PHYSICAL REVIEW B VOLUME 59, NUMBER 22 1 JUNE 1999-II Exchange coupling through spin-density waves in Cr 001... structures: Fe-whisker/Cr/Fe 001... studies B. Heinrich, J. F. Cochran, T. Monchesky, and R. Urban Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 Received 28 October 1998; revised manuscript received 9 February 1999 Exchange coupling through a spin-density wave in Fe-whisker/Cr/Fe 001 structures has been studied using Brillouin light scattering BLS and magneto-optical Kerr effect MOKE . The Fe-whisker 001 substrates provide nearly ideal templates: they are characterized by atomic terraces having dimensions in excess of several micrometers. Such templates are essential for the study of short-wavelength exchange coupling which is mediated by the intrinsic spin-density wave in Cr 001 . Atomically smooth Cr 001 layers similar to those of the Fe-whisker surfaces can be grown at raised substrate temperatures. Angular resolved auger electron spectroscopy measurements have shown that the Fe-whisker/Cr 001 interfaces are affected by an atom ex- change placement mechanism interface alloying . It will be shown that this interface alloying at the Fe- whisker/Cr interface profoundly affects the behavior of the short-wavelength oscillations. The phase of the short-wavelength oscillations is reversed compared to that expected for the spin-density wave in Cr 001 . The strength of coupling is significantly decreased from that obtained from first-principles calculations, and the first crossover to antiferromagnetic coupling occurs at 4 ML. BLS and MOKE have shown unambiguously that the exchange coupling in Fe-whisker/Cr/Fe 001 structures can be described by bilinear and biquadratic terms. Experiments carried out using Cu and Ag atomic layers between the Cr 001 and Fe 001 films, i.e., hetero- geneous interfaces, have shown that the exchange coupling in Cr 001 is strongly affected by electron multiple scattering. It will be argued that the exchange coupling through thick 8 ML and atomically smooth Cr 001 spacers can be described by localized interactions Heisenberg type and by electron multiple-scattering quan- tum well state contributions. This is in good accord with recent first-principle calculations by Mirbt and Johansson. However, interface alloying severely affects the behavior of the exchange coupling for Cr thick- nesses less than 8 ML. In this thickness regime the overall coupling exhibits mostly a long-wavelength behavior with a small superimposed short-wavelength contribution. This initial Cr thickness regime is respon- sible for changes in the phase of the short-wavelength oscillations and for the reduced strength of the exchange coupling due both to the localized and to the multiple-scattering contributions. We have observed no significant dependence of the exchange-coupling strength on the Fe film thickness for samples having the structure Fe-whisker/11Cr/nFe/20Au where n specifies an iron film thickness between 5 and 40 ML. However, prelimi- nary data show that the exchange coupling is significantly increased in specimens for which both sides of the iron film are covered by Cr, i.e., for structures of the form Fe-whisker/11Cr/nFe/11Cr/20Au. It appears that electron resonant states in the iron film play no important role in the strength of the exchange coupling when the iron is bounded on one side by the gold, but that they do become important when the iron film is bounded by Cr on both sides. BLS and MOKE studies on Fe-whisker/Cr/Mn/Fe 001 samples revealed that the antifer- romagnetic state of Mn is composed of compensated 001 atomic planes. The results of the above experimen- tal studies will be compared to recent theories. Points of agreement and of disagreement between the experi- mental results and recent first-principles calculations will be explicitly pointed out. S0163-1829 99 10921-4 INTRODUCTION mensurate with the Cr lattice spacing; the period of the long- wavelength oscillations was found to be 12 ML. Short- and long-wavelength oscillations have also been observed by Fe-whisker/Cr/Fe 001 systems have played a crucial role Grušnberg and co-workers in Fe/Cr/Fe samples grown on a in the study of exchange coupling between two ferromagnets GaAs 001 substrate covered with a thick buffer layer of separated by a nonferromagnetic spacer. Studies carried out Ag 001 .3 Heinrich and co-workers the SFU group have by Unguris, Celotta, and Pierce1 using scanning electron mi- carried out quantitative studies using Fe-whisker/Cr/Fe 001 croscopy with polarization analysis SEMPA , and the samples.4,5 The objective of the SFU group was to grow magneto-optic Kerr effect MOKE measurements by samples having the best available interfaces, to measure Purcell et al.2 using Fe-whisker/Cr/Fe 001 samples showed quantitatively the strength of the exchange coupling, and to that the exchange coupling oscillates with a short- compare these coupling strengths with ab initio calculations wavelength period of 2 monolayers ML . The SEMPA that explicitly include the presence of spin-density waves in images revealed in a very explicit way that short-wavelength the Cr. The requirement of smooth interfaces limited our and long-wavelength oscillations existed in the thickness study to samples which were grown on Fe-whisker templates range 5­80 ML of Cr. The period of the short-wavelength with the Cr spacers terminated at an integral number of Cr oscillations, 2.11 ML, was found to be slightly incom- atomic layers. It was found that the strength of the exchange 0163-1829/99/59 22 /14520 13 /$15.00 PRB 59 14 520 ©1999 The American Physical Society PRB 59 EXCHANGE COUPLING THROUGH SPIN-DENSITY . . . 14 521 coupling through the Cr 001 spacer is extremely sensitive to small variations in growth conditions. The measured ex- change coupling was found to be reproducible only in those samples that exhibited layer by layer growth. In our studies we concentrated on samples for which the Cr thickness ranged from 4 to 13 atomic layers. We wished to study a thickness regime ranging from a thin Cr interlayer for which the exchange coupling was dominated by the pre- dominantly antiferromagnetic long-wavelength 12 ML de- pendence on thickness to a thickness regime in which the exchange coupling was dominated by the 2 ML short- wavelength period. In particular, we wished to investigate the origin of the deviation of the thickness dependence of the coupling from the predictions of simple Cr spin-wave theory antiferromagnetic coupling for an even number of Cr atomic layers and ferromagnetic coupling for an odd number of Cr atomic layers . As will be discussed below, deviations from simple spin-wave theory can be ascribed to interface mixing of the Fe and Cr atoms. GROWTH Specimens were grown in an ultrahigh vacuum system UHV having a base pressure less than 10 10 Torr. Cr and Fe films were deposited on an iron-whisker 001 surface by evaporation from standard source ovens. The films were de- posited at a rate of approximately 1 ML per minute at a pressure of 5 10 10 Torr. Thicknesses were monitored using a standard quartz crystal gauge. The intensity of the reflection high-energy electron diffraction RHEED specu- lar spot was measured during the film growth. We used a 10 FIG. 1. Typical RHEED specular spot profiles for the growth of keV electron beam incident on the specimen at a grazing Cr on an Fe-whisker 001 template. The spot profile scan was taken angle 1 to 3 degrees . The specular spot intensity exhibited along the direction which is determined by the intersection of the the periodic variations characteristic of layer by layer electron-beam plane and the plane of the fluorescent screen in the growth. The existence of unattenuated RHEED intensity os- direction of the RHEED streaks . The spot profiles were monitored cillations of the specular spot during the growth of the Cr at the second anti-Brag reflection corresponding to 2 3 degrees. spacer did not guarantee reproducible values of the exchange a The spot profile at a maximum of the RHEED intensity oscilla- coupling between a thin Fe 001 film and the whisker 001 tions, corresponding to a completely filled top atomic layer. The substrate. It was necessary to establish conditions such that width of the specular spot profile is limited by the RHEED instru- new layers were initiated at a repeatable pattern of nucleation mental resolution. b The spot profile at a minimum of the RHEED sites. This condition could best be monitored by examining intensity oscillations, corresponding to a half filled top atomic layer. RHEED intensity oscillation amplitudes together with the The spot profile consists of the sum of three peaks: an attenuated width of the RHEED specular spot profile. The best results version of the profile of a due to incomplete cancellation of the were obtained for the case when the RHEED