PHYSICAL REVIEW B VOLUME 54, NUMBER 9 1 SEPTEMBER 1996-I Observation and interpretation of a partial Gd twisted spin state in an epitaxial Gd/Fe bilayer O. F. K. McGrath, N. Ryzhanova,* C. Lacroix, and D. Givord Laboratoire Louis Ne´el, CNRS, Boi te Postale 166, 38042 Grenoble cedex, France C. Fermon, C. Miramond, and G. Saux DRECAM/SPEC, CEA Saclay, 91191 Gif sur Yvette, France S. Young and A. Vedyayev DRFMC/SP2M/MP, Centre d'Etudes Nucle´aires de Grenoble, 38054 Grenoble cedex 9, France Received 22 February 1996 The interfacial coupling between Gd 0001 and Fe 110 in an epitaxial Gd/Fe bilayer has been studied by means of magnetometry and polarized neutron reflectivity with spin analysis. The results are interpreted in terms of a Gd twisted spin state in low applied fields. This original magnetic configuration was examined by theoretical calculations and found to be due to competing Gd-Gd and Gd-Fe exchange interactions with the Gd-Fe exchange interactions being long ranged and oscillatory. S0163-1829 96 05121-1 One of the most active areas of magnetism research over fields up to 80 kOe and temperatures from 10 to 300 K. The the past few years has been the study of exchange interac- in-plane low-field magnetization dependence along the 11¯0 tions between thin films. Most work has been devoted to the axes is shown in Figs. 1 a and 1 b for T 10 and 300 K, study of exchange coupling between magnetic slabs-either respectively. For fields greater than the coercive field 40 Oe magnetic rare earth elements (R) or transition metal ele- the approach to saturation is very slow. It is instructive to try ments (T)-separated by nonmagnetic spacers.1­7 Another and deduce the low field moment configuration of Fe and Gd particular aspect of magnetic interactions in thin film sys- from the above measurements. Consider, for example, the tems concerns exchange interactions between two magnetic measurements along the 11¯0 axis at 10 K. The value of the layers of different nature, i.e., interfacial exchange coupling. measured moment for H 150 Oe is 2.3 10 4 emu. If one This has attracted much less attention until now. In this Brief assumes that the magnetization of Fe and Gd in the film at 10 Report we present the results of a study of the interfacial K is the same as in the bulk 1740 emu cm 3 and 2010 exchange coupling in an R/T epitaxial bilayer Gd/Fe . Al- emu cm 3, respectively then the total Fe moment in the film though previous reports have appeared on the study of R/T is 3.3 10 4 emu and the total Gd moment is 1.9 10 4 emu. bilayers and multilayers, no attempts have been made to de- The measured value corresponds neither to the sum nor the duce the range of the R/T exchange interactions. In addition, difference of the expected Gd and Fe moments thus indicat- all previous reports have been devoted to polycrystalline ing that the magnetic configuration is not simply collinear systems.8­11 but more complex. The hypothesis of a complex configura- The films were grown by pulsed laser deposition. Initially tion is borne out by the high field measurements as shown in a buffer layer of W 110 was deposited on Al Fig. 1 c for H parallel to the 11¯0 direction of Fe at 300 K. 2O3 112 ¯0 , as described elsewhere.12 Fe 110 was subsequently deposited From fields of 1 to 20 kOe, the moment varies very slowly as at 500 K at a rate of 0.5 Å min 1. Gd was then deposited on the field is increased. At higher fields the susceptibility in- the Fe at a deposition rate of 0.5 Å min 1 in a vacuum of creases progressively. Complete saturation does not appear 5 10 10 Torr. The first 5 Å of Gd was deposited with the substrate temperature held at 500 K; the remainder was de- posited at ambient temperature. This approach enables the epitaxy to be initiated but prevents islanding. The epitaxial plane is 0001 and the epitaxial relationship for the Gd on the Fe was deduced from reflection high-energy electron dif- fraction to be the well known Nishiyama-Wassermann orientation.13 The Gd was found to adopt its bulk lattice parameter a 3.63 Å from the very early stages of deposi- tion 