PHYSICAL REVIEW B VOLUME 59, NUMBER 1 1 JANUARY 1999-I Biquadratic exchange in ferromagnetic/nonferromagnetic sandwiches: A spin-polarized low-energy electron microscopy study T. Duden and E. Bauer Department of Physics and Astronomy, Arizona State University, Tempe, Arizona 85287-1504 Received 23 June 1998 The magnetic domain structure of Co/Au/Co sandwich layers grown on W 110 is studied in situ by spin-polarized low energy electron microscopy as a function of Au spacer layer and top Co layer thickness with the goal to better understand the causes and consequences of biquadratic coupling for the resulting domain structure. It is found that biquadratic coupling not only strongly influences the coupling between the layers near the zero of the bilinear coupling but also at spacer thicknesses at which strong ferromagnetic coupling occurs. Biquadratic coupling appears in a spin reorientation transition between 4 and 5 monolayers. The existence of bilinear and biquadratic coupling produces a wrinkled in-plane magnetization. S0163-1829 99 05601-5 I. INTRODUCTION wich by spin-polarized low energy electron microscopy SPLEEM Ref. 14 in zero external field. A prototype sys- It is now well established that in many ferromagnetic/ tem which had been studied by a variety of techniques be- nonferromagnetic thin film systems sandwiches and super- fore, Co/Au/Co, was chosen for this purpose. Contrary to the lattices in addition to the Heisenberg bilinear exchange in- previous work, in which the Co layers had in general perpen- teraction between the magnetizations in neighboring layers dicular magnetization, experimental conditions were used also a biquadratic exchange interaction exists. The interlayer which lead to predominant in-plane magnetization. A strong exchange energy between neighboring layers i,j is then uniaxial in-plane magnetization is obtained if the first Co layer is grown epitaxially on W 110 . The out-of-plane Eij J1 1 cos J2 1 cos2 , 1 M component of this layer, which leads to a wrinkled mag- netization, decreases rapidly with thickness15 and allows the where J1 and J2 are the bilinear and biquadratic coupling simultaneous study of in-plane and out-of-plane coupling parameters and is the angle between the magnetizations while the strong in-plane anisotropy provides a fixed refer- Mi ,Mj in the two layers. The biquadratic exchange is in part ence for the coupling with the next layer. intrinsic, that is a property of the electronic structure of the According to previous studies of perpendicularly magne- system, in part extrinsic, that is a consequence of the geo- tized sandwiches the Au spacer thickness of maximum AF metric structure of the system. Several extrinsic mechanisms coupling is 5.5,16 5.35,17 or 4.8 Ref. 18 monolayers ML , have been proposed and in part verified: nonmagnetic the second thickness with AF coupling 9.4 Ref. 16 or 10.1 spacer thickness fluctuations,1 loose spins inside the spacer Ref. 17 ML, with maximum F coupling in between at about or at its interfaces,2 and magnetic dipole formation due to the 7 ML. Thus 90° coupling can be expected at about 4 ML and roughness of the magnetic layers.3 The intrinsic nature of the 6 ML but not at 7 and 8 ML unless J2 is abnormally large. biquadratic exchange has been demonstrated in a number of These considerations determined the Au thickness range se- theoretical papers.4­9 Recent model calculations show nicely lected. The thickness of the top Co layer was varied from the dependence of J2 upon spacer thickness and interface 1 to 7 ML in order to cover both perpendicular and in-plane conditions.10 J2 is oscillating like J1 , has about twice the magnetization regions. periodicity of J1 , is phase shifted relative to J1 so that maxima of J2 approximately coincide with zeroes of J1 and II. EXPERIMENTAL is much smaller than J1 . The phase shift gives the possibility that the biquadratic coupling determines the magnetic struc- The experiments were performed in the original LEEM ture of the system near the crossover from ferromagnetic F instrument described in Ref. 19 in which the original field to antiferromagnetic AF coupling. When J1 0, then emission gun was replaced by a spin-polarized illumination 90° in the minimum energy configuration. This 90° cou- system with polarization manipulator.20 The base pressure of pling had lead to the discovery of the biquadratic coupling the instrument was 2 10 10 Torr. During the depositions by Kerr microscopy.11 the pressure stayed