Magnetocrystalline volume and interface anisotropies in epitaxial films: Universal relation and Néel s model invited

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1 JOURNAL OF APPLIED PHYSICS VOLUME 93, NUMBER MAY 2003 Magnetocrystalline volume and interface anisotropies in epitaxial films: Universal relation and Néel s model invited Günther Bayreuther, a) Martin Dumm, Brigitte Uhl, Roland Meier, and Wolfgang Kipferl Institut für Experimentelle und Angewandte Physik, Universität Regensburg, Regensburg, Germany Presented on 14 November 2002 The thickness dependence of the fourfold in-plane magnetic anisotropy was first observed in epitaxial Fe 001 films and described by the volume anisotropy of bcc Fe with a positive anisotropy constant (K vol 1 0) superimposed by a negative interface term (K int 1 0). This results in a spin reorientation of the easy axis from 100 in thick films to 110 for thicknesses t Fe t crit 6 ML. To clarify the origin of the interface term Fe and bcc Fe 1 x Co x alloy films (x 0.8) epitaxially grown on different substrates Ag 001, Au 001, GaAs 001 were studied. As a result, magnetoelastic interactions can be ruled out because exactly the same anisotropies are found for tensile strain Fe on Ag 001 and Au 001 and for compressive strain Fe on GaAs 001. Also, K int 1 is not affected by the particular interface material or overlayer, e.g., vacuum or Au. A universal correlation was found between the volume and interface anisotropy constants: K int 1 /K vol 1 t crit 6 ML. It is shown that this is indeed expected within Néel s phenomenological theory of magnetic anisotropy if contributions from nearest and next-nearest neighbors are taken into account. Electronic hybridization effects in this case seem to play a minor role compared to the local symmetry. It is suggested that observed effects of overlayers on perpendicular interface anisotropies might be related to surface relaxations which have not been sufficiently studied so far and which, on the other hand, would not affect the fourth-order in-plane anisotropy according to Néel s model in agreement with present experimental results American Institute of Physics. DOI: / I. INTRODUCTION Magnetic anisotropy is a key property of ferromagnetic materials both from a fundamental point of view magnetic order itself is stabilized against thermal excitations by anisotropy and for many applications like magnetic memories or motors. On the other hand, a basic understanding of the origin of magnetic anisotropies is still quite limited for many real materials because of diverse complex effects of crystalline structure including lattice defects and strain, of sample shape and material composition on the anisotropy. Nevertheless, it is generally accepted that: i ii the physical mechanisms behind magnetic anisotropies are dipolar and spin-orbit interactions, and magnetic anisotropy is intimately related to the symmetries of the particular ferromagnetic body, i.e., to the local lattice symmetry as well as to the dimensionality and external shape. a Electronic mail: guenther.bayreuther@physik.uni-regensburg.de The role of the symmetry aspect was most clearly expressed by Louis Néel in his phenomenological theory of magnetic anisotropy 1 back in He developed a model which allowed to understand magnetic anisotropies and magnetostriction in a unified picture based on symmetry considerations alone; this will be discussed in more detail later. One of the most spectacular consequences of Néel s theory was the prediction of a perpendicular magnetic surface anisotropy which in some cases might turn the magnetization of a sufficiently thin film out of the plane against the shape anisotropy which by virtue of the demagnetizing field would usually keep the magnetization within the plane. Experimentally, surface or interface anisotropies should show up as a thickness dependence of the effective anisotropy constants. This is easily seen if we consider the total anisotropy energy of nth order in a film as the sum of a volume and two interface contributions: E n VK n v A K n s1 K n s2 f n i, where V and A are the film volume