intensity oscil- interference between electrons scattered from the different exposed lations exhibited a cuspy, unattenuated pattern and the spot surface levels 0 , and two flanking peaks due to the presence of profile oscillated repeatably between narrow peaks filled atomic islands and . The splitting of the two flanking peaks atomic layers and wider, split intensity peaks half filled determines the average lateral spacing of the Cr atomic islands. The layers ; see Figs. 1 a and b . These requirements could be average atomic spacing at Ts,opt is approximately 80­90 nm. achieved by maintaining the substrate temperature in a nar- row range of temperatures, 280 °C Ts,opt 320 °C. The Cr exhibited a unique behavior; the first RHEED intensity presence of the specular spot splitting, see Fig. 1 b , in a oscillation showed a strong peak with a very sharp cusp, see direction parallel with the RHEED streaks for half filled Fig. 2 a , even at substrate temperatures as low as 150 °C, atomic layers indicated that new atomic layers were formed indicating that the first atomic layer grows very smoothly. from nucleation centers which were separated by a well de- The situation changes when Cr is deposited on a Cr template. fined mean distance. The observed splitting corresponded to In that case the growth of Cr proceeds layer by layer only if a mean separation between atomic islands of 800­900 Ć at the substrate temperature is adjusted to an optimum growth Ts,opt .4 This interpretation is in agreement with the scanning temperature Ts,opt ; see Figs. 2 a and b . In order to get a tunnel microscope STM studies by Stroscio et al.6 Samples final Cr atomic layer nearly as smooth as the Fe-whisker grown at the optimum temperature showed unattenuated template the substrate temperature can be changed gradually, RHEED intensity oscillations with well defined cusps at the but the approach to Ts,opt has to be from temperatures less RHEED intensity maxima; see Fig. 2. The first monolayer of than Ts,opt . In a proper layer by layer growth the RHEED 14 522 HEINRICH, COCHRAN, MONCHESKY, AND URBAN PRB 59 FIG. 3. The RHEED intensity oscillations second anti-Brag re- flection for Fe growth on a Cr template. This growth was carried out for an Fe-whisker/Cr/Fe 001 sample having three different thicknesses for the deposited Fe layer. The growth was stopped, the shutter was moved, and the growth was again resumed as indicated in the figure. intensity oscillations maintain a cuspy unattenuated pattern, see Fig. 2 b , and the width of the specular spot oscillates between minima fully filled atomic layer and maxima half field atomic layer ; see Fig. 2 c . The width of the specular spot corresponding to a complete atomic layer of Cr is as narrow as that of the Fe-whisker template. In order to obtain a Cr spacer having a well defined thickness one has to avoid excessive growth at naturally occurring atomic steps. The growth from such atomic steps results in the atomic steps moving across the surface. Thus the atomic steps on the Cr surface are displaced from those on the Fe-whisker substrate surface and the thickness of the Cr layers would necessarily fluctuate by 1 ML across the sample surface. This mecha- nism can partly provide an explanation for why samples grown outside the optimum range of substrate temperatures showed a large biquadratic exchange coupling and a small bilinear coupling. The growth of Fe on a Cr 001 template proceeds very FIG. 2. The RHEED intensity oscillations second anti-Brag re- flection of Cr on an Fe whisker 001 template. One period of os- cillations, usually 60 seconds, corresponds to one additional atomic layer of Cr. a The first two oscillations at Ts 150 °C. The mea- surement was halted at the peak of the second oscillation. Note that the second maximum is significantly lower compared to that for the top surface of the Fe whisker template and to that for the first filled atomic layer of Cr. b The substrate temperature was increased to establish layer by growth. The gradual increase of the RHEED in- tensity minimum is due to a gradual increase of the distance be- tween the Cr nucleation centers during the growth: this was caused by an upward drift of the Fe whisker temperature. The size of the atomic islands was nearly the same as the lateral instrumental reso- lution of the RHEED gun and consequently one does not obtain a complete cancellation of the RHEED intensities at the half covered surfaces. The strength of the exchange coupling was found to be most reproducible for those samples where the minimum values of FIG. 4. The thickness dependence of the bilinear J1 and the RHEED intensity oscillations remained constant and were close biquadratic J2 exchange coupling. The biquadratic coupling to zero intensity. The growth in this figure was carried out at a can be measured only for AF coupled samples. The values of J2 for somewhat higher temperature than Ts,opt ; see the text. c The full the FM coupled samples 10, 12 ML were assumed to be the same width at half maximum of the specular spot as a function of the Cr as that for the AF coupled samples containing 9, 11, and 13 ML of layer thickness for the RHEED intensity oscillations shown in a Cr. Note that the coupling becomes AF for thicknesses greater than and b . The maxima and the minima correspond to half and fully 4 ML and the thickness dependence of J1 has a broad AF maximum filled atomic layers, respectively. Note that the spot profile mini- around 7 ML of Cr. Large short-wavelength oscillations appear for mum widths are equal to that of the Fe-whisker template. Cr thicknesses greater than 9 ML. PRB 59 EXCHANGE COUPLING THROUGH SPIN-DENSITY . . . 14 523 well for approximately 5­8 ML even at room temperature strength of the AF coupling, and decreases the strength of the RT . At the beginning of the growth the RHEED oscilla- FM coupling. The biquadratic coupling J2 was found to be tions have a large amplitude even for the second anti-Bragg approximately 0.25 ergs/cm2, nearly independent of Cr film condition; see Fig. 3. The amplitude of the RHEED oscilla- thickness. The observed weak FM coupling implies that J1 tions gradually decreases with increasing Fe layer thickness. 0.2 2J The RHEED intensity amplitude can be recovered by means 2 and leads to a bilinear exchange coupling strength of J of a subsequent increase in the substrate temperature. In most 1 0.7 ergs/cm2 for FM coupled samples. The coupling between the Fe and Cr atoms at the Fe/Cr depositions of Fe layers the first 5­8 ML were grown at RT. interface is expected to be strongly antiferromagnetic10,11 and The substrate temperature was then increased to 150­240 °C. in consequence the spin-density wave in Cr is locked to the The Fe layers deposited in this manner can be grown in a quasilayer by layer manner in which the growth proceeds by orientation of the Fe magnetic moments. Since the period of terrace nucleation and subsequent attachment of adatoms to the short-wavelength oscillations is close to 2 ML one would the atomic steps of the newly formed atomic islands. The expect AF coupling for an even number of Cr atomic layers surface roughness of the Fe films was mostly confined to the and FM coupling for an odd number of Cr atomic layers. For top two atomic layers.7 the period 2.11 ML the first phase slip in the short- All samples prior to their removal from the vacuum sys- wavelength coupling is predicted to occur at 20 ML. Surpris- tem were covered by a 20-ML-thick epitaxial Au 001 layer. ingly the SEMPA Ref. 12 and BLS Ref. 13 measurements The growth of Au exhibited well defined RHEED intensity showed clearly that the phase of the short-wavelength oscil- oscillations and the surface was terminated by a 5 1 recon- lations is exactly opposite to that expected. It is also impor- struction typical for Au 001 . tant to note that the strength of the exchange coupling Jmax 1. ergs/cm2 was found to be much less than that ob- MAGNETIC STUDIES tained from the first-principles calculations, J1 30 ergs/cm2.14 Our studies showed that the strength of the Quantitative Brillouin light-scattering BLS studies4,8 bilinear exchange coupling J have clearly exhibited short-wavelength oscillations in the 1 is very sensitive to the initial growth conditions: a lower initial substrate temperature re- exchange coupling; see Fig. 4. These studies showed also sults in a larger exchange coupling strength. The bilinear that the exchange coupling through Cr 001 contains both exchange coupling can be changed by as much as a factor of oscillatory bilinear J1 and positive biquadratic J2 exchange coupling terms. The exchange energy can be written 5 by varying the substrate temperature during the growth of the first Cr atomic layer.15 This behavior led us to believe E J that the atomic formation of the Cr layer is more complex 1 cos J2 cos2 , 1 than