PHYSICAL REVIEW B VOLUME 56, NUMBER 9 1 SEPTEMBER 1997-I Interplay between biquadratic coupling and the Ne´el transition in Fe/Cr94Fe6 001... superlattices Eric E. Fullerton,* C. H. Sowers, and S. D. Bader Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 Received 14 April 1997 The commensurate antiferromagnetic order of Cr94Fe6 alloy layers in epitaxial Fe/Cr94Fe6 001 superlattices was investigated by transport and magnetization techniques. Ne´el temperature TN values are strongly thickness dependent, with TN suppressed for Cr94Fe6 thicknesses 36 Å. Transport results indicate a broadening of the transition with an onset temperature T0 TN by 150 K for all samples. The biquadratic interlayer coupling of the Fe layers is enhanced for TN T T0 and suppressed below TN . T0 and TN are identified with the onset on cooling of inhomogeneous and homogeneous order, respectively, within the spacer layers. The regime of inhomogeneous ordering of the spacer is believed to promote biquadratic coupling because of the dominance of interfacial exchange energies. S0163-1829 97 08634-7 I. INTRODUCTION perature dependence of the magnetic susceptibility exhibits a Curie-Weiss behavior both above and below TN , with a The interplay between interlayer magnetic coupling and Curie-Weiss temperature of 10­30 K and a local Fe mo- antiferromagnetic AF ordering of Cr spacer layers in Fe/Cr ment of 3 B for Fe concentrations near 6 at. %. The re- superlattices provides interesting insights into the physics of sidual resistance increases linearly with Fe at a rate of 7 coupled magnetic superlattices. Bulk Cr is an itinerant AF cm per at. % Fe. In addition, the resistance anomaly be- that forms an incommensurate spin-density wave SDW be- low TN in Cr-Fe alloys is enhanced over that observed for Cr low its Ne´el temperature of TN 311 K.1 Previous results on and other Cr alloys. We exploit the resistance anomaly as a Fe/Cr 001 superlattices2­4 indicate that the AF incommen- probe of the AF ordering process in order to monitor the surate SDW ordering persists for Cr thicknesses tCr 45 Å. influence of ordering on the interlayer coupling. This raises interesting questions on the role of spin frustra- The interlayer coupling in Fe/Cr/Fe 001 structures is tion at rough ferromagnetic F -AF interfaces. The biqua- characterized by the phenomenological energy expression dratic 90° interlayer coupling observed in Fe/Cr superlat- E J1(m1*m2) J2(m1*m2)2 where J1 and J2 are the bilin- tices is directly related to the SDW order of the Cr spacer ear and biquadratic exchange-coupling terms and m1 , m2 layer. Biquadratic coupling exists for thin Cr layers 45 Å , are the magnetization of two adjacent Fe layers.9,10 J1 oscil- and is strongly temperature dependent increasing monotoni- lates in sign with increasing Cr thickness resulting in either F cally with decreasing temperature. However, for thick Cr or AF alignment of adjacent magnetic layers. In Fe/Cr/ layers, biquadratic coupling is only observed for T TN ; it Fe 001 structures, two oscillatory periods have been ob- vanishes for T TN upon formation of the SDW.2,3,5 served: a short, 2.1-monolayer ML period in samples with In the present work we further explore the role of the Cr atomically smooth Cr interfaces,11 and a long, 18-Å period ordering by doping the Cr spacer layer with 6 at. % Fe to which is independent of crystallographic orienta- alter the magnetic ordering with the Cr layers as well as the tion.12 These periods are governed by spanning vectors that coupling between the Fe layers. We find a temperature win- join extremal points of the Fermi surface normal to the lay- dow of 150 K above TN for which biquadratic coupling is ering direction.13 The short-period oscillation is universally enhanced that we attributed to inhomogeneous ordering of accepted to result from the nested feature in the 100 direc- the spacer. By inhomogeneous ordering, we mean that the tion of the Cr Fermi surface which also is responsible for the AF layer is dominated by the interfacial exchange energies SDW AF of Cr. The isotropic long period, while still a topic resulting in lateral AF domain sizes being limited by the of active debate, is understood to originate from a short interfacial terrace widths. Homogeneous