and area, K (n) v the volume (n) anisotropy constant energy per volume and K s1/2 the interface anisotropy constants energy per area of nth order. In many cases the contributions from both interfaces cannot be separated and, therefore, only their sum K s K s1 K s2 is considered. The dependence of the anisotropy energy on the orientation of the magnetization expressed by the direction cosines i relative to a given reference frame is described by the function f (n). For ferromagnets with cubic lattices usually a series expansion of the following form is used for the density of the anisotropy energy: 1 an K 0 K K In most practical cases, the K 2 term and higher ones are neglected. For 001 -oriented films which are exclusively discussed in this contribution, whenever the magnetization /2003/93(10)/8230/6/$ American Institute of Physics

2 J. Appl. Phys., Vol. 93, No. 10, Parts 2& 3, 15 May 2003 Bayreuther et al lies in the plane due to the demagnetizing field, the last term of Eq. 2 vanishes exactly because of 3 0. In this case Eq. 2 can be written as an K K 1 4 sin2 2, 2a where denotes the angle between the magnetization and the 110 direction. Equation 1 assumes that the exchange interaction within the film is sufficiently strong to keep all spins strictly parallel through the whole thickness. Under this condition which is valid for films thinner than the exchange length the total anisotropy energy can be expressed by an effective volume anisotropy with the energy density (n) E (n) /V or n eff K n eff f n i, K n eff K n v K n s /t. In the case of a perpendicular second order anisotropy (n 2) the volume term in a thin film is usually dominated by the demagnetizing or shape anisotropy with cgs units are used throughout K (n) d 2 M 2 s. With f (2) cos 2 ( ), where is the angle between the magnetization direction and the film normal, positive K (2) eff means an easy plane anisotropy, which is the case for a dominating shape anisotropy. For a negative K (2) s, i.e., for an interface anisotropy with perpendicular easy axis, a reorientation of the spontaneous magnetization from the film plane to the normal is expected if the film thickness, t, falls below a critical value, t crit. Néel s prediction of a possible perpendicular easy axis in ultrathin films was experimentally verified only 15 years later by Gradmann and Müller 2 in NiFe films grown on Cu in ultrahigh vacuum UHV. Since then, a large number of film and multilayer systems have been found where a perpendicular anisotropy with the easy axis along the film normal is strong enough to overcome the shape anisotropy. On the other hand, Néel s theory also implies in-plane surface anisotropies due to the altered coordination of surface or interface atoms. This was already pointed out by Gradmann 3 in However, relatively few experimental studies have been carried out on in-plane magnetocrystalline anisotropies in thin films. In-plane anisotropy means a magnetic anisotropy within the film and must not be confused with a perpendicular anisotropy with the film normal being the hard axis, the latter being correctly termed easyplane anisotropy. The main reason is that these can only be observed in highly perfect single crystal films epitaxially grown on appropriate substrates. From symmetry considerations, in 001 -oriented cubic films in-plane anisotropies with fourfold symmetry only should be observed, while for other orientations like 110, or films grown on vicinal substrate surfaces also contributions with twofold symmetry are possible. This means that in general second and fourth order terms have to be expected in epitaxial films of cubic ferromagnetic 3d metals. In the following, experimental studies of in-plane anisotropies are discussed exclusively with the emphasis on fourth-order terms. Their interpretation within Néel s model is compared to the case of perpendicular anisotropies in the last section. 