Surface Magnetic Anisotropy Research Articles

ANISOTROPIES IN ULTRATHIN FILMS OF IRON GROWN ON SILVER

Ferromagnetic resonance and Brillouin light scattering have been used to measure the uniaxial magnetic anisotropies in ultrathin films of Fe(001) grown epitaxially on Ag(001) substrates. Brillouin light scattering has also been used to obtain magnetic surface anisotropies for bulk iron. Surface anisotropies obtained for the bulk (001) surface are compared with the uniaxial magnetic anisotropies obtained using thin films, and with the theoretical predictions of Gay and Richter. The bulk surface anisotropies are in good agreement with those measured on thin films and also with the theoretical calculations based upon the reduced symmetry at a surface.

Magnetic surface anisotropy of cobalt and surface roughness effects within Neel's model

Neel's phenomenological model of magnetic surface anisotropy is generalised to hexagonal close-packed structures in order to determine the magnetic surface anisotropy of cobalt. The results obtained are in fair agreement with experimental values for the Au(111)/Co interface. It is also shown that Neel's model allows the surface roughness to be easily taken into account.

Theory of magnetic surface anisotropy and exchange effects in the Brillouin scattering of light by magnetostatic spin waves (invited)

A new theory of the Brillouin shift in the inelastic scattering of light by magnetostatic spin waves is presented. Contrary to previous work, the present calculations do include exchange effects and treat the magnetic surface anisotropy constants Ks and Kss directly rather than via the stratagem of effective volume anisotropies. The experimental data for {110} Fe on W are explained about as well by the present theory as by previous work. A detailed analysis reveals the previously unnoticed fact that the signs of Ks and Kss for (1̄10) Fe on W are opposite to those for (1̄10) Fe on GaAs. Some new spin-wave modes arising from exchange are predicted and shown to occur outside the frequency range which has been investigated experimentally. A quantitative explanation is proposed for the occasional applicability of a theory based on effective volume anisotropies and zero exchange.

Nonlinear magnetic susceptibility tensors of ferromagnetic films

Nonlinear magnetic susceptibility tensors of ferromagnetic films are studied by the method of n+1 time Green functions based upon the Heisenberg model with the surface magnetic anisotropy. It is proved that the ferromagnetic film, which loses translational invariance in one direction, has nonlocal magnetic susceptibility tensors. We derive the second-, third-, and fourth-rank susceptibility tensors in terms of a nonlocal formulation and the relation between the surface magnetic anisotropy of the film and the spin-wave resonance modes excited by the uniform microwave field. A number of nonlinear effects such as second- and third-harmonic generation, frequency mixing, signal amplification, etc., exist in the microwave region. These effects are obviously large near the spin-wave resonance.

Effects of magnetic surface anisotropy near the (110) Fe/MnF2 interface

Epitaxial (110)56 Fe samples have been grown on (111) Ag and then covered with MnF2 in ultrahigh vacuum. Three 57 Fe layers have been placed at various depths from the Fe/MnF2 interface to permit Mössbauer spectroscopy. A linear temperature dependence of the hyperfine field for 57 Fe layers up to at least 10 layers into the sample is observed. This persistence of surface magnetic effects into the deep layers of the (110) Fe sample can be understood within the framework of a classical spin-wave calculation by Rado.

Ferromagnetic resonance of exchange-coupled magnetic layers.

The ferromagnetic resonance-line shapes, fields, and intensities of exchange coupled magnetic multilayers are calculated as a function of exchange coupling and number of layers. We find that the number of magnetic excitations equals the number of layer pairs that make up the layered structure. The magnetic dispersion of these excitations is easily calculable from the theoretical formulation developed earlier. It is suggested that the multitude of ferromagnetic resonance lines in magnetic superlattices observed experimentally elsewhere may be explained in terms of an earlier calculation involving surface magnetic anisotropy fields only.

Ferromagnetic resonance method for determining the magnetic surface anisotropy of amorphous films.

The theory of a ferromagnetic resonance (FMR) method for determining the magnetic surface anisotropy of amorphous films is presented. This method enables one to deduce the surface anisotropy constant ${K}_{s}$ of an amorphous material from the dependence of the magnetic resonance field on the film thickness. The analysis includes spin-wave modes and surface-induced modes, perpendicular and parallel FMR configurations, and thin as well as ultrathin films. No approximations are made other than the linearization of the equation of motion and the assumption that skin-depth effects and electromagnetic propagation effects are negligible. Good agreement is found between the theory of the method and experimental FMR data on ultrathin films of amorphous Fe-B alloys. The reliability of the ${K}_{s}$ values deduced by means of the theory from experimental FMR and superconducting quantum-interference device data is briefly discussed.