2 Å . The bilayer was protected by a deposition of Y with the substrate held at ambient temperature. The Y was found to epitaxy directly on the Gd. The exact thicknesses of the layers were determined by specular x-ray and neutron reflectivity and found to be Y 150 20 Å, Gd 63 5 Å, Fe 133 3 Å, and W 455 5 Å. The field dependence of the total magnetic moment of the FIG. 1. Total moment measurements: a low field at 10 K, b film was investigated by a vibrating sample magnetometer in low field at 300 K, and c high field at 300 K. 0163-1829/96/54 9 /6088 4 /$10.00 54 6088 © 1996 The American Physical Society 54 BRIEF REPORTS 6089 FIG. 3. Schematic representation of the moment configuration in the Gd/Fe bi-layer showing the Gd twisted spin state see text and Table 1 . Fe abrupt; Fe/W 10 Å. The same parameters were used to fit the data for different temperatures and different neutron spin directions. Initial attempts to fit the data to a simple model where all the Fe moments and all the Gd moments remain parallel amongst themselves with the Fe block and the Gd block canted at an angle to the applied field were unsuccessful Fig. 2 a . The best fit was found for a more complex model Fig. 2 b where the Fe moments stay par- allel amongst themselves and where the Gd moments nearest the interface are antiparallel and then exhibit a twisted state FIG. 2. Polarized neutron reflectivity measurements; experimen- further from the interface, as schematized in Fig. 3. The mo- tal data are shown by data points and the best fits are shown by ments and their orientation are given in Table I. Each value, continuous lines. except the thickness, can be changed by 10% and then an adjustment of the other values gives a reasonable fit. All to have occurred for fields even as high as 80 kOe. densities were taken as bulk densities except for Fe where In order to further analyze the moment configuration in the average density is found to be 5% less than bulk Fe it is the bilayer, polarized neutron reflectivity with spin analysis minimum at the W/Fe interface and increases with the thick- was performed on the G2-2 spectrometer at the Orphe´e re- ness . actor at Saclay, France. This spectrometer-a new facility of The Gd moment decreases rapidly as the temperature in- the Laboratoire Le´on Brillouin-enables both non-spin-flip creases. The mean Gd moment at 350 K is found to be 1.6 (R ,R ) and spin-flip reflectivities R to be measured. B . At low temperature 70 K the reflectivity profile is very During the measurements a field larger than 5 Oe is applied similar to the 300 K data. It corresponds to a 2 B moment to ensure a good neutron polarization. For this work the neu- for the Fe and a moment of about 6.5 B for the Gd. tron wavelength was 4.14 Å, the flipping ratio was 60, and Although the observed magnetic configuration is not fully the flux after analysis was 104 n/s 1 cm 2. The three reflec- unambiguous due to the number of parameters involved in tivity profiles R , R , and R were measured by vary- the fitting procedure, it must be stressed that it corresponds ing the angle of incidence of the beam onto the sample at to the simplest model found to fit the experiment. In addi- temperatures of 80, 300, and 350 K with an applied field of tion, this twisted Gd state can in fact be understood in the 300 Oe. The sample was oriented so that the in-plane light of our understanding of magnetic interactions in bulk Fe 11¯0 axis to Gd 11¯00 was parallel to the applied field and hence the quantization axis. TABLE I. Thickness profile of the magnetic moment and orien- The reflectivity profiles obtained at 300 K are shown in tation for T 300 K and H 300 Oe from best fits to PNR data. Fig. 2. A large splitting between the R (q) and R (q) reflectivity profiles is observed which indicates the existence Thickness Moment Orientation of a large component of the magnetization along the direc- Element Å angle with respect to H tion of the applied field. The most striking feature is however B the presence of a distinctive spin-flip reflectivity R Fe 130 1.9 4.8 which shows that the