3 Early observations of fourth-order in-plane interface anisotropies were reported by Heinrich et al. 4 They found that in bcc-fe 001 films grown on Ag 001 the effective in-plane fourth-order anisotropy constant (K 1 will be used for the fourth-order anisotropy constant, K (4), in agreement with previous conventions, K 1, showed a behavior according to Eq. 3 with the volume and the interface constant having opposite sign so that K 1 decreases as a linear function of the inverse thickness. From this fact they concluded the existence of an interface contribution and they suggested a network of crystallographic defects with fourfold symmetry to be the origin of this interface term. 4,5 This interpretation, however, does not seem very convincing because defects with such a symmetry have not been observed. The basic question to be discussed here therefore is about a more plausible origin of the fourfold interface anisotropy. The experimental results of Heinrich for Fe 001 / Ag 001 were later confirmed by some of the present authors 6 for the same system and for Fe 001 /Au 001. In addition, an in-plane spin reorientation in 001 -oriented bcc films was observed: for decreasing thickness the easy axes switched from 100, 010, etc. as in bulk Fe to 110, 110, etc., at a critical thickness of t crit 7 ML corresponding to a sign reversal of K 1. The same behavior of the fourth-order anisotropy was later found in Fe 001 films grown on GaAs An important hint to an understanding of the fourthorder interface anisotropy arose from studies of bcc- Fe 34 Co 66 (001) films grown on GaAs For this alloy composition the volume parameter K 1 (v) is negative in contrast to bcc-fe which has K 1 (v) 0; unexpectedly, the interface term, K 1 (s), also showed a sign reversal, i.e., K 1 (s) 0 instead of K 1 (s) 0 for bcc-fe, and now the easy axis of the fourfold anisotropy switched from 110 to 100 below 7 ML. 8 To clarify the question about a fundamental correlation between the fourfold volume and interface magnetic anisotropy constants in epitaxial films single-crystalline Fe 1 x Co x bcc-alloy films with different compositions were studied; this allows a continuous variation of the volume anistropy constant K 1 (v) from erg/cm 3 to erg/cm 3 without a significant change of lattice parameters. This will be described in the following. II. EXPERIMENT Single-crystalline Fe and Fe 1 x Co x alloy films were grown by molecular beam epitaxy MBE on a GaAs 001 substrate. 8,9 Fe 1 x Co x alloys form stable bcc structures with a lattice constant nearly identical to -Fe for x 0.8. GaAs 001 substrates were prepared by annealing the wafer in UHV at 600 C and subsequent Ar-ion sputtering at the same temperature. These preparation conditions lead to Garich surfaces with a 4 2 reconstruction which are clean with atomically flat terraces several 100 nm wide as indicated by Auger electron spectroscopy AES, reflective high energy electron diffraction RHEED and in situ scanning tunneling microscopy STM. 10 Fe and Fe 1 x Co x alloy films were deposited at room temperature. It has been shown previously that magnetically dead layers are totally absent in

3 8232 J. Appl. Phys., Vol. 93, No. 10, Parts 2& 3, 15 May 2003 Bayreuther et al. FIG. 1. MOKE magnetization loops for 17 ML Fe 78 Co 22 /GaAs 001 with magnetic field applied in the film plane along the 110, 1-10 and 100 directions. Fe films grown under these conditions. 11 Two Knudsen cells were used for co-evaporation: one with an Fe 32 Co 68 alloy and a second one with pure Fe. The flux of the Fe 32 Co 68 cell was kept constant for a growth rate of 0.5 ML/min, whereas the flux of the Fe cell was varied from 0.6 to 0.7 ML/min. The growth rates of both materials were controlled in situ by quartz monitors. X-ray fluorescence spectroscopy XFS was used ex situ for a more precise determination of composition and film thickness. To make sure that for different film thicknesses the substrate properties and the alloy compositions match as closely as possible, stepped double-wedge samples in a thickness range of 3 17 ML were produced by means of a movable shutter in the MBE chamber. Finally, the films were covered by 25-ML-thick epitaxial Au 001 protective layer. Magnetic properties of the films were determined by superconducting quantum interference device SQUID magnetometry and by the