ordering refers to spanning-vector associated with either the ``lens'' or the AF domains that are large compared to the lateral length N-centered ellipse feature of the Fermi surface.14­17 scales of the interfacial roughness. The biquadratic coupling term is found to be nonoscilla- Bulk Cr-Fe alloys have been studied extensively.6 Fe im- tory and favors 90° alignment of adjacent Fe layers. The purities reduce TN up to 16 at. % where AF order is sup- origin of the biquadratic coupling is less well understood pressed and a spin glass is formed. The incommensurate than the bilinear coupling. Slonczewski10 proposed two SDW (AF1) phase persists up to concentrations of 2.5 mechanisms: fluctuations in the spacer thickness which av- at. % Fe and then is replaced by commensurate AF0 order. erages over a short-period oscillation, and superparamagnetic Therefore, in the present study we investigate coupling with- impurities ``loose spins'' within the spacer. The first out the additional complication of SDW order. The Ne´el mechanism was developed for Fe/Cr 001 because of the transition in Cr-Fe alloys is first order with a measured latent prominent short-period coupling observed in this system.18 heat of 5 J/mole for 6 at. % Fe.7 Both neutron scattering and The mechanism assumes that the Cr layer can be described susceptibility results indicate that the Cr AF state coexists by terraces separated by monoatomic steps. The coupling with magnetic moments localized at the Fe sites.6,8 The tem- across each terrace region will be F or AF and will alternate 0163-1829/97/56 9 /5468 6 /$10.00 56 5468 © 1997 The American Physical Society 56 INTERPLAY BETWEEN BIQUADRATIC COUPLING AND . . . 5469 from one neighboring terrace to the next. If the terrace widths are small compared to an Fe domain, the energy of the system is lowered by perpendicular alignment of the en- tire Fe layer magnetization with respect to that of the adja- cent Fe layer. Shender and Holdsworth19 have generalized this problem to remove the restrictions on the form of the terraces and find that the biquadratic coupling depends on the effective dimension of the disorder. The fluctuation model was modified to include the intrin- sic AF ordering of Cr or Mn spacers, and is referred to as a proximity magnetism model. The form of the energy expres- sion describing the 90° coupling is given by J E 2 2 2 2 , 1 FIG. 1. X-ray diffraction results for an Fe 15 Å /Cr where is the relative angle between adjacent magnetic 94Fe6 (46 Å)] layers. This coupling arises from inhomogeneous ordering of 40 superlattice grown on MgO 100 . The inset shows the rocking curve scan of the main superlattice reflection 2 64.87° . the AF interlayers in which a spiral structure is formed within a terrace which rotates with opposite sense of rotation diffraction results for an in neighboring terraces. This model was successfully used to Fe(15 Å)/Cr94Fe6(46 Å) 40 su- perlattice. The x-ray scan confirms the 001 growth with a explain the magnetism of the CoFe/Mn superlattices.20 The 0.7° mosaic spread, as indicated by the full width at half applicability of this model to the Fe/Cr system is not estab- maximum of the rocking curve scan of the 002 reflection lished and will depend on the magnetic ordering of the Cr in shown in the inset of Fig. 1 . Also, superlattices peaks are the presence of a stepped or rough interface. observed about the 002 reflection indicating a well-defined Experiments on epitaxially sputtered Fe/Cr 001 superlat- superlattice structure. Magnetic properties were measured by tices found the incommensurate Ne´el transition of the Cr superconducting quantum interference device magnetometry spacers observed in transport methods vanishes for Cr thick- equipped with both longitudinal and transverse coils. nesses tCr 45 Å.2 For tCr 45 Å for Cr, TN increases rapidly Mangeto-transport was measured by means of a standard and asymptotically approaches the bulk value for thick Cr four-probe technique in a Quantum Design Physical Proper- spacers. For tCr 51 Å, neutron scattering finds a transverse ties Measurement System in fields up to 9 T. SDW (AF1) is formed with a single Q normal to the layers and the nodes of the SDW near the Fe-Cr interfaces.3 For the t III. NE´EL