Experimental studies of surface magnetism with polarized electrons

The same electron spectroscopies that are so powerful for studying surfaces generally, can be made sensitive to magnetic properties when electron spin polarization is included as a parameter, for example by probing with a spin polarized electron beam or measuring the spin polarization of emitted electrons. Such properties as the spontaneous magnetization, Curie temperature, temperature dependence of the magnetic order, anisotropy, spin-dependent electronic structure, magnetization curves, elementary excitations, and magnetic microstructure may be different from the bulk in a thin film or at the surface of a semi-infinite ferromagnet. Recent results on chemisorption induced changes in surface magnetism studied by spin polarized inverse photoemission, on magnetic surface anisotropy investigated by polarized photoemission, and on magnetic microstructure determined by scanning electron microscopy with polarization analysis, have been selected for discussion as illustrations of polarized electron studies of surface magnetism.

In situ Brillouin scattering from surface-anisotropy-dominated Damon-Eshbach modes in ultrathin epitaxial Fe(110) layers.

Epitaxially grown Fe(110) layers on W(110) with thicknesses between 8 and 150 \AA{} have been investigated in situ by Brillouin scattering. Below 60 \AA{} a so-far-unobserved strong increase of the frequency of the Damon-Eshbach mode by a factor of up to 3 has been found with decreasing layer thickness. This novel behavior is described quantitatively by a model, which takes explicitly into account magnetic surface anisotropies. An additional growth-induced uniaxial magnetic surface anisotropy due to steps in the Fe layer could be identified.

Magnetic Surface Anisotropy of the FeCu Interface in Superlattices

Magnetic Surface Anisotropy of the FeCu Interface in Superlattices

Surface demagnetizing field as a source of uniaxial surface anisotropy in GdCoMo thin amorphous films

Surface magnetic anisotropy energy was studied for (Gd 0.26Co 0.74) 0.96Mo 0.04 and (Gd 0.29Co 0.71) 0.96Mo 0.04 thin amorphous films by means of microwave spectroscopy at the X-band within the temperature range 4–295 K. Excitations of surface spin waves were observed in the spin wave resonance spectra. The experiment was performed in a rotating external magnetic field. The angular dependence of the resonance field for the uniform mode (spin wave vector k=0) and the surface mode made it possible to determine the surface uniaxial anisotropy constant K s and its temperature dependence. An inhomogeneity of the saturation magnetization M s within a close-to-surface layer of thickness d can generate the surface anisotropy energy with anisotropy constant K s given by the formula: K s=4 πM b s ( M b s− M surf s) d, where the indexes b and surf correspond to the bulk and surface values, respectively. The temperature dependence of K s calculated by means of the formula agrees qualitatively with temperature dependence of K s found in the experiment.

Strong influence of magnetic surface anisotropies on the Damon-Eshbach mode frequency of ultrathin Fe(110) layers (abstract)

Epitaxially grown Fe(110) layers on W(110) with thicknesses between 8 and 150 Å have been investigated in situ by Brillouin scattering. A strong increase of the frequency of the Damon-Eshbach (surface spin wave) mode by a factor of up to 3 has been observed with decreasing layer thickness below 60 Å. The frequency increase is accompanied by a strong line width broadening. In good agreement with earlier observations,1–3 the change over of the easy axis of the saturation magnetization from [001] to [1-10] could directly be observed at a critical thickness dc=95±5 Å with an applied residual magnetic field of 30 G. The anomalous behavior of the Damon-Eshbach mode is quantitatively described by a model fit, which takes explicitly into account magnetic surface anisotropies. The magnetic in-plane surface anisotropy constant Ks,p=2.4×10−2 erg cm2 has been calculated from the literature value of the bulk anisotropy constant K1, the residual applied magnetic field and the critical thickness dc, using the homogeneous magnetization approximation.2 The fitted value of the magnetic out-of-plane anisotropy constant Ks=2.8±0.7 erg/cm2 is smaller than the value obtained for the case of Fe(110) on GaAs(110).1 While for Fe thicknesses larger than 30 Å the film quality is not very crucial for the spin-wave spectra, 10-Å-thick films show a strong increase of the Damon-Eshbach mode frequency with increasing density of steps on the surface. Since these steps are aligned parallel to the [001] direction as observed by LEED, we attribute the frequency increase to additional uniaxial surface anisotropies induced by the steps. On the other hand, the formation of islands leads to a frequency decrease due to reduced anisotropies.

Magnetic properties of [100] oriented Cu-Ni superlattices

We have fabricated Cu-Ni superlattices with exclusive [100] modulating orientation by using a dc magnetron sputtering system. The layer thicknesses of both Cu and Ni range from 5 to 125 Å. The high quality of the samples is confirmed by the intense satellite peaks in the x-ray diffraction. The spontaneous magnetization at 5 K, which is found to be inversely proportional to the Ni layer thickness, vanishes at two Ni atomic planes. A very large difference in magnetic surface anisotropy has been found between [100] and [111] textured Cu-Ni superlattices, displaying the important role of modulating orientation on the magnetic properties of superlattice.

Ferromagnetic phase transition of the film and surface

A ferromagnetic phase transition of the film and surface is studied by the Green’s function method based upon the Heisenberg model with surface magnetic anisotropy. It is proved that the order parameter (spontaneous magnetization) changes with the position in the ferromagnetic film which loses translational invariance in one direction. Expressions for the Curie temperature and spontaneous magnetization of each atomic plane in the film have been derived. The properties of magnetic order of the surface atomic plane are very different from those of the other atomic planes in the film. One expects that the extraordinary phenomena will exist in ultrathin films, since for strong surface magnetic anisotropy, as the thickness of film is decreased, the Curie temperature rises, etc.