had been previously acknowledged. Angular resolved where is the angle between magnetic moments of the Fe Auger spectroscopy ARAES ,15­17 STM,18 and proton in- film and the surface magnetization of the Fe whisker. duced Auger electron spectroscopy AES Ref. 19 have The results of the exchange coupling measurements can shown that the formation of the Fe/Cr 001 interface is be described as follows. The exchange coupling crosses to strongly affected by an interface atom exchange mechanism antiferromagnetic coupling at 4 ML of Cr. For Cr spacer interface alloying . The above studies revealed very clearly thicknesses dCr 8 ML the strength of the short-wavelength that the Cr undergoes interface mixing when the substrate oscillations is quite weak, 0.1 ergs/cm2. The exchange cou- temperature is adjusted for optimum growth. The tunneling pling in this range is antiferromagnetic only due to the pres- spectroscopy measurements suggested that the surface is pre- ence of an antiferromagnetic AF long-wavelength bias. dominantly Cr at a Cr coverage of 2 ML.18 The ARAES This AF bias is peaked around 6­7 ML. It is interesting to showed that the interface mixing was confined mainly to two note that the strength of the long-wavelength AF bias is very Fe atomic layers; see Fig. 5. The proton induced AES nearly the same as that observed in Fe/Cr/Fe 001 epitaxial studies19 also showed that the interface atom exchange pro- multilayers prepared by sputtering where the relatively large cess does not proceed appreciably for layers beyond the interface roughness annihilated the presence of the short- Fe/Cr interface. The ARAES studies showed that interface wavelength oscillations.9 The exchange coupling in these alloying during the growth already starts at low substrate sputtered films showed long-wavelength oscillations with a temperatures, Tsub 100 °C. The interface alloying increases rapidly decreasing strength of the coupling for thicknesses with increasing substrate temperature; see Fig. 5. It should be greater than 10 ML of Cr. It follows that the antiferromag- noted that interface alloying due to the atom exchange netic bias shown in Fig. 4 for the first 7­8 ML of Cr is most mechanism is not, in general, symmetric: it occurs chiefly at likely due to the long-wavelength oscillations in the ex- one interface.7 Interface alloying is driven by the difference change coupling. For a Cr spacer thicker than 8 ML, dCr in binding energies between the substrate and adatoms. The 8 ML, the exchange coupling is dominated by the short- binding energies are proportional to the melting points of the wavelength oscillations. In this thickness range the samples solids. Interface alloying has been observed in systems for are antiferromagnetically AF coupled for an odd number of which the substrates have lower melting points than do the Cr atomic layers, Jtot J1 2J2 1.0­ 1.5 ergs/cm2, and fer- adatom solids.7,20 The melting point of Fe 1808 K is lower romagnetically FM coupled for an even number of Cr than the melting point of Cr 2130 K and thus the condition atomic layers, Jtot 0.2 ergs/cm2. The total exchange cou- for interface alloying at the Fe/Cr interface is satisfied, but pling through the Cr spacer for the parallel orientation of the condition is not satisfied at the Cr/Fe interface. Mošss- magnetic moments is given by Jtot J1 2J2, and therefore bauer studies by Keune and Schrošr et al.21 have shown that the biquadratic exchange contribution J2 0 increases the interface mixing for the deposition of Fe atoms on a Cr sub- 14 524 HEINRICH, COCHRAN, MONCHESKY, AND URBAN PRB 59 FIG. 5. The substrate temperature dependence of the fraction of FIG. 6. A comparison of observed and calculated scattered light Cr atoms in the first layer deposited on an Fe-whisker substrate frequency shifts for a structure composed of a bulk whisker-Fe 001 , the fraction of Cr atoms contained in the whisker surface layer substrate, an 11-ML-thick Cr 001 spacer, a 20-ML-thick Fe 001 , and the fraction of Cr atoms contained in the first whisker film, and a 20-ML-thick Au cover layer. The 5145 Ć laser light was subsurface layer . The fractional coverages were obtained from incident at 45° and the scattered light was collected in the back- fitting the angular dependence of the Auger Cr 529 eV peak in- scattering configuration. The saturation magnetization was taken to tensity using angular resolved Auger electron spectroscopy be 21.4 kOe for both the bulk Fe and the Fe thin film. The in-plane ARAES with the SSC computer program provided by Chuck cubic anisotropies used were 4.76 105 erg/cm3 for the bulk Fe and Fadley.50 3.5 105 erg/cm3 for the thin film. The perpendicular uniaxial sur- face anisotropies were taken to be 0.5 erg/cm2 for the bulk Fe and strate is not important for deposition temperatures near room 1.0 erg/cm2 for the Fe thin film. The uniaxial surface anisotropy for temperature such as we used to deposit Fe films on the Cr the Fe film was obtained by independent measurements using Ag layers. substrate/Cr/Fe/Au 001 samples. The in-plane cubic anisotropy for The results of typical BLS and MOKE studies are shown the Fe film was determined using Eq. 1.40 in Ref. 4. Ob- in Figs. 6 and 7. The MOKE and BLS measurements exhibit served surface mode frequencies s and up-shifted bulk magnon two critical fields. For fields H H edge frequencies e. Observed down-shifted bulk edge frequen- 2 the magnetic moments in the Fe whisker and in the ultrathin film were clearly par- cies e. Observed up-shifted thin-film frequencies tf. Ob- allel to the applied external field, and the sample can be fully served down-shifted thin-film frequencies tf. Curve a has been saturated in sufficiently large fields. For H H calculated using a coupling strength J 2 the magnetic tot J1 2J2 moments were noncollinear, the magnetic moments deviated 1.45 ergs/cm2; curve b has been calculated for Jtot from the external field direction. As illustrated in Fig. 6, the 1.50 ergs/cm2; curve c has been calculated using Jtot J1 2J2 Stokes and anti-Stokes modes are split by 4 GHz for fields 0.70 ergs/cm2; curve d has been calculated using Jtot H H 0.60 ergs/cm2. The cusp fields are H1 1.0 kOe and H2 1 and for a 20-ML-thick Fe film. This splitting is the consequence of dipolar coupling when the direction of the dc 4.0 kOe. We estimate that J1 1.1 erg/cm2, and J2 0.2 erg/cm2. magnetic moments in the Fe whisker and in the Fe film are antiparallel.8 In all our samples the field dependence of the the complex behavior of the Cr spin-density wave when the magnetization loops is consistent with the assumption that magnetic moments of the ferromagnetic layers are not locked the angular variation of the exchange coupling can be ex- in phase with the spin-density wave of the Cr spacer in the pressed in terms of bilinear and biquadratic exchange cou- lowest energy state. J2 is expected to be 14% of J1 . The pling terms Eq. 1 . The separation between the H2 and H1 coefficient 0.16 can indicate that a part of J2 is related to the fields, H2 H1 , calculated using only the bilinear ex- intrinsic contribution of the biquadratic exchange coupling in change coupling term was always smaller than the measured spin-density wave Cr. Biquadratic exchange coupling in separation m : one needed to add the biquadratic exchange spacers that possess short-wavelength oscillations in J1 can coupling term with J2 positive to obtain the observed sepa- also be caused by lateral variations of the spacer ration m . The positions of critical fields H1 and H2 were thickness.23,24 The strength of the biquadratic exchange cou- calculated using a full micromagnetic calculation for an Fe- pling depends on the lateral scale of the thickness variations. whisker/Cr/20 Fe sample including both bilinear and biqua- When the lateral thickness variations occur on a scale that is dratic exchange coupling terms. In these calculations the an- much less than the in-plane exchange correlation length, that gular spatial variations of the magnetic moments inside the is on a length of the order of the domain-wall width, the whisker and across the film were included.22 The theory de- biquadratic exchange coupling due to lateral thickness varia- scribed in Ref. 22 was used to determine the strengths of J1 tions becomes negligible; see Eq. 2.17 in Ref. 4. The STM and J2 by comparison with the experimental Kerr data. A studies18 have shown that the interface alloying is distributed large number of measurements showed that a part of J2 was laterally on an atomic length scale, and in this case the in- proportional to the measured value of J1 . We found that terface roughness caused by any interface alloying should J2 0.1 (0.16 J1 ). This is an interesting result that re- make a negligible contribution to J2 . The atomic roughness quires a brief comment. Stoeffler and Gautier predicted the at the second interface, Cr/Fe, is different from that at the presence of a biquadratic exchange coupling term for Fe lay- first interface, Fe/Cr, and is not due to interface alloying. The ers coupled through Cr 001 .14 The origin of this coupling is roughness at the second interface can be caused by two ef- PRB 59 EXCHANGE COUPLING THROUGH SPIN-DENSITY . . . 