TRANSITION Cr 31 Å and 44 Å, the magnetic scattering is described by AF0 ordering without clear evidence of an incommensurate Shown in Fig. 2 are transport results for a 2000-Å thick Ne´el transition in magnetization or transport studies. The crossover from commensurate to AF1 SDW order with in- creasing Cr thickness was first observed by Ungurus, Ce- lotta, and Pierce11,21 for Cr films on an Fe whisker by means of magnetic imaging experiments. This crossover has also recently been observed by Schreyer et al.4 by means of neu- tron scattering from Fe/Cr 001 superlattices grown by mo- lecular beam epitaxy. This behavior is understood theoreti- cally as arising from a critical thickness needed to support SDW order.22 II. EXPERIMENTAL PROCEDURE The 001 -oriented Cr94Fe6 films and Fe/Cr94Fe6 superlat- tices were grown by dc magnetron sputtering onto epitaxially polished single-crystal MgO 100 substrates. The Cr94Fe6 layers are deposited by co-sputtering from elemental sources using the relative deposition rates of the sources to adjust the composition. A 100 Å-Cr buffer layer was initially deposited at a substrate temperature TS of 600 °C to establish the epi- taxial orientation with the substrate.12 The substrate was then cooled to 150­500 °C to grow the Cr94Fe6 films and 150 °C to grow superlattices with 15-Å Fe layers and Cr-Fe layers varying from 8­440 Å. Thin Fe layers were chosen to mini- FIG. 2. Transport results for a 2000-Å thick Cr94Fe6 alloy film mize the current carried by the Fe layers in the transport grown at TS 500 °C. a vs T. The arrow indicates TN deter- measurements. The structures were characterized by x-ray mined from the minimum of d /dT vs T. b Magnetoresistance diffraction using Cu-K radiation. Shown in Fig. 1 are x-ray measured at 2 and 25 K. 5470 ERIC E. FULLERTON, C. H. SOWERS, AND S. D. BADER 56 FIG. 4. d /dT vs T for the 36-, 46-, and 56-Å samples of Fig. 3. The arrows indicate TN and the onset temperature T0 where the FIG. 3. Resistivity results for a series of Fe 15 Å / resistivity deviates from a linear T dependence. The curves are Cr94Fe6(tCr-Fe)]40 superlattices. The tCr-Fe values are shown. The offset for clarity and the horizontal lines indicate d /dT 0 for resistivity scale is for the 225-Å sample. The scale is offset 10, 15, each sample. 30, 45, and 50 cm for subsequent samples. The arrows indicate TN determined from the minimum of d /dT vs T, as shown in Fig. ers less than 33 Å. Shown in Fig. 4 is d /dT for the 36-, 4. 46-, and 56-Å Cr-Fe spacers. From the d /dT curves, we extract two temperatures: TN determined by the minimum in Cr94Fe6 film grown at TS 500 °C. The characteristic in- d /dT and the onset temperature T0 , which we define as the crease in resistivity below TN is evident in Fig. 2 a . TN is temperature at which the resistivity deviates from its linear determined operationally from the point of inflection of the vs T behavior. This definition of TN was previously shown to vs T i.e., the minimum in d /dT). Using this criterion, we agree with neutron diffraction results in Fe/Cr superlattices.3 obtain TN 212 5 K which agrees with TN 211 K ob- For all the samples studied, T0 was 150 K higher than TN . tained for a bulk Cr-Fe alloy with 6.5 at. % Fe.6 The rela- tively high residual resistivity of the film in Fig. 2 a as compared to pure Cr films also agrees with bulk results. The IV. MAGNETIZATION AND MAGNETORESISTANCE transition, however, is considerable broader and does not ex- hibit the first-order jump in observed in bulk crystals. This Shown in Fig. 5 are the magnetotransport results for difference may result from a nonuniform Fe distribution or samples shown in Fig. 4 measured at T T0 , TN T T0 , clustering in the alloy arising from nonequilibrium thin-film and T TN . For T T0 the MR is small and positive for growth. For Cr94Fe6 films grown at lower TS 150 °C , TN small fields. The negative high-field MR has been sub- increases to 260 K which again may result from differ- tracted from the data. This positive MR results from the ences in the Fe distribution. Shown in Fig. 2 b is the mag- anisotropic magnetoresistance AMR as the Fe layers rotate netoresistance MR measured at 2 and 25 K. The MR is from the Fe 100 easy-axis direction to saturated along