magneto-optic Kerr effect MOKE. III. RESULTS The measurements show that all the films are ferromagnetic at room temperature for thicknesses above 4 ML. All films show a uniaxial in-plane anisotropy with the easy axis along 110 and a superimposed fourfold term. The magnetization loops along the hard 110 axis h.a. are free from hysteresis indicating a magnetization reversal by reversible rotation. This is seen in Fig. 1 for a 17 ML film. From h.a. FIG. 2. Effective uniaxial in-plane anisotropy constant, K u eff squares, and fourfold in-plane magnetic anisotropy constant, K 1 eff triangles vs inverse film thickness for Fe 34 Co 66 (001) films on GaAs 001. FIG. 3. Effective fourth-order in-plane magnetic anisotropy constants, K 1 eff vs inverse film thickness for Fe 1 x Co x /GaAs 001 films with four different alloy compositions x 0, 0.22, 0.33, 0.66, determined from MOKE loops from Ref. 9. loops the effective anisotropy constants are obtained in the following way. Assuming that the magnetic energy is the sum of the anisotropy and the Zeeman energies, the magnetic energy density with a field H applied under an angle against the 110 direction is m 1 4 K 1 eff sin 2 2 K u eff sin 2 HM s cos, where means the angle between the magnetization and the 110 direction. The equilibrium orientation of the magnetization is calculated by minimization of m ( ). For the field and magnetization reversal along the uniaxial hard axis, 110, this leads to an analytical expression for the reversible inverted magnetization loop, H(m), given by H m 2K 1 eff 2m 3 m /M s 2K u eff m/m s, where m denotes the magnetization component along the axis of the applied field normalized to the saturation magnetization, M s.fromafitofeq. 5 to the experimental loop, H(m), for 1 m 1 the effective anisotropy constants of second and fourth order, K U eff and K 1 eff, are obtained. The resulting effective anisotropy constants measured at room temperature are shown in Fig. 2 as functions of the inverse thickness for x Both quantities scale linearly with 1/t the deviation for t 5 ML is due to the Curie temperature, T c, approaching the measuring temperature with decreasing thickness. This means that second- and fourthorder anisotropies both have remarkable interface contributions. The fact that K U eff 0 for t means that the uniaxial anisotropy is a pure interface contribution (K U vol 0) originating from the two-fold symmetry of the GaAs 001 surface. 7 In the present study the uniaxial anisotropy proved to be quite useful for the precise determination of the fourthorder components, but here it will not be discussed further. The fourth-order constant also is linear in 1/t Fig. 2 and the same behavior is observed for all compositions as seen in Fig. 3 so that the data are well described by the relation from Eq. 3 : 4 5

4 J. Appl. Phys., Vol. 93, No. 10, Parts 2& 3, 15 May 2003 Bayreuther et al ferromagnets, 4,5 and this is the primary point which must be addressed in order to understand the origin of the interface anisotropy. IV. DISCUSSION FIG. 4. Fourth-order in-plane interface anisotropy constant, K 1 int vs volume constant, K 1 vol, for Fe 1 x Co x /GaAs 001 films with alloy compositions: x 0, 0.21, 0.22, 0.33, 0.66 from Ref. 9. K eff 1 K vol 1 tk int 1 /t. 6 It becomes clear that the interface constant slope always has the opposite sign than the volume constant intercept with vertical axis. This becomes even clearer if K int 1 is plotted versus K vol 1, as shown in Fig. 4. There is a definite proportionality between both anisotropy constants with a negative ratio K int 1 /K vol 1 0, which according to Eq. 6 directly gives the critical thickness for the reorientation (K eff 1 0): t crit K int 1 /K vol 1 6 ML, 7 which within the experimental error is the same for all compositions see Fig. 4. This general correlation between the fourth-order volume and interface anisotropy constants has never been reported before and may look quite unexpected. In order to further check the influence of the interface material, an in situ experiment was carried out where MOKE loops were continuously measured while an Fe 001 film