in the 10 10 Torr range and was typically The fact that J2 can be as large or even larger than J1 in around 6 10 10 Torr. The W 110 crystal could be heated certain thickness ranges can lead to a rich magnetic phase from the back side by radiation up to 500 K and by electron diagram, with an asymmetric phase for large J2 /J1 bombardment up to 2000 K. It was precleaned in the prepa- ratios.12,13 The goal of this paper is to explore the zero field ration chamber by heating for several hours in an oxygen region of this phase diagram by varying the thickness of the atmosphere at a pressure of about 2 10 6 Torr. Between nonmagnetic spacer layer and of one of the ferromagnetic the experiments it was cleaned regularly by annealing at ap- layers. This can be done most conveniently by imaging the proximately 1400 K in 5 10 7 Torr oxygen for 30 min in magnetic domain structure during the growth of the sand- the preparation chamber, followed by flashing to 2000 K in 0163-1829/99/59 1 /474 6 /$15.00 PRB 59 474 ©1999 The American Physical Society PRB 59 BIQUADRATIC EXCHANGE IN . . . 475 FIG. 1. LEEM images of the submonolayer growth of Co on W 110 at about 750 K. Electron energy 1.5 eV, field of view 10 m a , c , d and 8 m b diameter. For explanation see text. FIG. 2. Typical SPLEEM image series of a 7 Co/6 Au/7 the main chamber. Criteria for a clean surface were i the Co/W 110 sandwich. Row a : Uncovered bottom Co layer. Row absence of W carbide segregation at surface imperfections b : 6 Au/7 Co. Row c : 3 Co/6 Au/7 Co. Row d : 7 Co/6 Au/7 upon annealing at about 1300 K and ii step flow growth of Co. Energy 1.2 eV; field of view here and in Figs. 5­7 approxi- the first Co monolayer during the deposition at 750 K. This mately 6 6 m2. growth pattern is very sensitive to surface contamination by segregated or adsorbed impurities which cause pinning of the contrast became very weak. On top of the stack, the second growth fronts and nucleation on the terraces. This is illus- Co layer was deposited in 1 ML doses. Typical deposition trated in Figs. 1 a and 1 b which show the initial growth of rates, both of Co and Au, were 1/8 ML/min. After each Co on a clean and on a contaminated surface, respectively. monolayer dose, a measurement cycle was performed to The first monolayer is filled in two steps: First, a pseudomor- monitor the resulting magnetic structure. The images were phic ps monolayer is formed in which close-packed acquired from the final screen using a CCD camera. For each cp islands nucleate and grow until the cp monolayer is magnetic image, two images resulting from the average of 64 completed. Figure 1 c shows a typical image of an incom- consecutive video frames were taken. Between each image plete ps ML; Fig. 1 d an image of an incomplete cp ML. the polarization vector of the incident electron beam was The strong contrast between the uncovered W surface and ps inverted. The magnetic signal was then obtained by a nor- ML regions in Fig. 1 c and between the ps and cp ML malized subtraction using the formula regions in Fig. 1 d allows a very accurate determination of the time needed to complete the ps and cp ML's. The A 127 100K I I / I I , 2 completion of the ps and the cp monolayer provides a precise where A is the normalized asymmetry, K is a contrast en- rate calibration before each experiment. After completion of hancement factor ranging from 7 to 15, and I ,I are the the cp monolayer the temperature was reduced to about 400 intensities of the images with opposite spin polarization. Due K and the deposition continued to the desired thickness to noise the resolution in these SPLEEM images is not as 7 ML . At this temperature the mobility is high enough and good as in the original LEEM images and varies from 20 to the two-dimensional nucleation rate low enough so that large 60 nm at the worst, depending upon the magnitude of the terraces form several 100 nm diameter which show pro- magnetic signal.21 nounced thickness dependent quantum size contrast. This contrast allows to observe the completion of the successively III. RESULTS grown layers and the characterization of the Co film rough- ness. Once the desired Co film thickness was reached, the The kind of SPLEEM images taken during the growth of heating was turned off. After the temperature had decreased the sandwiches is illustrated in Fig. 2. It shows three images to values slightly above RT Au was deposited as a spacer for every growth stage with P parallel to W 1-10 , 001 