the large and negative. Both the magnitude and shape of the MR 110 . This shows that the Fe layers are either uncoupled or curve agree with bulk measurements and are characteristic of ferromagnetically coupled in this temperature range with the magnetic alloys.8 The presence of local moments provides saturation field proportional to the cubic anisotropy. For TN spin-flip scattering channels which are frozen out in high T T0 the MR behavior becomes negative and isotropic magnetic fields. and is characteristic of the giant magnetoresistance GMR , Shown in Fig. 3 are the resistivity curves for a series of and the saturation field increases. As temperature decreases Fe 15 Å /Cr94Fe6 superlattices. For thicker Cr-Fe layers to T TN , the MR changes sign back to that for AMR be- e.g., 225 Å the resistivity curve is similar to the Cr-Fe film havior for the 46- and 56-Å samples and is strongly reduced results of Fig. 2. As the Cr-Fe layer thickness is reduced, the for the 36-Å sample. For the 29-Å sample, the MR is nega- minimum in vs T as well as the inflection point character- tive and decreased monotonically with increasing T. These izing TN indicated by the arrows , shifts to lower tempera- results are summarized in Fig. 6, showing the T dependence tures. TN decreases systematically with decreasing Cr-Fe of the MR. For tCr-Fe 36 Å, GMR is only observed in the spacer thickness in a qualitatively similar fashion to that ob- intermediate temperature range TN T T0 as indicated by served for Fe/Cr superlattices.3 For the 29-Å Cr-Fe spacer, the arrows. This change in behavior is also observed in the the resistivity decreases monotonically with decreasing tem- magnetic behavior. Shown in Fig. 7 are magnetization results perature without showing the upturn characteristic of the for the 36-Å sample. For T T0 , a square hysteresis loop is Ne´el transition in Cr-Fe alloys. These results suggest a sup- observed consistent with the AMR behavior observed in Fig. pression of the homogeneous ordering for Cr-Fe spacer lay- 5. For T T0 , the remanent magnetization decreases indicat- 56 INTERPLAY BETWEEN BIQUADRATIC COUPLING AND . . . 5471 FIG. 6. Magnetoresistance values vs T for superlattices the 29-, FIG. 5. Low-field magnetoresistance curves for the samples 36-, 46-, and 56-Å samples. is defined such that 0 is char- shown in Fig. 4. Top panel 56-Å spacer layer , middle panel 46 acteristic of AMR behavior and 0 is GMR. The arrows indi- Å , and bottom panel 36 Å . H is parallel to the current and par- cate the TN and T0 values as determined in Fig. 4. allel to the Fe 110 hard axis. The linear high-field contribution to the MR has been subtracted from the data. For each panel, the top via transport is found to decrease with decreasing Cr thick- curve is for T T0 , the middle curve T0 T TN , and the bottom ness in a qualitatively similar fashion to that previously re- curve T TN . ported for Fe/Cr superlattices. This behavior is understood as arising from frustration caused by interfacial roughness.2 For ing the onset of interlayer coupling. The remanent value of thin layers, the Cr layers are coupled to the Fe layers and will 0.58 and the shape of the hysteresis loop can be quantita- order locally i.e., within the lateral terrace length as shown tively modeled assuming a combination of ferromagnetic bi- schematically in Fig. 10 a . Such a configuration is obtained linear coupling, biquadratic coupling, and cubic anisotropy. in calculations of F/AF systems with rough interfaces.23­25 For lower temperatures, a square hysteresis loop is again As the spacer layer thickness increases, this configuration is regained. The temperature dependence of the remnant mag- unstable and will crossover to homogeneous ordering shown netization is plotted in Fig. 8. We observe the onset of bi- schematically in Fig. 10 b . In this configuration, the disor- quadratic coupling below T0 and then a suppression below der is located near the interface and the center of layer ex- TN . The change in magnetic properties of the magnetic layer hibits long-range order. A transition from homogeneous or- is also reflected in the coercive fields, HC . We find enhanced dering to inhomogeneous ordering is also expected with HC values below TN . An example