14 525 FIG. 8. Calculated MOKE signal for a 20 ML Fe 001 film exchange coupled to a bulk Fe 001 substrate and assuming an in- homogeneous distribution of the bilinear coupling strength J1 . The biquadratic coupling strength J2 has been set equal to 0.3 ergs/cm2 for all curves. The probability of a coupling strength J1 J,P(J), has been taken to be P(J) 1/( J)1/2 * exp (J J )/ J 2 FIG. 7. The longitudinal MOKE signal for the same sample as with J 1 erg/cm2. Curve A J 0. Curve B J in Fig. 6 as a function of the applied magnetic field. H1 1.3 kOe 0.2 ergs/cm2. Curve C J 0.5 ergs/cm2. and H2 4.8 kOe. Notice that the saturation field H2 is higher in MOKE than that in BLS. The difference between the MOKE and Neutron-diffraction and MOKE studies by the Bochum BLS measurements of the critical field H2 is caused by lateral in- group,25 using Fe/Cr/Fe 001 samples having a high density homogeneities in exchange coupling, see the text for the details. of atomic steps, showed that the ground state in Fe/Cr/ These values of H1 and H2 correspond to J1 1.16 erg/cm2 and Fe 001 multilayers exhibits a noncollinear orientation of the J2 0.27 erg/cm2. magnetic moments for which the approach to saturation can fects: a by terminating the Cr growth not exactly at a full be described by the Slonczewski magnetic proximity coverage of the last atomic layer, and b by changing the model26 in which the exchange energy depends quadratically distribution of atomic terraces during the growth. Effect a on the angle between the magnetic moments of the ferromag- most likely plays a minor role in carefully prepared samples netic layers, ( )2. All our MOKE and BLS measure- where the Cr interlayer is continuously monitored by means ments carried out on Fe-whisker/Cr/Fe 001 samples that of RHEED; see above. The interface roughness due to the were prepared with the best possible interfaces low density redistribution of atomic steps at the top Cr surface, case b , of atomic steps are consistent with the use of bilinear and could lead to the most serious consequences. In this case the biquadratic exchange coupling terms, Eq. 1 . In particular, Cr thickness varies by 1 ML across the sample surface and the BLS data show unambiguously that for fields slightly the lateral scale of the variations in Cr thickness would be above the critical field H2 the iron film and whisker moments given by the mean distance between the Cr nucleation cen- are parallel, whereas for fields slightly less than the critical ters, 800­900 Ć. This thickness variation could result in a field H1 the thin film and whisker moments are antiparallel.8 significant decrease of the bilinear exchange coupling J1 due The approach to saturation at the critical field H2 as observed to a near cancellation of positive and negative contributions using MOKE, and the onset of the antiferromagnetic con- to J1 . At the same time the large scale lateral variations in figuration at the critical field H1 , see Fig. 7, is more gradual the Cr spacer thickness would lead to a large contribution to than is calculated using the sum of bilinear and biquadratic J2 . For such large scale lateral inhomogeneities the approxi- exchange coupling terms of Eq. 1 ; see Fig. 8, curve A. The mations used to derive Slonczewski's formula23 are not di- calculated approach to saturation clearly exhibits a well de- rectly applicable. The angle between the magnetic moments fined kink at the field H2 : the experimental measurements of the two coupled Fe layers deviates strongly from its mean usually show a concave gradual approach to saturation; see value from place to place along the surface. For large lateral Fig. 7. According to the calculations the antiferromagnetic inhomogeneities micromagnetic calculations were carried configuration of the Fe magnetic moments is reached via a out by Arrott.24 Model calculations showed that the calcu- first-order phase jump; the experimental measurements show lated magnetization loops were similar to those obtained us- a more gradual s-shaped change. These experimental MOKE ing the bilinear and biquadratic exchange interactions, Eq. features can be explained by an inhomogeneous distribution 1 , with a strong biquadratic exchange coupling contribution of the exchange coupling strength. A 10% variation in the for which the total magnetic moment does not show any exchange coupling across the measured area would result in lower critical field H1 , and the ground state is noncollinear. hysteresis loops that are very similar to those observed using However, the measured hysteresis loops and BLS measure- MOKE; compare Fig. 7 with Fig. 8. In fact an inhomoge- ments exhibit a behavior in which the biquadratic exchange neous distribution of the exchange coupling also explains coupling is much less than J1 . Therefore one can conclude observed differences between values of the critical fields H2 that the observed low values of the bilinear exchange cou- that have been obtained using the MOKE and the BLS tech- pling are not due to the redistribution of atomic steps, but are niques. The BLS measurements on Fe/Cr/Fe 001 always more likely to be the direct consequence of interface alloy- yield lower values for the critical field H2 , with correspond- ing. ing lower values of the exchange coupling strength, com- 14 526 HEINRICH, COCHRAN, MONCHESKY, AND URBAN PRB 59 pared with that obtained using MOKE. The BLS thin-film fields are not available the approach to saturation in a resonant modes were also visibly broadened for external strongly coupled but inhomogeneous system can easily be fields greater than the saturation field H2 , where the thin- interpreted in terms of the Slonczewski magnetic proximity film magnetic moment is parallel to the Fe-whisker moment. model. One should always consider the possibility of inho- The thin-film resonance mode was observed to be much mogeneous coupling. The combination of BLS and MOKE narrower at a field midway between H measurements provides a test for the presence of inhomoge- 1 and H2 where the thin-film and whisker magnetizations are nearly neous interlayer coupling. orthogonal.8 The difference between critical fields measured Recent calculations27 predict that the exchange coupling using BLS and MOKE, as well as the broadening of the BLS through Cr 001 spacers which have ideal interfaces can be signal for fields greater than H described by Slonczewski's proximity model26 in which the 2 , can be explained by an inhomogeneous distribution of J exchange energy increases quadratically with the angle be- 1 and J2 . The BLS tech- nique measures the frequencies of the rf resonance modes. tween the magnetic moments of the Fe layers, exchange en- The mode corresponding to the thin Fe film covering the Cr ergy ( )2. In that case, for AF coupling, the total mag- spacer exhibits a resonance at a field that is the algebraic netic moment approaches saturation gradually; there is no average of local inhomogeneous resonance fields corre- torque free solution in high fields. The BLS and MOKE mea- sponding to the distribution of local exchange coupling surements using Fe-whisker/Cr/Fe 001 samples having a strengths , and the broadening of this BLS resonance peak is low density of atomic steps exhibit much weaker coupling related to the distribution of the local resonance fields. On than that obtained from the first-principles calculations,27 and the other hand, in the MOKE studies a complete saturation is there is strong evidence see above that the measured observed only after the external field reaches a value corre- samples can be fully saturated in sufficiently large external sponding to the maximum value of the critical field H fields. The discrepancy between the experimental results and 2 dis- tribution: this maximum value of H the theoretical expectations is very likely caused by the pres- 2 is larger than the field corresponding to the rf resonance peak algebraic average . ence of interface alloying at the Fe/Cr interface. Interface The observed differences between the MOKE and BLS mea- alloying significantly decreases the exchange coupling and surements clearly indicate that the coupling through Cr is not may even change the functional angular dependence of the even homogeneous across an area a few micrometers in di- coupling between the Fe layer magnetic moments. It is inter- ameter corresponding to the laser spot size in the BLS mea- esting to note that the first calculations carried out by Stoef- surements. It is