oe . peak yields the magnitude of the AFM component. The ratio between I and I gives the orientation of the compo- nents. Notice that the AFM and FM components are at 90° to each other, satisfying the condition necessary for the validity of any model consisting of two sublattices with magnetiza- tion of the same size but oriented in different directions. If that model is accepted, the sublattice magnetizations have the values calculated in Table III. With these results one can reconstruct the spin structure of the sample, which yields one similar within 10° to that obtained from direct fitting of the reflectivity data. The discrepancy between the two meth- ods is due to the fact that the two-sublattice method has error FIG. 7. Neutron reflectivity measured without polarization bars of up to 5° in the absolute orientation of the moments analysis along the easy 100 axis at T 160 K. a Field cooled in although the error bar for the relative orientation is very 6 Oe showing the presence of the AFM peak and b data taken small . after saturating the sample in a field of 3.5 kOe in which the AFM Hard-axis measurements with polarization analysis at peak is absent. the same temperature 205 K and field 40 Oe show that the AFM peak arises solely from spin-flip scattering, as would be expected for a configuration in which the moments of Decreasing the field to 6 Oe decreases the tilt from about sequential layers are alternatively aligned symmetrically about H. There is no splitting between the R and R AFM 30° to between 10° and 20°, as would be expected, but the peaks, since R R . Fitting the reflectivity and polar- basic structure remains the same. The fit to the data and the ization data we find that the maoments are aligned at 45° spin structure are shown in Figs. 6 a and 6 b . Table IV and 45° to the field. gives the magnitudes and orientations of the two sublattice magnetizations and the spin structure obtained from the analysis of the peak intensities. TABLE IV. Amplitude and orientation of the sublattice magne- The orthogonality of the AFM and FM components is a tizations with reference to the applied field 6 Oe . condition necessary for the validity of a two-sublattice model, but is by no means sufficient. The same diffracted intensities could, in principle,21 be obtained from a sample made of FM and AFM domains as in the two-axis structure proposed here. However, this holds only in the limit of the kinematic approximation. Close to the critical edge the de- viation of the neutron momentum in the material compared to the vacuum value provides additional information. Figure 6 shows the low-momentum reflectivities R R R and R R R . The low-k oscillations are due to the interference of neutron waves reflected from the surface and the substrate; these ``total thickness oscillations'' occur in the region of momenta where all details of the superlattice are averaged out. For the two neutron spin states and the reflectivity minima occur at different k values. If the system is homogeneous20 53 POLARIZED-NEUTRON-REFLECTIVITY CONFIRMATION OF . . . 2479 k 2 k2 crystallographic easy axis. When cooled below T 0 4 bN cB , N in a field below the coercive field Hc 15 Oe of the Fe layers, the Fe k 2 k2 layers remain in this metastable configuration. Applying a 0 4 bN cB , modest field (H H and k 2B/k, where B is in proper units the magnetic c) aligns the layers and the system can- not get back to the 90° configuration without warming above induction of the bulk sample. From Fig. 6 it can be seen that T the overall magnetization of the sample is well fitted as being N . biquadratically coupled. If, instead, the system was com- III. CONCLUSIONS posed of AFM and FM domains, the displacement k would have been larger due to the larger net magnetization of the We have studied the magnetic properties of an sample. But, then there would have been damped oscillations FE 14 Ć /Cr 74 Ć 20 superlattice above and below the NeŽel due to the fact that the AFM coupled portions of the sample transition of the Cr layers. Resistivity measurements yield would have zero net magnetization and, hence, would not TN 187 K for this sample. For T TN , the Fe layers align contribute to the shifted oscillations . alternately at nearly 0° and 90° with respect to an applied magnetic field, consistent with the presence of biquadratic D. Temperature dependence of the coupling coupling. The spins are tilted slightly away from the parallel and perpendicular positions due to the applied magnetic The behavior of the system as temperature is lowered be- field. The 90° configuration is stable