magnetization is not completely paral- Gd 10 5.4 176 lel nor antiparallel to the applied field. Gd 10 5.2 176 The moment configuration was analyzed by fitting the ex- Gd 10 5.0 158 perimental reflectivities. The calculation procedure for the Gd 10 4.8 147 spin-flip and non-spin-flip reflectivity profiles is described in Gd 10 4.4 131 Ref. 14. Off-specular reflectivity was very small so the inter- Gd 10 4.0 131 face roughness was taken into account by introducing an Y 14 1.0 131 alloy layer at each interface. The interface thicknesses then Y 158 0.0 obtained are as follows: UHV/Y 20 Å; Y/Gd 14 Å; Gd/ 6090 BRIEF REPORTS 54 RT compounds.15 The coupling between 3d and 4 f spins is other between Gd and Fe magnetic moments. It is assumed mediated by 5d electrons through 3d ­ 5d band hybridiza- that the magnetic moments in Fe are ferromagnetically tion, which is stronger for the minority 3d band, and thus aligned due to the strong exchange coupling in metallic Fe. antiferromagnetic.16,17 The configuration observed in the bi- Let z be the coordinate perpendicular to the bilayer plane, layer may be qualitatively understood by making the addi- then the expression for the generalized RKKY interaction I tional hypothesis that the Gd-Fe (4 f -3d) interactions are zz between the total magnetic moments of the layers situ- long ranged and oscillatory which is reasonable as they are ated at positions z and z is mediated by itinerant 5d electrons. Close to the Gd/Fe inter- face the Gd moments are antiparallel to the Fe moments as in n E n E bulk GdFe alloys. After approximately eight Gd planes from I zz dE dE E E the interface the Gd-Fe interactions change sign and they then favor parallel coupling between the Fe and Gd mo- G zz E G zz E J z ments. They are therefore in competition with the Gd-Gd interactions which tend to keep the Gd moments ferromag- G z zE G z zE J z , 1 netically coupled. The result of this competition is a progres- where is the in-plane component of electron momentum, sive rotation of the Gd moments similar to that observed in G retarded and G advanced are Green functions of an helimagnetic structure. After a further eight planes the itinerant d electrons, J(z) is the intra-atomic exchange in Gd-Fe interactions become negligible and the rotation of the Gd J Gd or the d-d exchange in Fe J Fe , and n(E) is the Gd moments stops. 0 0 Fermi distribution function. For a free electron model these These simple ideas were confirmed by calculations per- Green functions have to be a solution of the following: formed for Ruderman-Kittel-Kasuya-Yosida RKKY -type interactions. These were performed for the bilayer by assum- 2 2 ing that all interactions Fe-Fe, Gd-Fe, and Gd-Gd are me- k2 z G zz z z , 2 diated by itinerant d electrons which are characterized by k 2m z2 1 and k 2 2 which represent the Fermi momentum for d electrons where k2(z) kf (z) 2, kf(z) k1 if z is within the Gd in the Gd layer and the Fe layer, respectively. It is supposed film, kf(z) k2 if z is within the Fe film, and G(zz ) 0 for that itinerant d electrons may travel in both the Fe and Gd z and z at the outer boundaries of the film. Solving Eq. 2 films suffering partial reflection at the Gd-Fe interface due to for Green functions and substituting its expression in 1 we the potential barrier and that they are ideally reflected at the may fulfill the integration in in an asymptotic limit and get outer interfaces of the bilayer. These itinerant d electrons the following expression for I(zz ) I(nn ) for z a0n, interact via direct intra-atomic exchange interactions with z a0n , where n is an integer and a0 is the interplanar electrons in localized Gd 4 f shells and with d electrons in distance of Gd along the 0001 direction: Fe. This gives rise to two kinds of oscillatory RKKY-type interactions-one between Gd magnetic moments and the I nn J0 n J1 nn , 3 cos 2a 2 k sin2a J 0k1 n 1 k2 1 k2 sin2a0k1 n 1 0Nk1 0 n JGdJFe E f a , 3a 1k2 k1 k2 2 n 1 1 2 2 JGd 2 E f k1 k2 n 1 2 2 N 2 2 JGd 2 E sin 2a J f 1 k1 k2 2 sin2a0k1 n n 0k1min nn 1 nn 2 , 3b k1 k2 2 n n 2 2 min nn 1 2 where JGd J Gd