and layer. The Au deposition rate was calibrated before the Co 110 from the left to the right. The 1-10 direction is the deposition by the time needed to form 1 ML. Only the initial easy axis direction in the bottom Co layer. Therefore, there is growth of the Au layer could be monitored via quantum size no magnetic signal in the 001 image. The 110 image contrast. In the later stages of growth of the spacer layer the shows the perpendicular component of M. Row a shows 476 T. DUDEN AND E. BAUER PRB 59 on the Au-covered Co layer not shown . At 3 ML Co row c very weak in-plane contrast appears again and the out-of-plane contrast has its maximum intensity. It replicates the domain structure of the bottom layer perfectly in the regions in which the substrate step density is low and has much larger domains than the bottom layer in regions with high substrate step density. From 4 to 5 ML Co a dra- matic change occurs: the out-of-plane contrast disappears and strong contrast is now seen in both in-plane component images 0°, 1-10 and 90°, 001 . This M distri- bution does not change up to the thickest top Co layers stud- ied 7 ML, row d . The trends seen in Fig. 2 are, with minor deviations, typi- cal for Au spacer thicknesses from 4 to 8 ML, the thickest spacer studied. In the sandwich with 3 ML Au the in-plane and out-of-plane contrast does not disappear at about 2 ML Co and develops strongly again with increasing Co thick- ness, completely replicating the domain structure of the bot- tom layer. This is probably due to F coupling through gaps in the thin Au spacer. The trends seen with the thicker spacer layers may be summarized as follows: i The minimum contrast in the 0° image occurs at 2 ML Co. ii The out-of- plane component image has maximum contrast at 3­4 ML Co. iii The relative contrast of the 90° and of the 0° com- ponent images increases with the thickness of the Au spacer and also somewhat with increasing thickness of the top Co layer within the thickness range studied. These trends can be quantified by calculating pixel by pixel the local direction of M from the three M component images and displaying them FIG. 3. Distributions of the M directions extracted from the in a locally orthogonalized projection of the unit sphere. This images in Fig. 2. For explanation see text. is illustrated in Fig. 3 for the example shown in Fig. 2. The center is the 0° direction, to the left and the right are the the images of the bottom Co layer, row b those after depo- 90° directions and the out-of-plane directions are at the top sition of 6 ML Au, row c those after deposition of 3 ML and at the bottom. Figure 3 a shows that the 6 ML Au have Co, and row d of 7 ML Co on top of the Au spacer. The not changed the uniaxial anisotropy of the bottom Co layer. 6 ML Au weaken the signal due to spin-independent attenu- 1 ML Co b causes already such a strong magnetic signal ation but change neither the in-plane nor the out-of-plane M attenuation that the magnetic order in the bottom layer is component distribution row b . 1 ML Co strongly reduces hardly recognizable. 2 ML Co smears out the apparent M the contrast and at 2 ML Co no in-plane contrast is recog- distribution even more not shown . At 3 ML Co c the nizable while the out-of-plane contrast is already larger than out-of-plane orientation is dominating but at 4 ML Co d there is already a significant in-plane component which leads to intermediate M orientations and finally from 5 to 7 ML e and f , respectively M is completely in-plane but ro- tated with respect to the easy axis direction of the bottom Co layer. The angle of the maximum of the M distribution in the top Co layer of the complete sandwich depends upon the thickness of the Au spacer as shown in Fig. 4. No measure- ments were made at 9 ML, unfortunately, so that it is not clear whether or not 60° is the maximum value. The coupling of the 0° component is ferromagnetic at all Au spacer thicknesses studied except at 5 ML Au where it is AF. This is illustrated in Figs. 5 a and 5 e for the 0° com- ponent and in 5 b and 5 d for the out-of-plane component. The out-of-plane image of the Au-covered bottom Co layer b shows only locally out-of-plane M, with most of the im- age at the neutral grey level. The same is true after deposi- tion of 4 ML Co but with reversed contrast corresponding to AF coupling d . At 3 ML Co c , however, where the out- FIG. 4. Peak positions of the in-plane M distribution in the of-plane component has its maximum, M is perpendicular in completed sandwich, measured from the easy axis direction in the the whole top layer, with AF coupling wherever there is an bottom Co layer W 1-10 . out-of-plane component region in the bottom layer b . The PRB 59 BIQUADRATIC EXCHANGE IN . . . 