Nonlocal magnetic susceptibility tensor and spin-wave resonance of the ferromagnetic film (abstract)

The magnetic susceptibility and spin-wave resonance is studied by the method of Green’s function based upon the Heisenberg model with the surface magnetic anisotropy. It is proved that the ferromagnetic film which loses translational invariance in one direction has a nonlocal magnetic susceptibility tensor. Applying the method of nonlocal magnetic susceptibility formulation, which results in self-coherence of magnetization in the film, the relation between the surface magnetic anisotropy of film and the modes of spin wave exited by the uniform microwave field is derived, and the expressions of position and intensity of resonance peaks are given. According to the nonzero condition of self-coherence of magnetization in the film, three cases have been shown that the uniform microwave field should be able to excite spin wave: (1) Free surface boundary condition (D=0): Only the uniform mode (K=0) should be excited. (2) Symmetrical surface anisotropy boundary condition: For the strong surface anisotropy (D=J), the nz=1,3,5,... odd modes [k=nzπ/(n+1)] should be excited. For the weak surface anisotropy (D≪J), the nz=(2εn)1/2/π, 2,4,6,... even modes (k=nzπ/n) should be excited. (3) Asymmetrical surface anisotropy boundary condition: In general, all the modes should be excited. There is no k=0 spin wave in both cases (3) and (2).

Conditional replaceability of magnetic surface anisotropies by effective volume anisotropies in the ferromagnetic resonance of ultrathin films

Specific conditions are proposed for the replaceability of magnetic surface anisotropies by effective volume anisotropies and for the concomitant replaceability of the actual ferromagnetic resonance (FMR) surface mode or spin wave mode by a uniform mode. These conditions are then applied to the parallel and perpendicular FMR configurations in monocrystalline and amorphous ferromagnetic films. The significance and limitations of the results are discussed.

Magnetic surface anisotropy and ferromagnetic resonance in single-crystal GdAl2

Ferromagnetic resonance in bulk single-crystal specimens of GdAl2 shows two overlapping absorption lines. The variation of this structure with the temperature of the specimen and the crystallographic orientation of the magnetisation M0 is described. The line with the lower resonance field is attributed to the normal bulk mode and that at higher field to a surface-induced mode. The latter is shifted to a higher field by magnetic surface anisotropy. At higher temperatures (T>80K) the bulk mode is more intense but as T is reduced the relative strength changes and below about 30K the surface-induced mode is entirely dominant. For specimens with (110) surfaces the mode separation is greatest when M0 is oriented between (111) and (111) directions and least when M0 is along (001) and (001). The model employed to interpret these phenomena is based upon a classical equation of motion for M0, Maxwell's equations and boundary conditions for the magnetisation at the sample surface which involve the magnetic surface anisotropy. By interpreting the separation of the resonance lines as a function of the orientation of M0 the expression for the magnetic surface anisotropy energy as a function of this orientation is deduced and values for the necessary three magnetic surface anisotropy constants are deduced as a function of temperature. The main surface anisotropy gives an easy direction of magnetisation perpendicular to the surface. The easiest directions within the surface are (001) and (001). Interpretation of the resonance linewidth and relative intensity of the two modes is not satisfactory. It is suggested that this is because the measured lines are influenced by inhomogeneous broadening which is absent from the theory.

Magnetic surface anisotropy of amorphous Fe-B ultrathin films

The magnetic surface anisotropy constants K S of amorphous Fe x B 100- x was determined by performing ferromagnetic resonance (FMR) measurements on ultrathin films and adapting a recent FMR theory to amorphous materials. For a given Fe content x the same value of K S is obtained at two frequencies and two FMR configurations.

Magnetic surface anisotropies

A review is given on experimental methods to determine magnetic surface anisotropies, and on experimental results for well-defined single-crystal surfaces, both for out-of-plane and in-plane anisotropies. Results are compared with Néel's phenomenological theory.

In-plane magnetic surface anisotropies in Fe(110)

In-plane magnetic surface anisotropies have been detected for Fe(110) on W(110) using in situ Conversion Electron Mossbauer Spectroscopy (CEMS). The phenomenon used for the determination of this anisotropy was a switching of the spontaneous magnetizationJ s from [001] to [1¯10] with decreasing thickness. Analysis of the data is performed using a homogeneous magnetization approximation for competing surface and bulk anisotropies, which is justified by a micromagnetic analysis and established experimentally by CEMS. In-plane surface anisotropy constants for the clean Fe(110) surface, the Fe metal-interface and the FeGaAs interface are determined toK s,p FeUHV =0.065 erg·cm−2,K s,p FeMetal =0.040 erg ·cm−2, andK s,p FeGaAs =0.047 erg ·cm−2, all with an estimated accuracy of the order of 10%.