is shown in Fig. 9 for the increasing temperature.23 For temperatures in the vicinity of 46-Å sample. TN , the ordering of the spacer layer is dominated by the We only observed AF bilinear coupling for Cr-Fe thick- interfacial exchange energy and will locally respond to the nesses of 8­10 Å which corresponds to the first AF- Fe layers. For thicker spacer layers and low temperatures, the coupling maximum for Cr spacers. We did not observe the intrinsic AF ordering of the spacer should dominate and ho- oscillatory coupling for thicker Cr-Fe spacers previously ob- mogeneous AF ordering is expected Fig. 10 b . For small served for Cr.12 This most likely results from the high resis- spacer thicknesses or T near TN , inhomogeneous ordering is tance of the Cr-Fe alloy compared to that of Cr spacers. expected. Therefore, we could not study the interaction between TN Within either the fluctuation or proximity magnetism and the bilinear coupling in the present samples. models the existence of biquadratic coupling implies inho- mogeneous ordering of the Cr or Cr-Fe interlayers. That is, V. DISCUSSION AND CONCLUSION the AF interlayer has to respond to local fluctuations at the interface. Therefore, biquadratic coupling is expected for a These results again highlight the direct relationship be- magnetic configuration shown in Fig. 10 a . For a homoge- tween the intrinsic AF order of the spacer layer and the bi- neously ordered layer, the magnetism of the Cr layers will be quadratic interlayer coupling. The Ne´el transition measured insensitive to the relative orientation of the Fe layers, and 5472 ERIC E. FULLERTON, C. H. SOWERS, AND S. D. BADER 56 FIG. 9. Coercive field HC values for the Fe 15 Å /Cr94Fe6 46 Å 40 superlattice with H applied along the Fe 100 easy axis. Arrows indicate TN and T0 values determined in Fig. 4. biquadratic coupling. For the thinnest Cr-Fe layers, the ho- mogeneous ordering is never achieved and the biquadratic coupling increases monotonically with decreasing tempera- ture. This interpretation is consistent with Ref. 4 which cor- related the presence of biquadratic coupling in Fe/Cr 001 superlattices with the observation, via neutron scattering, of frustrated AF0 order. FIG. 7. Magnetic results for the Fe 15 Å /Cr94Fe6 36 Å 40 In conclusion, we have investigated the AF ordering of superlattice with H applied along the Fe 100 easy axis. The top Cr94Fe6 alloy layers in epitaxial Fe/Cr94Fe6 001 superlat- panel is for T T0 , the middle panel T0 T TN , and the bottom tices. Ne´el temperature TN values are found to be strongly panel T TN . thus the biquadratic coupling should be suppressed. There may still be an effect on the coercive field as observed for thin Fe layers on a Cr substrate.26 Thus to interpret the present results, the onset temperature T0 is the boundary be- tween the paramagnetic spacer and inhomogeneous ordering. In the fluctuation model, the Cr-Fe interlayer would be viewed as having an enhanced susceptibility as T approaches TN , whereas the proximity magnetic model assumes inho- mogeneous AF order. TN then denotes the transition to ho- mogeneous order, and is concomitant with the suppression of FIG. 10. Schematic representation of two possible magnetic or- dering configurations for an AF spacer layer in the presence of rough interfaces. In both cases, domain walls indicated by broad lines are initiated and terminated at interfacial steps. a Domain FIG. 8. Remanent magnetization Mr /Ms values for the walls connect steps at adjacent Fe layers resulting in inhomoge- Fe 15 Å /Cr94Fe6 36 Å 40 superlattice with H applied along the neous ordering of the AF spacer layer and b domain walls connect Fe 100 easy axis. Arrows indicate TN and T0 values determined in steps of the same Fe layers resulting in homogeneous ordering Fig. 4. within the center of the AF layer indicated by the dashed line. 56 INTERPLAY BETWEEN BIQUADRATIC COUPLING AND . . . 5473 thickness dependent, with T tion between the AF ordering process and the biquadratic N suppressed for Cr94Fe6 thick- nesses less than 33 Å. Transport results indicate a broad- interlayer coupling. ening of the transition with an onset temperature T0 TN by 150 K for all thicknesses. 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