important to point out that it is very difficult fler and Gautier14 yielded an angular dependence that is well to exactly reproduce the strength of the exchange coupling described by bilinear and biquadratic exchange coupling from one Cr growth to the next. Small variations in the terms Eq. 1 with J2 /J1 14%. This calculation is in growth conditions can lead to variations in J agreement with our observations. However, the calculations 1 as large as a factor of two. It was possible to obtain the results shown in were carried out for a spin system that was not completely Fig. 4 only after an extensive series of experiments using relaxed. Fully relaxed first-principle calculations of the an- different growth conditions. Quantitatively reproducible re- gular dependence of the interlayer exchange coupling in sults were obtained only for a very specific set of conditions: samples having an intermixed Fe/Cr interface are needed in the RHEED intensity oscillations must be cuspy and unat- order to address this problem of the theoretical angular de- tenuated during the growth; the RHEED specular spot profile pendence of the exchange coupling in the presence of al- corresponding to an intensity maximum must be as narrow as loyed interfaces. the spot profile for the bare whisker surface; and, most im- portantly, the minimum RHEED intensities must remain ROLE OF INTERFACE ALLOYING very close to zero throughout the entire growth. It is difficult to satisfy all of these conditions during any one growth. The Recently, Freyss, Stoeffler, and DreysseŽ28 investigated the RHEED intensity oscillations shown in Fig. 2 in which the phase of the exchange coupling for intermixed Fe/Cr inter- intensity minima gradually increase during the growth is faces. The calculations were carried out using a tight-binding common; see Fig. 2 caption. The problem in establishing the d-band Hamiltonian and a real-space recursive method for required growth conditions lies in the fact that the Fe whis- two mixed layers: Fe 001 /CrxFe1 x /Cr1 xFex /Crn , where kers must be lightly attached to the Mo support block in n represents the number of pure Cr atomic layers. This simu- order to avoid damaging them. Thus the thermal contact be- lates our experimental studies which were carried out on tween whisker and support block is not reproducible, and specimens for which the first few atomic Cr layers were hence the temperature of the whisker cannot be precisely grown at lower substrate temperatures where the surface al- measured. Variations in whisker temperature during the Cr loying is mainly confined to the two interface atomic layers. growth lead to variations in interface alloying at the Fe/Cr The calculations were able to account for two important ex- interface, and hence lead to variations in the coupling perimental observations. First, the crossover to antiferromag- strength between the Fe whisker and a subsequently grown netic coupling and onset of short-wavelength oscillations Fe film. was predicted to occur at 4­5 ML of Cr, in good agreement In our view the observation of a gradual approach to satu- with our observations, see Fig. 4, and in agreement with the ration using MOKE does not necessarily imply an exchange NIST studies using the SEMPA imaging technique. Second, coupling energy proportional to ( )2 as proposed in the the phase expected for perfect interfaces AF coupling for an Slonczewski magnetic proximity model.26 MOKE measure- even number of Cr monolayers, FM coupling for an odd ments can only be carried out to fields as large as the maxi- number of Cr monolayers was found to be reversed for x mum available. This means that if sufficiently large applied 0.2. In other words, a Cr layer containing more than 20% PRB 59 EXCHANGE COUPLING THROUGH SPIN-DENSITY . . . 14 527 iron acted as if it were part of the ferromagnetic iron layer whisker/11Cr/2Ag/20Fe 001 /20Au. The growth of Ag at rather than acting like part of the Cr spacer layer. This result Tsub 105 °C resulted in nearly perfect layer by layer is also in very good agreement with our studies. Samples for growth. The growth of Cu using Tsub 65 °C was less perfect which the Fe/Cr interface was prepared at 150 °C, and show- but still showed well defined RHEED oscillations, even for ing only a weak interface diffusion (x 0.2),15,16 exhibited a the second anti-Bragg condition, indicating that the atomic phase for the exchange coupling that was reversed from that deposition of the Cu layers was reasonably smooth. Mea- expected for perfect interfaces. surements carried out using BLS and MOKE gave similar We tried to avoid interface mixing by decreasing the sub- results, and the results for a 1 ML interface layer were simi- strate temperature during the growth of the first Cr atomic lar to the results for the 2 ML interface layer for both the Cu layer. We found that the quality of the subsequently depos- and Ag layers. The results of BLS and MOKE studies were ited Cr layers was noticeably poorer once the initial substrate qualitatively the same as those shown in Figs. 6 and 7. Speci- temperature was decreased below 100 °C. Since we were not mens were prepared during the same molecular beam epitaxy able to defeat interface mixing using a direct approach, we MBE growth having two different spacer configurations on decided to use heterogeneous Cr spacers. N Cr layers were the same whisker. The Cr 001 spacer was common to both deposited on the Fe-whisker substrate using the standard regions, but a shutter covered half the whisker during the Cu recipe known to produce a smooth layer-by-layer growth and Ag depositions. In this way the effect of Cu or Ag layers Ts,opt 300 °C, see the section on growth . However, the on the exchange coupling could be studied free from uncer- last deposited atomic layer, the N 1 layer, was prepared tainties in the coupling strength due to slight variations in the using codeposition of Cr with Fe to produce a Cr-Fe alloy. Cr growth conditions. The results of the measurements using RHEED intensity oscillations and RHEED patterns were ba- 2 ML of Cu or Ag were as follows: sically unchanged and showed that the Cr-Fe alloy layer was 1a Fe whisker/11Cr/20Fe/20Au; J atomically flat. Two alloy concentrations were used: Cr 1 0.4 erg/cm2, J2 0.18 erg/cm2; 85%-Fe 15% and Cr 65%-Fe 35%. BLS and MOKE 1b Fe whisker/11Cr/2Cu/20Fe/20Au; J measurements29 revealed that the exchange coupling be- 1 0.81 erg/ cm2, J tween a thin 20 ML iron film and the whisker substrate was 2 0.3 erg/cm2; 2a Fe whisker/11Cr/20Fe/20Au; J essentially the same as that observed for a pure N layer Cr 1 1.3 erg/cm2, J2 0.35 erg/cm2; spacer layer. The system behaved as if the Cr alloy layer 2b Fe whisker/11Cr/2Ag/20Fe/20Au; J formed part of the iron film. This result strongly supports the 1 1.0 erg/ cm2, J idea that interface alloying at the Fe-whisker/Cr interface 2 0.35 erg/cm2. The behavior of the exchange coupling in the Fe-whisker/ leads to the observed phase reversal of the short-wavelength 11Cr/1­2Cu/Fe 001 samples is most surprising. The exchange coupling oscillations relative to a system having strength of the exchange coupling in these samples was perfect interfaces. Moreover, this picture has recently re- found to increase twofold compared to that observed in ceived strong support from magnetic circular dichroism mea- samples having a simple 11 ML Cr spacer layer. This is an surements carried out by Schneider et al.30 Their data have unexpected result. In all of our previous studies, using Fe/ shown that the magnetic moment of the first Cr layer depos- Cu/Fe 001 structures containing a wide range of heteroge- ited on iron is parallel with the iron moment. neous Cu spacers, the exchange coupling was always found The fact that one needs only a small concentration of Fe to decrease due to the presence of alloyed atomic layers in- to reverse the phase of the coupling is a rather surprising side the nonmagnetic spacer.31 The situation for the Fe/Cr/ result, especially considering the further recent calculations Cu/Fe 001 specimens is definitely different. Mirbt and Jo- by the Strasbourg group.28 The article by Freyss, Stoeffler, hansson presented calculations32 that are in accord with our and DreysseŽ mentioned above28 also contains calculations results. Their calculations show that the enhanced coupling carried out for a single interfacial alloyed layer: they treated strength in Fe/Cr/Cu/Fe 001 samples is due to a change in the system Crn /CrxFe1 x /Fe(001), where Fe 001 is a thick the spin dependent reflectivity of the Cr spacer electrons at substrate and n is the number of pure Cr atomic layers. Their the Cr/Cu/Fe interface. The presence of the Cu atoms calculations showed that for iron concentrations less than changes the spin dependent interface potential due to hybrid- 50% the Cr-alloy layer behaves like a pure