Fe 0 Gd(T)/ Gd 0 , JFe J 0 Fe(T)/ Fe 0 , tate away from the antiparallel configuration depending on Gd(T) and Gd(T) are the magnetizations of Gd and Fe at the ratio of JFe/JGd. We therefore suppose that the angle n temperature T, 2 2 2 between the direction of the magnetization in the nth Gd 1 4 (k1 k2)/k2/2a0(k1 k2), 2 1/ k layer at position n with respect to the direction of the Fe 1a0 , (E f ) is the density of states in Gd, a1 is the inter- planar distance in Fe 2 Å , and N is the total number of magnetization is varying as Gd atomic layers 24 . The first two terms in 3a are usual RKKY Gd-Fe interactions which are integrated over the in- plane coordinates and over Gd-Gd interactions and the re- n , for 1 n n0 , maining terms are due to the reflections of itinerant electrons 0 at the Gd-Fe interface and at the outer boundaries. If we n n n n0 , for n0 1 n n0 n1 , 1 suppose that JFe Gd Fe Gd 0 /J0 TC /TC 3, then the leading term is the first term in 3a and J n 0 , for n0 n1 1 n 24, 0(n ) 0 for (n 1) /4a0k1 so the magnetization in several monolayers adjacent to the Gd-Fe interface has to be antiparallel to the Fe magnetiza- 4 tion. For (n 1) /4a0k1 the Gd magnetization may ro- where n0 is the number of Gd layers where the magnetization 54 BRIEF REPORTS 6091 of Gd is antiparallel to Fe, n1 is the number of layers over the Gd magnetization is either parallel or antiparallel to the which the magnetization rotates, and 0 is the angle between Fe one, making a kind of antiphase arrangement. Gd and Fe in the 24 n0 n1 remaining layers Fig. 3 . The In summary we have made experimental investigation of total energy, F, of the Gd subsystem may be written as the moment configuration in a rare earth­transition metal epitaxial bilayer and found the Gd moments not to be collin- 24 24 ear in zero or low applied fields. We have shown that the F J0 n cos n J1 nn cos n n . 5 experimental results are consistent with a Gd twisted state in 1 n n the Gd layer. We have shown that the experimental results The value of F has to be minimized with respect to the n are consistent with a Gd twisted state in the Gd layer. We 0 , n have proposed an interpretation for its origin, which shows, 1 , and 0 variables for given values of k1 , k2 , and m JFe/JGd. We have done this numerically for several sets in particular, that the interfacial Gd-Fe exchange interactions of values of k are long ranged and oscillatory. Finally, it should be noted 1 , k2 , and m and found that for values of k that such a Gd twisted state is fundamentally different from 1 0.07 Å 1, k2 0.7 Å 1, and m 3, the obtained values of n the so-called twisted phases which have been observed in 0 , n1 , and 0 are 4, 8, and /2, respectively, in semiquan- titative agreement with experiment 8, 12, and 2 /3, respec- Fe/Gd polycrystalline multilayers.11,18 The propagation vec- tively . The value of n tor which characterizes rotation of the moments in rare-earth 0 /4a0k1 and the values of n1 and metals is always parallel to the c axis cf. the helimagnetic 0 depend essentially on the value of m. For example, for m 10 then n structures observed in several rare-earth metals . In polycrys- 1 1 and 0 0, and for m 0 then 0 . talline multilayers, the direction which is perpendicular to These results are clear from a physical point of view: if the sample surface may correspond to various crystallo- Gd-Fe exchange is much larger than ferromagnetic Gd-Gd graphic directions. In epitaxial films, it is strictly the c direc- exchange, then the direction of the Gd magnetization is gov- tion which is perpendicular to the surface. This explains that erned by the sign of the Gd-Fe exchange; on the other hand, the magnetic state described in the present paper is unique to if it is weak then the Gd stays ferromagnetic. In order to epitaxial films. check the model, experiments at higher temperature should be made: m is expected to increase with temperature due to A.V. acknowledges the C.E.A. for financial support and the faster decrease of Gd compared with Fe. Close to Tc , N. 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