was grown on GaAs 001 and subsequently covered by an epitaxial Au layer. Figure 5 clearly shows that the anisotropy constants remain totally unchanged by the Au covering layer; this was verified up to t Au 10 ML. This confirms the earlier finding about the negligible influence of the interface material on the fourfold in-plane anisotropy in bcc FIG. 5. In situ MOKE magnetization loops of a 13 ML Fe 001 /GaAs 001 film before and after covering with 1.8 ML Au 001. The first attempt of an explanation of a four-fold interface anisotropy by Heinrich and co-workers, 4,5 assuming lattice defects with a fourfold symmetry is not convincing because the identical presence of such exotic defects in films grown on a variety of substrates under different conditions is highly unlikely. Also, magnetoelastic interactions of fourth order which practically have never been discussed although they should exist can be excluded as the dominating mechanism when the experimental results for different systems are considered: the strain due to the lattice misfit, f, between substrate and film lattice constant apparently is of little influence because K 1 is the same for Fe/Au 001 with f int 0.61% after rotation of one of the lattices by /4 and for Fe/GaAs 001 with f 1.4% for twice the Fe lattice constant, i.e., even reversing the sign of the misfit strain in the films f 0 in Fe/Au Ref. 6 and Fe/Ag Ref. 6 f 0 in Fe/GaAs 001 does not significantly change K int 1. Next, we attempt an explanation based on the broken cubic symmetry at the interfaces alone within the framework of L. Néel s pair energy model. In Néel s theory the anisotropy energy is described as the sum of interaction energies of pairs of atoms in the crystal lattice. The interaction energy, w, between two atoms at a distance r is expanded in a series of Legendre polynomials multipole expansion : w g 2 r cos 2 3 g 1 4 r cos cos Higher terms are neglected, because it is assumed that the series expansion converges rapidly ( g 2 (r) g 4 (r) g 6 (r) ). is the angle between the unit vector of the magnetization direction mˆ and the pair axis unit vector ˆ of the two atoms: cos x m x y m y z m z, 8a g 2 r 1 m r, 8b is the pseudodipole coefficient, and g 4 r q s r, 8c is the pseudoquadrupole coefficient. l and q are the pair interaction energies, only depending on the distance r. m r and s r are the linear variations for a distorted lattice. The general expression 9 is simplified in the following way: First, m r and s r can be neglected because the lattice mismatch of 1.4% between Fe 1 x Co x and GaAs is rather small and independent of composition. Second, we are interested only in the fourfold anisotropies within Néel s model, so we do not consider the isotropic and the twofold contributions expressed by the cos 2 terms. Thirdly, we assume

5 8234 J. Appl. Phys., Vol. 93, No. 10, Parts 2& 3, 15 May 2003 Bayreuther et al. the magnetization to always lie in the 001 plane, which means that m z 0. Then the interaction energy for an atom pair becomes w 4 q x m x y m y 4. 9 In order to calculate the anisotropy energy density bulk inside the crystal, we add up all contributions of the nearest and next nearest neighbor pairs all other pairs being neglected. With the underlying bcc lattice of the ferromagnet we get the following result: bulk 2 3 NN w 4 NN NNN w 4 NNN qnn x m x y m y 4 NN 1 2q NNN NNN x m x y m y NNN 16 9 qnn 2q m 2 x m 2 y, 10 where is the lattice constant, q NN the pair interaction energy of nearest neighbors, and q NNN the interaction energy of next-nearest neighbor pairs. From the comparison of Eq. 10 with Eq. 2a ( an K vol ) we obtain K vol NNN 16 9 qnn 2q. 11 The anisotropy energy density of the interface moments can be calculated in the same way, but now for an atom at the 001 interface four nearest neighbors and one next-nearest neighbor are missing. Furthermore, it must be taken into account that the interface anisotropy energy introduced in Eq. 1 as an additional energy is the difference between the anisotropy energy of interface and bulk atoms. Hence, we obtain and int 1 2 w NN 4int w NN 4 NN NNN w NNN 4int w NNN qnn