Cr atomic layer. ization of the Cu electron states with the Fe electron states. This result is not in agreement with our experimental obser- Since the Fe majority spin band lies closest to the Fermi vations that even a concentration of Fe as small as 15% level the effect of hybridization will be most pronounced for causes the alloy layer to behave like Fe rather than like pure the majority spin Fe band. The hybridization with Cu results Cr. The discrepancy with theory remains to be explained. in a downward energy shift that moves the Fe majority spin band below the Fermi level. An energy gap is created at the ROLE OF MULTIPLE SCATTERING Cu/Fe interface, and consequently the majority spin electrons in Cr undergo a nearly perfect reflection. The states for mi- Heterogeneous Cr spacers were prepared in order to test nority spin electrons are very little affected by the Cu, and the effect of interface composition on the exchange coupling therefore their reflectivity is left unchanged. It follows that strength. Two specimens were grown with a Cu interface the spin reflection asymmetry is increased leading to an in- layer between the Cr spacer and the Fe thin film: Fe-whis- creased coupling.33­35 The effect of a Ag spacer on the cou- ker/11Cr/1Cu/20Fe 001 /20Au and Fe-whisker/11Cr/2Cu/ pling in Fe/Cr/Ag/Fe is less dramatic. Calculations show that 20Fe 001 /20Au, where the integers represent the number of the spin asymmetry in reflectivity is somewhat decreased atomic layers. Two specimens were grown with a silver in- leading to an overall decrease in the exchange coupling. The terface layer: Fe-whisker/11Cr/1Ag/20Fe 001 /20Au and Fe- theoretical calculations of Mirbt and Johansson suggested 14 528 HEINRICH, COCHRAN, MONCHESKY, AND URBAN PRB 59 that a proper model for exchange coupling through spin- the top Cr surface atomic layer is smooth, with large atomic density waves in Cr has to include two contributions: a a terraces corresponding to those of the Fe whisker, and is spin dependent potential due to the magnetic moments on the unaffected by interface alloying during the deposition of the antiferromagnetic Cr atoms; b a spin dependent potential at Mn. Therefore variations in the exchange coupling due to the the Fe/Cr and Cr/Fe interfaces. The first contribution for Cr addition of the Mn layers are primarily due to the presence of layers thinner than 24 ML can be described by a Heisenberg- the Mn atomic layers and their magnetic state. There is no like Hamiltonian14 with AF coupling between the Cr mag- intermediate Cr-Mn mixed region similar to the Cr-Fe mixed netic moments on adjacent 001 planes and a strong AF region that occurs at the Fe-whisker/Cr interface. coupling between the Cr and Fe atomic moments at the in- The following samples were studied: i Fe 001 /11Cr/ terfaces for perfect interfaces, and with modified exchange 1Mn/20Fe 001 /20Au; ii Fe 001 /11Cr/2Mn/20Fe 001 / interactions for alloyed interfaces.28 The second contribution 20Au; iii Fe 001 /12Cr/3Mn/20Fe 001 /20Au; and iv leads to spin dependent reflectivities at the interfaces. The Fe 001 /11Cr/3Mn/20Fe 001 /20Au. Sample i was grown spin reflectivites are parameters closely associated with para- together with Fe 001 /11Cr/20Fe 001 /20Au on the same magnetic behavior. In the Mirbt and Johansson calculations32 whisker using a shutter. This configuration allowed one to the contribution of the spin-density wave oscillatory ex- compare the strength of the coupling in samples with and change coupling is out of phase with that of the multiple without Mn but having a common Cr layer. MOKE and BLS scattering in samples of Fe/Cr/Cu/Fe. This means that ac- measurements showed that 1 ML of Mn did not change the cording to their theory the strength of the exchange coupling phase of the coupling. The coupling was found to be AF for should be decreased by the presence of a Cu layer at the both the 11 ML Cr spacer and the composite spacer, speci- interface. However, the measured exchange coupling in Fe/ men i . The BLS and MOKE results were qualitatively simi- Cr/Cu/Fe 001 samples was found to be increased compared lar to those shown in Figs. 6 and 7. The exchange coupling to that in samples having a pure Cr spacer layer Fe/Cr/Fe . strengths for i were as follows: Fe 001 /11Cr/20Fe/20Au; The experimental result implies that the spin-density and J multiple scattering contributions to the total exchange cou- 1 0.68 erg/cm2, J2 0.24 erg/cm2; Fe 001 /11Cr/1Mn/ 20Fe/20Au; J pling act in phase. The phase of the multiple scattering is 1 1.7 erg/cm2, J2 0.55 erg/cm2. Note that the exchange coupling was significantly enhanced by the Mn very dependent on the structural details of the interfaces, layer. It is commonly believed that the Mn magnetic moment consequently it is not surprising that the observed phase of is strongly ferromagnetically coupled to the Fe magnetic the multiple scattering in real Fe/Cr/Fe samples was found to moment37,38 and therefore the sign of the coupling should be be opposite to that calculated assuming ideally smooth inter- unchanged in agreement with the observations. For the com- faces. posite specimen containing 2 ML of Mn, Fe 001 /11Cr/2Mn/ 20Fe/20Au, the results were J1 0.62 erg/cm2, J2 MAGNETIC STATE OF Mn 001... IN Fe/Cr/Mn/Fe 0.14 erg/cm2. Therefore the phase of the coupling was again found to be the same as that for the pure Cr layer. The It is known that even small concentrations of Mn in Cr second atomic layer of Mn was expected to be AF aligned results in a strong and commensurate antiferromagnetism.36 with respect to the first Mn atomic layer.37,38 Assuming that It was therefore thought to be of interest to investigate the the Mn 001 planes are magnetically uncompensated, this phase and the strength of the exchange coupling between Fe would lead to a phase reversal of the exchange coupling layers separated by layers of a Cr-Mn alloy. To this end we when specimen ii was compared with the specimen con- attempted to grow Fe/Cr-Mn/Fe structures. Unfortunately we taining a pure Cr interlayer. Such a phase reversal was not found that the Mn atoms have very strong tendency to seg- observed. The exchange coupling in sample iii was found regate on the surface during the growth. It was necessary to to be ferromagnetic and the coupling in sample iv was maintain a substrate temperature greater than 200 °C in order found to be antiferromagnetic. This shows that the exchange to obtain a good layer by layer growth. At this temperature coupling oscillates with the same phase and the same peri- the top surface layer contained a strongly enhanced concen- odicity of 2 ML as was observed using pure Cr spacer layers. tration of Mn 50% . In view of this surface segragation, Although the sign of the coupling for the 3 ML Mn case and since the interfaces play a very crucial role in exchange sample iv was the same as for a pure Cr spacer of the coupling, we decided to grow pure layers of Mn between the same thickness, the magnetizations of the whisker and the 20 Cr and the Fe layers. Eleven or 12 ML of Cr were grown on ML Fe film were noncollinear in the ground state, H 0; see an Fe 001 whisker using growth conditions optimized for Fig. 9. For an 11 ML pure Cr spacer the whisker and Fe thin layer-by-layer growth see the section on growth . Mn layers film magnetizations are oriented antiparallel at H 0. were deposited on the Cr at a substrate temperature of The presence of a strong biquadratic exchange coupling in 120 °C. The substrate was allowed to cool to room tempera- the sample with the 3-ML-thick Mn layer, sample iv , can tures and 20 ML of Fe 001 were deposited on the Mn, and be related to the interface roughness. The growth of the third a protective layer of 20 ML of Au 001 were deposited on atomic layer of Mn did not proceed as well as for the first the iron. At 120 °C the deposition of the first two atomic two atomic layers. Consequently the third deposited Mn layers of Mn proceeds in a good layer by layer growth with atomic layer was probably partially filled, resulting in atomic large RHEED intensity oscillations at the second anti-Bragg terraces and corresponding atomic steps. The magnetic mo- scattering condition. At substrate temperatures well below ments around the atomic steps are probably magnetically un- 100 °C the Mn does not segregate on Fe. In this way one is compensated, and this could result in a random oscillation of able to grow well defined Fe/Cr/Mn/Fe structures having the magnetization between being parallel and antiparallel to smooth and abrupt interfaces. It should be pointed out that the Fe film magnetic moment. The coupling between the Fe PRB 59 EXCHANGE COUPLING THROUGH SPIN-DENSITY . . . 