477 FIG. 5. SPLEEM images from various growth stages of a 7 FIG. 7. Topographic image a , 0 ° b , 90 ° c , and in-plane Co/5 Au/7 Co sandwich. a , b In-plane and out-of-plane image angular M distribution d images of a 7 Co/6 Au/7 Co sandwich of the Au covered bottom layer. c , d Out-of-plane images after grown near room temperature. The four grey levels indicate the M deposition of 3 and 4 ML Co, respectively, on top of the Au spacer. directions marked by arrows. Image a was taken after the deposi- e , f 0 ° and 90 ° in-plane images W 1-10 and W 001 , re- tion of the bottom Co; images b and c after completion of the spectively after deposition of 6 ML Co. sandwich. Electron energy 1.2 eV. development of the 90° component does not seem to depend IV. DISCUSSION upon the type of interlayer coupling, F of AF, as seen in Fig. 5 f and in the dependence of upon spacer thickness The initial strong contrast decrease with increasing thick- Fig. 4 . ness of the top Co layer mentioned in Sec. III is attributed to AF coupling is known to depend strongly upon the struc- the strong absorption of spin-down electrons in Co Ref. 22 tural perfection of the spacer layer which can be varied by so that the subsequent contrast increase may be attributed to the deposition conditions. For this reason sandwiches with a the magnetization in the top layer. The most striking results 5 ML thick Au spacer were also prepared at elevated tem- which have to be explained are i biquadratic coupling, that peratures 400 K at which the Au crystallites become is a 90° component of M, is present in all except the thinnest larger and, therefore, the surface of the Au film rougher. layer which has pure F coupling, possibly mediated by mag- Figure 6 shows the consequences for the magnetic structure. netic contacts through pinholes. ii The 90° component ap- Figures 6 a and 6 b are the 0° images after Au deposition pears suddenly in the transition from 4 ML to 5 ML simul- and after completion of the sandwich; Fig. 6 c is the 90° taneously with the disappearance of the perpendicular image of the complete sandwich. There is no 0° coupling component, reminiscent of the spin reorientation transition whatsoever but only a very fine-grained weakly pronounced SRT in Co layers on Au 111 .23 iii The parallel compo- domain structure in b but pronounced domains in c . Cou- nent always reproduces the domain pattern of the bottom pling is, thus, predominantly biquadratic. layer but the 90° component has a completely unrelated do- For comparison with the wrinkled magnetization in Co main structure which varies strongly from experiment to ex- layers on W 110 in which the wrinkling is out-of-plane,15 periment and frequently has much smaller domains. An Fig. 7 shows the in-plane wrinkle d in the top Co layer exception is the system grown at elevated temperature caused by the noncoincidence of the 0° and 90° M distribu- 400 K which at the AF coupling thickness 5 ML shows tions for a typical example, a 7 Co/6 Au/7 Co sandwich and no AF coupling but only decreasing F contrast in the parallel the relation of the wrinkle to the substrate topography which image and increasing perpendicular contrast up to 4 ML. is transmitted through the bottom Co layer a . Image d is After the SRT at 5 ML the parallel contrast is very fine- obtained from images b and c by calculating pixel by grained while the 90° domain pattern is much more coarse- pixel the in-plane rotation angle and assigning to each grained. iv The rotation of the average M direction in the value a grey level in the image. top layer relative to that of the bottom layer increases with Au spacer thickness; this indicates an increasing J2 /J1 ratio because in equilibrium cos J1/2J2 . If there is no anisot- ropy in the top layer, J2 has to be larger than J1/2 for M to rotate.12 The fact that biquadratic coupling is everpresent, even close to the extrema of J1 5 ML and 7 ML at which the intrinsic J2 should be negligible, suggests that it is extrinsic. The most likely extrinsic mechanism are spacer thickness fluctuations leading to alternating F and AF coupling1 and FIG. 6. Domain structure in a 7 Co/5 Au/7 Co sandwich grown bipolar coupling caused by the roughness of the Co-Au at