m x 2 m y 2, 12 K int q NN It can be seen, that the next-nearest neighbors do not affect the in-plane anisotropy constant K int 1 at a bcc 001 interface. For the ratio K int 1 /K vol 1 we get the following expression: K 1 int vol 2qNN K 1 8q NN 9q NNN. 14 It is obvious from Eq. 13 that for pure Fe q NN q FeFe 0, because K int 1 is found to be negative in the experiment. In all other cases q NN represents an average value of q FeFe,q FeCo, and q CoCo. K int 1 becomes positive for x 0.3 according to the data in Figs. 3 and 4 and, hence q NN more and more negative for increasing Co content. This means that q FeCo and q CoCo together are responsible for the negative contribution. In order to separate these two parameters, alloy films with different degrees of chemical short range order should be investigated in the future. Assuming random alloys, the ratio q NN /q NNN can be expected to be independent of composition because the atomic distances are the same in all samples. Then, it is obvious from Eq. 14 that K 1 int /K 1 vol has the same negative value for all compositions, i.e., the critical thickness of the in-plane spin reorientation transition according to Eq. 7 is independent of composition, and this is exactly what is experimentally found. In summary, Néel s theory both explains why the fourthorder in-plane anisotropy shows change of sign in ferromagnetic bcc alloys and why the interface term is independent of the substrate and the covering material. Or in other words, the basic assumption of Néel s model that anisotropies are exclusively determined by the local symmetry or the geometric arrangement of magnetic atoms, respectively, is valid as far as the fourfold in-plane anisotropy in bcc ferromagnets is concerned. Effects of hybridization of electronic states generally expected at metallic interfaces with a related modification of spin-orbit coupling seem to play only a minor role for these specific anisotropies. One might ask, whether the same model and theory can be used to explain the uniaxial i.e., second-order perpendicular anisotropy usually observed at interfaces and in magnetic multilayers as mentioned in Sec. I. Indeed, this is not the case as is most clearly seen from observations on Fe 110 films grown on different substrates and covered by different materials. By a comparative study Fritzsche et al. 12 were able to separate the contributions from both interfaces and to derive single-interface perpendicular anisotropy constants, K s, for various interfaces with Fe 110 (K s 0 means a perpendicular easy axis according to the definition used by Néel, namely, 12 for UHV: K s 0.97 erg/cm 2 ; Ag 111 : 0.72 erg/cm 2 ; Au 111 : 0.82 erg/cm 2 ; Cu: 0.52 erg/cm 2 ; Cr 110 : 0.12 erg/cm 2 ; and W 110 : 1.92 erg/cm 2. It has also been reported that the perpendicular anisotropy constant of ultrathin Co 0001 films strongly changes upon submonolayer coverage by Au 111, Pd 111, or Cu Similar effects had been observed earlier in Co/ Pd 111 covered with Cu, Ag, and Pd. 14 How can these observations be reconciled with Néel s theory? We notice that surface relaxation, i.e., the difference in vertical lattice spacing between the surface and underlying layers and their change upon deposition of overlayers even in submonolayer quantities, has not been taken into account in these studies. As a consequence, within Néel s theory we expect a distinct modification of the perpendicular magnetic surface anisotropy due to the dependence of the coupling contants, l and q, on the atomic distances. However, the inplane anisotropy discussed above will not be affected because with the magnetization in the plane all contributions with perpendicular pair axes vanish according to Eq. 8a cos 0. This would explain why the in-plane fourth-order