14 529 FIG. 10. The critical field H2 obtained from MOKE measure- ments as a function of the Fe 001 thickness for an Fe-whisker/ FIG. 9. Longitudinal MOKE signal for the sample Fe/11Cr/ 11Cr/wedged Fe/20Au specimen. The Cr layer was deposited using 3Mn/20Fe/20Au 001 . J2 0.8 erg/cm2, J1 J2 . The rapid change optimal conditions for a smooth growth. The wedge-shaped iron in the MOKE signal around H 0 corresponds to the remagnetiza- film was grown by means of a slowly moving shutter. tion process of the Fe whisker. Note that there is no field region where the magnetic moment of the 20-ML-thick Fe film lies anti- THE DEPENDENCE OF THE EXCHANGE COUPLING parallel to the Fe-whisker magnetization. The ground state is non- ON THE THICKNESS OF THE Fe FILM collinear. The spin-dependent potential in multilayer films creates electron confinement and resonant states which are respon- and Mn atoms is most likely confined to a nearest neighbor sible for the oscillatory behavior of the exchange coupling. exchange interaction, and that would result in a lateral spatial According to theoretical calculations44,45 such states are not variation of the coupling between the Mn and Fe atomic restricted to nonmagnetic spacers, but are also present inside moments thereby providing the proper conditions for the on- the ferromagnetic layers, and the coupling cannot be entirely set of a strong biquadratic exchange coupling.23 described by an interaction that is localized at the interfaces. The assumption that the magnetic state of Mn in Fe/Cr/ The energy terms coming from the electron confinement in Mn/Fe 001 structures can be described by commensurate the ferromagent layers due to multiple reflections and the antiferromagnetism with uncompensated 001 planes is not interference of such states with the states inside the spacer necessarily correct. In recent calculations by Krušger et al.39 layer results in a variation of the interlayer exchange cou- the magnetic structure of bct Mn in bulk was studied as a pling with the ferromagnetic layer thickness. Calculations function of the tetragonal distortion, c/a. The calculations and experimental studies on the Co/Cu/Co 001 Ref. 46 showed that bct Mn grown on Fe 001 is in a magnetic state and the Fe/Au/Fe 001 systems47 have shown that the ex- that is at the border line between the AF1 configuration, change coupling contains a component that oscillates as a having the magnetic moments parallel in 001 planes, and function of the ferromagnetic layer thickness. However, the the AF3 110 configuration, having ferromagnetic planes ori- oscillatory part is smaller than the total strength of the ex- ented along 110 , and fully compensated 001 planes hav- change coupling so that the sign of the coupling is deter- ing zero net magnetic moment. The calculations showed that mined by the thickness of the nonferromagnetic spacer layer. the lowest energy state is just marginally the AF3 110 state, Okuno and Inomata48 reported a strong oscillatory depen- only 4 meV/atom lower in energy than the AF1 state. The dence on iron thickness of the exchange coupling in Fe/Cr/ AF3 110 state would not lead to an alternating sign of ex- Fe 001 specimens. The period of the oscillation was 6 ML. change coupling with increasing Mn thickness, and would be However, the specimens used in their work were multilayers in agreement with our experimental observations. The above characterized by rough interfaces, and the exchange coupling calculations show that the independence of the sign of the exhibited no short period 2 ML variations with Cr thick- exchange coupling on Mn thickness is not at variance with ness. We have measured the dependence of the exchange expectations based on the assumption that Mn grown on coupling strength on iron film thickness using an Fe 001 Fe 001 takes on the bulk bct Mn structure. This view is whisker substrate, an 11 ML layer of Cr, and a wedge-shaped further supported by recent theoretical and experimental Fe layer prepared by means of a slowly moving shutter. This studies. Wu and Freeman40 showed that one atomic layer of structure was capped by a 20 ML layer of gold. The Cr was Mn on Fe 001 is compensated ordered antiferromagneti- deposited using optimum conditions for a smooth growth. cally . Recent experimental studies using magnetic circular The results are shown in Fig. 10. There is no evidence for an x-ray dichroism MCXD Refs. 41 and 42 showed no net oscillatory dependence of the coupling strength on iron film magnetic moment for higher Mn coverages on Fe 001 . thickness. Figure 10 clearly shows that the upper saturation Also, recent electron capture experiments using the scatter- field H2 increases gradually with decreasing Fe layer thick- ing of He ions showed no magnetic moment for higher Mn ness as expected from micromagnetic calculations assuming coverages on Fe.43 These results are consistent with the con- a constant value for the strength of the interlayer exchange clusion that the Mn 001 atomic planes are antiferromagneti- coupling. We have also prepared a specimen cally ordered and magnetically compensated. Fe 001 /11Cr/nFe/20Au in which four different iron thick- 14 530 HEINRICH, COCHRAN, MONCHESKY, AND URBAN PRB 59 two iron whisker substrates; each substrate carried two speci- mens containing the same 11 ML of Cr. For Fe whisker #1 the structure and coupling strengths observed were: 1a whisker/11Cr/20Fe/20Au; J1 0.82 erg/cm2, J2 0.3 erg/cm2; 1b whisker/11Cr/20Fe/11Cr/20Au; J1 1.6 erg/cm2, J2 0.33 erg/cm2. Clearly the substitu- tion of Cr for Au at the upper Fe film surface caused a substantial increase in the coupling strength. For Fe whisker #2 the structure and coupling strengths observed were: 2a whisker/11Cr/18Fe/11Cr/20Au; J1 1.75 erg/cm2, J2 0.36 erg/cm2: 2b whisker/11Cr/15Fe/11Cr/20Au; J1 1.25 erg/cm2, J2 0.35 erg/cm2. In the latter structure only the Fe thickness was varied by 3 ML and this change has clearly had an effect FIG. 11. Fe thickness dependence of the critical field H2 as on the bilinear coupling strength J1 . Note that the biqua- measured using MOKE , using BLS , and the critical field dratic coupling term is essentially the same for all four speci- H1 obtained from MOKE measurements . All four samples mens. Since the exchange coupling for Cr/Fe/Cr films de- were prepared during the same MBE growth. The shutter was pends upon the Fe film thickness, it follows that the Fe/Cr moved three times by 2 mm along the whisker during the prepara- interfaces support the formation of electron resonance states tion of the Fe thin films. This means that the Cr 001 spacer was in the Fe films. On the other hand, the Fe/Au interfaces tend common to all samples and each sample was 2 mm long. The solid to suppress electron resonance states. The full thickness de- lines are computer fits to the experimental data using the functional pendence of the exchange coupling in the Fe whisker/Cr/Fe/ form (const 1/d). This functional form is obtained from simple Cr/Au 001 system will be carried out in a separate study. micromagnetic calculations Ref. 4 assuming a constant value for the exchange coupling and assuming that the Fe whisker can be treated like a thick film. CONCLUSIONS nesses corresponding to n 10, 20, 30, 40 ML were grown Fe whiskers provide the best available templates for the on the same whisker by means of a moveable shutter. Each growth of Fe/Cr/Fe 001 structures because their surfaces are iron thickness region was 2 mm long. Here again, the Cr atomically smooth over regions whose dimensions exceed a layers were deposited using optimum conditions to produce a micron. By monitoring the RHEED intensity oscillations and smooth growth. The results of the measurements are shown specular spot line profiles during the growth one is able to in Fig. 11 and listed in Table I. There is no evidence for an prepare atomically smooth Cr 001 layers for which the last oscillatory dependence of the exchange coupling on iron deposited Cr atomic layer grows with a smoothness similar thickness. No dependence on Fe film thickness of the ex- to that of the initial Fe whisker template. Samples grown at change coupling was also reported by Parkin.49 We conclude the optimum temperature 300 °C showed unattenuated that Fe 001 /Cr/Fe 001 /Au samples having a low density of RHEED intensity oscillations having well defined cusps at interfacial steps, and that exhibit short-wavelength oscilla- the RHEED intensity maxima. The first monolayer of Cr tions as a function of the Cr layer thickness, display no mea- exhibits a unique behavior; the first RHEED intensity oscil- surable variations of the exchange coupling strength as a lation shows a strong peak having a very sharp cusp even at function of the Fe film thickness. It appears that the ex- substrate temperatures as low as 150 °C. This indicates that change coupling between Fe layers separated by a Cr spacer the first atomic layer is very smooth and reproduces the tem- can be ascribed to interactions that are