elevated temperature. a 5 Au/7 Co/W 110 . b , c Completed interfaces.3 Bipolar coupling can not only produce a notice- sandwich, 0 ° and 90 ° image, respectively. able J2 but contributes also to the perpendicular 478 T. DUDEN AND E. BAUER PRB 59 anisotropy,24,25 adding to the Au/Co interface anisotropy. on W 110 . The out-of-plane and the in-plane M The largest value of in Fig. 3, 60°, requires J2 wrinkle have, however, quite different causes: competition J1 , and this at 7­8 ML where J1 has its maximum value between in-plane and out-of-plane anisotropy there, compe- 0.016 erg cm 2,16 0.03 erg cm 2 Ref. 18 so that J tition between bilinear and biquadratic coupling here. A mi- 2 should be about 0.02 erg cm 2. Calculations in the free electron croscopic model of the competition between differently approximation for flat interfaces give much smaller J coupled regions leads to the picture of static magnetization 2 /J1 ratios.4­9 Recent more sophisticated calculations of the bi- waves.30 quadratic exchange parameters near the 100 surface of Fe, The sudden transition from the perpendicular M compo- for example, give a biquadratic/bilinear ratio of about 1/6 in nent to the 90° and parallel M component is a SRT which the close-packed directions.26 Ab initio calculations for the is, however, quite different from that of Co layers on thick system Co/Cu/Co 100 with flat interfaces and semi-infinite Au 111 layers on W 110 .23 There, no 90° component is Co subsystems show an amplitude ratio J seen because there is no Co layer to couple to and the strain 2 /J1 of about 1:10.27 With increasing interface roughness J in the epitaxial Au layer on the W 110 surface leads to a 2 /J1 increases significantly. In a spacer with the average thickness of n ML uniaxial in-plane anisotropy. Here, the strain is assisted by consisting of about 40% n ML, 50% n 1 ML, and 10% the bilinear coupling while the biquadratic coupling intro- n 2 ML thick regions, for example, biquadratic coupling is duces the 90° component, causing the in-plane rotation of M. energetically more favorable.27 In the absence of realistic The differences of the domain sizes in the out-of-plane intrinsic J and in-plane M images have been dealt with previously:15,23 2 values for the Co/Au 111 /Co system only roughness will be considered here. in-plane the monodomain is the minimum energy configura- The bottom Co layer was prepared for optimum smooth- tion in the absence of magnetic defects such as those caused ness. The surface under these conditions is a three-level sys- by substrate steps; out-of-plane the striped or checkerboard tem with average terrace sizes of several 100 nm diameter pattern is preferred due to dipolar interactions. New are the made visible by quantum size contrast.28 The growth of Au domain size differences in the in-plane components. They on this surface close to room temperature is too fine-grained can be accounted for as follows. The parallel M component to be followed via quantum size contrast. RHEED patterns of domain pattern is already present before the SRT. It is deter- the growth of Au on Co 0001 have been interpreted as mined by the bilinear F or AF coupling with the bottom layer smoothing of the Co surface by the first 1.5­2 ML Au.29 and, therefore, completely reproduces the bottom layer do- However, it is unlikely that the Co surface itself becomes main pattern. The SRT only increases the magnitude of the smoother, rather the Au-covered surface by filling in the in-plane parallel M component. The 90° M component do- lower levels of the Co surface with Au. This is suggested by main pattern on the contrary is produced during the SRT in the topographic images of highly stepped regions in which the presence of the biquadratic coupling. Its domain size is chainlike contrast develops between the smaller Co islands largely influenced by roughness fluctuations which cause in- during the initial Au deposition. Above 2 ML significant plane dipoles and corresponding M direction changes. The roughness develops as seen in the appearance of a RHEED thickness fluctuations depend strongly on the detailed depo- transmission pattern. In LEEM this leads to the loss of topo- sition conditions and can change inadvertently from experi- graphic contrast. This suggests the model of a smooth bot- ment to experiment. There is an indication of a slight domain tom Co-Au interface and a rough top Co-Au interface, with growth with increasing top layer thickness which can be