6 J. Appl. Phys., Vol. 93, No. 10, Parts 2& 3, 15 May 2003 Bayreuther et al anisotropy is independent of the covering materials including vacuum while the perpendicular anisotropy is not. It also makes it plausible why the largest deviation from the naive model is observed for Fe/W which has a larger lattice mismatch f 10% than any other combination and, hence, a very strong relaxation effect is expected which could explain the unusual value of k s 0 in this case. Actually, no information is available about the change of vertical lattice spacings for the films investigated in Refs. 13 and 14. LEED measurements combined with dynamic theory would be required to find a possible correlation between surface relaxation and perpendicular magnetic anisotropies. V. SUMMARY The origin of the fourth-order interface anisotropy has been investigated in epitaxial Fe 001 and Fe 1 x Co x (001) films. This system allows a continuous variation of the volume anisotropy constant K 1 from to 4 (v) 10 5 erg/cm 3 without any significant change of lattice parameters. As an unexpected result it was found that the fourth-order volume anisotropy constant, K vol 1, is proportional to the fourfold in-plane interface anisotropy constant, K int 1, with a negative constant of proportionality. In addition, the substrate and covering materials do not have a significant influence on the in-plane fourth-order anisotropy. It is shown that both observations can be consistently explained in the framework of Néel s pair energy model which is based on symmetry considerations alone. On the other hand, marked effects of overlayers on out-of-plane interface anisotropies which have been reported in the literature, might be connected with surface relaxations which have not been sufficiently studied in previous investigations. It is also shown that, according to Néel s model, such relaxations would not affect the fourth-order in-plane anisotropy in agreement with present experimental results. More detailed and precise in situ experiments will be required in order to find out whether, in addition to the dominating symmetry effects found here, there are subtle band structure effects which might have escaped the measurement in the present study, and whether a similar genreal relationship holds between volume and interface anisotropies in ferromagnetic films with fcc structure. In the light of the results of bcc alloys presented here one might expect that also in fcc films the fourth-order magnetocrystalline anisotorpy is not suppressed in ultrathin epitaxial fcc-co 110 films on Cu as suggested in the literature, 15,16 but is reduced due to a competition of volume and interface terms as found for the bcc-fe 1 x Co x 001 films in the present study. ACKNOWLEDGMENTS Support by the Deutsche Forschungsgemeinschaft under Grant No. FOR 370 and of the Federal Ministry of Education and Research BMBF is gratefully acknowledged. 1 L. Néel, Rend. Acad. Sci. 237, ; J. Phys. Radium 15, U. Gradmann and J. Müller, Phys. Status Solidi 27, U. Gradmann, J. Magn. Magn. Mater , B. Heinrich, J. F. Cochran, A. S. Arrott, S. T. Purcell, K. B. Urquhart, J. R. Dutcher, and W. F. Eglhoff, Jr., Appl. Phys. A: Solids Surf. 49, B. Heinrich and J. F. Cochran, Adv. Phys. 42, M. Brockmann, S. Miethaner, R. Onderka, M. Köhler, F. Himmelhuber, H. Regensburger, F. Bensch, T. Schweinböck, and G. Bayreuther, J. Appl. Phys. 81, ; T. Leeb, M. Brockmann, F. Bensch, S. Miethaner, and G. Bayreuther, ibid. 85, M. Brockmann, M. Zölfl, S. Miethaner, and G. Bayreuther, J. Magn. Magn. Mater , M. Dumm, M. Zölfl, R. Moosbühler, M. Brockmann, T. Schmidt, and G. Bayreuther, J. Appl. Phys. 87, M. Dumm, B. Uhl, M. Zölfl, W. Kipferl, and G. Bayreuther, J. Appl. Phys. 91, R. Moosbühler, F. Bensch, M. Dumm, and G. Bayreuther, J. Appl. Phys. 91, M. Zölfl, M. Brockmann, M. Köhler, S. Kreuzer, T. Schweinböck,S.Miethaner, F. Bensch, and G. Bayreuther, J. Magn. Magn. Mater. 175, F. Fritzsche, H. J. Elmers, and J. Gradmann, J. Magn. Magn. Mater. 135, P. Beauvillain, A. Bounouh, C. Chappert, R. Mégy, S. Ould-Mahfoud, J. P. Renaud, D. Weller, and J. Corno, J. Appl. Phys. 76, B. N. Engel, M. H. Wiedmann, R. A. van Leeuwen, and C. M. Falco, J. Magn. Magn. Mater. 126, B. Hillebrands, J. Fassbender, R. Jungblut, G. Güntherodt, D. J. Roberts, and G. A. Gehring, Phys. Rev. B 53, R J. Fassbender, G. Güntherodt, C. Mathieu, B. Hillebrands, R. Jungblut, J. Kohlhepp, M. T. Johnson, D. J. Roberts, and G. A. Gehring, Phys. Rev. B 57,