localized to the inter- plate. The situation changes when Cr is deposited on a Cr faces. However, our recent experiments do indicate that the template. In that case the growth of Cr proceeds layer by exchange coupling is sensitive to the Fe film thickness when layer only if the substrate temperature is adjusted to an op- the iron film is capped with Cr to produce the structure timum growth temperature, Ts,opt 250­ 300 °C. In order to Fe 001 /11Cr/Fe/Cr/20Au. Specimens were prepared using obtain a final Cr atomic layer having a low density of atomic steps one must deposit the first Cr layer at a temperature greater than 100 °C. ARAES studies have shown that inter- TABLE I. The dependence of the bilinear J1 and biquadratic J2 face alloying is present at the Fe-whisker/Cr interface even at exchange coupling parameters on iron film thickness for an substrate temperatures as low as 100 °C. This means that the Fe-whisker/11 Cr/d Fe/20Au specimen, where d is the iron film first deposited layer of Cr is atomically smooth but is chemi- thickness in monolayers. J1 and J2 are in erg/cm2; see Eq. 1 of the cally inhomogeneous due to interface alloying with the Fe text. substrate as the result of an atom exchange mechanism. It should be noted that this atom exchange mechanism does not BLS MOKE operate when Fe is deposited on Cr, so that, in principle, the d J1 J2 J1 J2 Cr/Fe interface can exhibit an abrupt change in composition 10 0.74 0.23 1.0 0.25 in contrast with the Fe/Cr interface. We showed that the 20 1.02 0.23 1.1 0.33 initial stages of the Cr growth strongly affect the strength 30 0.96 0.23 1.15 0.31 and the type of exchange coupling. Lowering the substrate 40 0.95 0.23 1.08 0.34 temperature during the growth of the first Cr atomic layer helps to increase the strength of the exchange coupling. PRB 59 EXCHANGE COUPLING THROUGH SPIN-DENSITY . . . 14 531 BLS and MOKE measurements have shown that the ex- further studied by fabricating specimens having the structure change coupling in Fe/Cr/Fe 001 structures having a low Fe 001 whisker/NCr/nX/20Fe 001 /20Au where N is the density of atomic steps is well described by the sum of bi- number of atomic layers of Cr and n is the number of atomic linear and biquadratic angular terms; Eq. 1 . The bilinear layers of a different metal X. We used X Cu, Ag, and Mn. exchange coupling strength exhibits short- and long- The number of Cr atomic layers was restricted to N 11 and wavelength oscillations. The long-wavelength oscillations 12 for these experiments. The results of studies using MOKE are dominant for Cr thicknesses less than 8 ML. The short- and BLS to investigate specimens containing Cu or Ag in- wavelength oscillations are dominant for thicknesses greater terface layers indicated that the exchange coupling through than 8 ML. The biquadratic coupling term is always present, atomically smooth Cr layers greater than 8 but less than 24 but is less than 20% of the bilinear exchange coupling term. ML thick can be understood as a combination of a spin- The Fe magnetizations are always collinear in the ground density wave contribution describable by a Heisenberg type state of the Fe/Cr/Fe 001 system: they are either parallel of Hamiltonian14 plus a quantum well contribution due to FM coupling or antiparallel AF coupling . It has been multiple scattering at the interfaces. This conclusion is sup- pointed out that deviations between measured magnetization ported by the recent first-principles calculations reported by loops and magnetization loops calculated using bilinear and Mirbt and Johansson.32 However, alloying at the interface biquadratic interfacial coupling terms, Eq. 1 , are caused by between the iron-whisker substrate and the Cr, mediated by lateral variations in the exchange coupling parameters. These an atom exchange mechanism, severely affects the exchange lateral variations amount to 15% of the mean value and are coupling through Cr layers less than 8 ML thick. In this characterized by a lateral scale that is smaller than 10 m. regime the exchange coupling exhibits a large antiferromag- They are very likely caused by interfacial alloying at the netic background plus a small superimposed short- Fe/Cr interface. Interface alloying affects several features of wavelength contribution. The Fe/Cr transitional region re- the short-wavelength oscillations: a The first crossover to verses the phase of the short-wavelength oscillation and antiferromagnetic coupling occurs at 4 ML; b the strength severely reduces the strength of the coupling relative to that of the short wavelength oscillations is weak for Cr thick- expected for a perfectly sharp interface. nesses between 5­9 ML; c the phase of the short- The results of MOKE and BLS experiments using speci- wavelength oscillations is reversed from that expected for mens containing Mn interface layers (X Mn) can be under- perfect interfaces and a Cr spacer containing a spin-density stood assuming that the 001 planes of the Mn are fully wave; d the strength of the measured exchange coupling is magnetically compensated. This assumption agrees with re- significantly smaller than that obtained from first-principles cent theoretical calculations39 for bulk bct Mn having the Fe electron band calculations. Recent theoretical calculations in-plane lattice spacing. It is also in agreement with magnetic have been able to explain points a and c . Points b are d x-ray dichroism and electron capture measurements carried have not yet been fully addressed, but one intuitively ex- out on Mn grown on an Fe 001 template.41­43 The phase of pects, and the results of calculations indicate,14 that a first- the exchange coupling through the Fe-whisker/Cr/Mn/ principles calculation taking into account interfacial alloying Fe 001 samples was unaffected by the presence of the Mn at the Fe/Cr interface would lead to significantly decreased layers: the strength of the coupling was increased by the values of the exchange coupling compared to those obtained factor 2.5 for the case of 1 ML of Mn. The specimen con- for perfect interfaces. However the full angular dependence taining three atomic layers of Mn exhibited a noncollinear of the exchange coupling should be calculated in order to magnetic ground state and a large contribution to the biqua- explain the experimental fact that the coupling can be de- dratic exchange coupling term Eq. 1 . This noncollinear scribed by bilinear and biquadratic coupling terms and not by ground state and relatively large biquadratic exchange is the proximity effect term ( )2 that is expected to be valid most likely caused by interface roughness. Uncompensated for ideal interfaces. magnetic moments of the Mn atoms in partially filled atomic The exchange coupling was not found to depend in any terraces can result in magnetic frustration of the Fe magnetic measurable way on the Fe film thickness when the iron film moments at the Mn/Fe interface and this frustration would was terminated with a gold layer. This means that the ex- likely result in a strong contribution to the biquadratic ex- change coupling in Fe-whisker/Cr/Fe/Au 001 is not affected change coupling. Further studies of the net magnetic moment by quantum well and resonance states in the Fe film. There in Mn layers are needed, perhaps using magnetic x-ray di- is, however, evidence that the thickness of the iron film does chroism, to find out whether the noncollinear ground state in affect the coupling strength when the iron surface is bounded these samples is caused by interface roughness or whether it by Cr at both surfaces. Experiments on specimens containing constitutes an intrinsic property of Fe/Cr/Mn/Fe 001 speci- a Cr spacer layer and a thin Fe layer capped by Cr will be the mens containing thicker Mn layers. subject of future investigations. First-principles calculations are needed to understand why electron standing-wave effects ACKNOWLEDGMENTS in an iron film terminated by gold appear to be absent com- pared with those in a thin film terminated by Cr at each The authors would like to thank K. Myrtle for his help surface. with specimen preparation. The authors would also like to The role played by the interface in exchange coupling thank the Natural Sciences and Engineering Research Coun- between iron films separated by a chromium interlayer was cil of Canada for grants that supported this work. 14 532 HEINRICH, COCHRAN, MONCHESKY, AND URBAN PRB 59 1 J. Unguris, R. J. Celotta, and D. T. Pierce, Phys. Rev. Lett. 67, 25 A. Schreyer, J. F. Ankner, Th. Zeidler, H. Zabel, M. Schafer, J. 140 1991 ; 69, 1125 1992 . A. Wolf, and P. Grušnberg, Phys. Rev. B 52, 16 066 1995 . 2 S. T. Purcell, W. Folkerts, M. T. Johnson, N. W. E. McGee, K. 26 J. C. Slonczewski, J. Magn. Magn. Mater. 150, 13 1995 . Jager, J. aan de Stegge, W. B. 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