at- increasing roughness in the spacer thickness range studied tributed to the striving for monodomain formation. The re- here. The lateral dimensions of the Au crystals are below the verse situation, that is the formation of small domains in LEEM resolution limit which may be as poor as 50 nm under parallel M and large domains in 90° M during the SRT is the poor contrast conditions encountered. The crystals must simply due to the fact that the Au film is not continuous be at least several ML's thick in order to produce the re- during the high temperature deposition as evident in the F ported RHEED pattern intensity distributions.29 pattern up to the SRT at the thickness at which maximum AF In any case, the Au surface is certainly rougher than the coupling is expected. This is an extreme case of interface bottom Co surface, that is at least a three-level system and roughness and thickness fluctuations so that J2 is dominat- consists, for example at 6 ML Au thickness of at least 5, 6, ing. Under such growth conditions no AF coupling can be and 7 ML thick regions with lateral extensions of less than expected. 100 nm. This means that the sandwich consists of many very small AF, 90° and F coupled regions which are needed in the V. SUMMARY thickness fluctuation model of the biquadratic coupling. The observation that the 90° component appears suddenly in the We have presented a microscopic picture of how the vari- transition from 4 ML to 5 ML suggests that already the ous forms of magnetic interlayer interactions influence the 5 ML Au film has a significant 6 ML fraction. In view of this magnetic domain structure of Co/Au/Co sandwiches. The re- roughness the magnetic dipole mechanism probably also sults show that biquadratic coupling is always sufficiently contributes to J2 which is proportional to the square of the strong in this system to have a major effect on the virgin height differences.3 The M distribution in the top Co layer domain structure. The spin reorientation transition in this can be obtained by vector addition of the intensities of the system leads to a rotation of the magnetization of the top two in-plane component images. This was done in the same layer relative to that of the bottom layer by as much as 60°, manner as previously for in-plane and out-of-plane images of indicating equal magnitude of bilinear and biquadratic ex- Co layers on W 110 .15 The result is shown in Fig. 7. This change even at the maximum of the bilinear exchange. The angle image is very similar to the angle image of Co layers extrinsic thickness fluctuation and magnetic-dipole mecha- PRB 59 BIQUADRATIC EXCHANGE IN . . . 479 nism can qualitatively account for the observations. The Only when the Co films are so thin that their Curie tempera- strong biquadratic coupling contribution leads to a wrinkled ture TC is below the temperature at which structural changes in-plane magnetization in the top Co layer in which the do- occur is it possible to recover a state similar to the original main boundaries are determined by substrate steps similar to one by annealing above TC and cooling in zero field.31 This the wrinkled out-of-plane magnetization in Co layers on is rarely the case as the sample shows which was grown at W 110 . elevated temperature. It should be noted that the usual methods for the study of interlayer interactions which make use of an external mag- netic field cannot study the zero field line of the phase dia- ACKNOWLEDGMENT gram. Once the system has been magnetized it cannot be brought into the zero field virgin state any more because this The authors wish to acknowledge the loan of the would require to create a huge number of domain walls. SPLEEM equipment by the TU Clausthal, Germany. 1 J. C. Slonczewski, Phys. Rev. Lett. 22, 3172 1991 . 18 Y. Roussigne, F. Ganot, C. Dugautier, P. Moch, and D. Renard, 2 J. C. Slonczewski, J. Appl. Phys. 73, 5957 1993 . Phys. Rev. B 52, 350 1995 . 3 S. Demokritov, E. Tsymbal, P. Gruenberg, W. Zinn, and I. K. 19 E. Bauer and W. Telieps, in Surface and Interface Characteriza- Schuller, Phys. Rev. B 49, 720 1994 . tion by Electron Optical Methods, edited by A. Howie and U. 4 R. P. Erickson, K. B. Hathaway, and J. R. Cullen, Phys. Rev. B ValdreŽ Plenum, New York, 1988 , p. 185. 47, 2626 1993 . 20 T. Duden and E. Bauer, Rev. Sci. Instrum. 66, 2861 1995 . 5 R. Bruno, J. Magn. Magn. Mater. 121, 248 1993 ; Phys. Rev. B 21 T. Duden and E. Bauer, Surf. Rev. 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