over a large sample low 205 K depends strongly on the magnetic-field history. area, and forms a coherent structure throughout the superlat- Data at 160 K were collected in three different ways. Initially tice. Both neutron reflectivity and magnetization measure- the sample was cooled in a magnetic field of 40 Oe from 205 ments are consistent with this picture. Proof of biquadratic K. This produced a structure in which the AFM peak is ex- coupling, as opposed to a combination of FM- and AFM- tremely small, indicating that the sample is almost com- coupled domains, comes from the splitting of the AFM peak pletely FM aligned. If, however, the sample is cooled below and the shift in the low-k oscillations in the neutron reflec- 205 K in a low field 6 Oe , the AFM peak is still present, tivity. A simple analysis of the AFM and FM Bragg peaks albeit at a slightly lower intensity Fig. 7 a . The peak width shows that the results are well represented by a two spin is the same, and the splitting of the R and R AFM peaks system in which the AFM and FM components are at 90° to indicates that the sample is still in a single-domain state. The each other, thereby eliminating the possibility of inhomoge- slightly diminished intensity of these peaks is due to the neities within the sample stacking arrangement. For tempera- decrease in the spin-flip reflectivity, which can be attributed tures just below T to a tilt of the perpendicular spins toward H. A third mea- N the Fe layers become uncoupled, but by cooling the sample through T surement was made after saturating the sample from 6 Oe to N in a small field, a metastable biquadratic arrangement can be stabilized. This work high- a field of 3.5 kOe at 160 K and then reducing the field back lights the subtle interplay between the interlayer coupling of to 6 Oe, which is comparable to the conditions under which the Fe and the AF ordering of thick Cr spacers. the magnetization measurements were made. In agreement with the square hysteresis loop, this showed a complete ab- ACKNOWLEDGMENT sence of the AFM peak Fig. 7 a . The FM peak did not change in peak width, intensity, or polarization. This result This work was supported by the U.S. Department of En- suggests that at 160 K, the layers are truly uncoupled. When ergy, Basic Energy Sciences­Materials Sciences, under Con- the spins are in a 90° alignment, each Fe layer is along a tract No. W-31-109-ENG-38. 1 P. Grušnberg, R. Schreiber, Y. Pang, M. B. Brodsky, and C. H. 9 J. Ungaris, R. J. Celotta, and D. T. Pierce, J. Magn. Magn. Mater. Sowers, Phys. Rev. Lett. 57, 2442 1986 . 127, 205 1993 . 2 S. S. P. Parkin, N. More, and K. P. Roche, Phy. Rev. Lett. 64, 10 U. Rucker, S. Demokritov, E. Tsymbal, P. Grušnberg, and W. Zinn, 2304 1990 . J. Appl. Phys. 78, 387 1995 . 3 J. Ungaris, R. J. Celotta, and D. T. Pierce, Phys. Rev. Lett. 67, 11 B. Rodmacq, K. Dumesnil, P. Mangin, and M. Hennion, Phys. 140 1991 . Rev. B 48, 3556 1993 . 4 S. T. Purcell, W. Folkerts, M. T. Johnson, N. W. E. McGee, K. 12 A. Schreyer, J. F. Ankner, H. Zabel, M. Schafer, C. F. Majkrzak, Jager, J. ann de Stegge, W. B. Zeper, W. Hoving, and P. Grušn- and P. Grušnberg, Physica B 198, 173 1994 . berg, Phys. Rev. Lett. 67, 903 1991 . 13 For a general discussion, see K. B. Hathaway, in Ultrathin Mag- 5 Eric E. Fullerton, M. J. Conover, J. E. Mattson, C. H. Sowers, and netic Structures II, edited by B. Heinrich and J. A. C. Bland S. D. Bader, Phys. Rev. B 48, 15 755 1993 . 6 Springer-Verlag, Berlin, 1994 , pp. 45­81. M. Ruhrig, R. Schaefer, A. Hubert, R. Mosler, J. A. Wolf, S. 14 S. Demokritov, E. Tsymbal, P. Gruneberg, W. Zinn, and I. K. Demokritov, and P. Grušnberg, Phys. Status Solidi A 125, 635 1991 . Schuller, Phys. Rev. B 49, 720 1994 . 15 7 C. J. Gutierrez, J. J. Krebs, M. E. Filipkowski, and G. A. Prinz, J. J. C. Slonczewski, J. Appl. Phys. 73, 5957 1993 . 16 Magn. Magn. Mater. 116, L305 1992 . J. C. Slonczewski, Phys. Rev. Lett. 67, 3172 1991 . 8 17 Z. Celinski, B. Heinrich, and J. F. Cochran, J. Magn. Magn. E. E. Fullerton, K. T. Riggs, C. H. Sowers, S. D. Bader, and A. Mater. 145, L1 1995 . Berger, Phys. Rev. Lett. 75, 330 1995 . 2480 ADENWALLA, FELCHER, FULLERTON, AND BADER 53 18 E. Fawcett, Rev. Mod. Phys. 60, 209 1988 . Kleb, and G. Ostrowski, Rev. Sci. Instrum. 58, 609 1987 . 19 E. Fawcett, H. L. Alberts, V. Yu. Galkin, D. R. Noakes, and J. V. 21 A. Schreyer, K. Brošhl, J. F. Ankner, C. F. Majkrzak, Th. Zeidler, Yakmi, Rev. Mod. Phys. 66, 25 1994 . P. Bošdeker, N. Metoki, and H. Zabel, Phys. Rev. B 47, 15 334 20 G. P. Felcher, R. O. Hilleke, R. K. Crawford, J. Haumann, R. 1993 .