Effect of small magnetic corrections to susceptibility on the angular dependences of the reflectivity of polarized X-rays from multilayer structures

The X-ray resonant magnetic scattering (XRMS) method allows for the determination of optical constants including magnetic corrections, which are significant near the atomic X-ray absorption edges, by the shift of the Bragg angle of the reflection from periodic multilayers. Recently, Valvidares et al. [Phys. Rev. B 78, 064406 (2008)] revealed significant differences in the shape of “magnetic” Bragg reflection peaks from a [Co₇₃Si₂₇(50 Å)/Si(30 Å)]₁₀ film for two opposite states of antiferromagnetic interlayer ordering. Valvidares et al. assumed that these features can be explained by the presence of the reflection-induced magnetic resonance correction. We have demonstrated that such corrections in the case of antiferromagnetic structures do not lead to a shift of the Bragg peak, but the shape of magnetic peaks is explained by the interference of the magnetic and nonmagnetic reflection amplitudes.     

Theoretical analysis of the spectra of X-ray resonant magnetic reflectivity

We have developed the general computer code for the calculations of reflectivity with polarization analysis from an arbitrary anisotropic multilayer, which allows us to test different approaches for the Bragg reflectivity spectrum treatment. We have proved the validity of the usage of the Bragg peak position for the determination of the energy dependence of the diagonal component of resonant susceptibility tensor, but revealed the essential discrepancy of this procedure for the off-diagonal term determination. The explanation lies in the polarization mixture by multiple reflections at large glancing angles. By the model calculations we have shown that in L-MOKE geometry the observed difference of the integrated Bragg peak reflectivity for the (+) and (−) field direction is predominantly caused by the magnetization of the central part of resonant layer at the first-order Bragg peak, but it is very sensitive to the interface magnetization at the second-order Bragg peak.     

Frequency dependences of FMR in films with angular dispersion of the magnetic anisotropy

On the basis of a statistical model of noninteracting blocks, it is clarified that films with high angular dispersion (₀ 15–35°) are characterized by an asymmetric resonance curve whose amplitude _r and width H depend, in contrast to uniaxial films, on the angle of film rotation in its plane in large field domains and whose frequency dependences are related substantially to the angular dispersion; the presence of domains in the angular dependence of the resonance field where H_r is constant; an effective magnetic anisotropy field dependent on the frequency and with the limit valueH _K ^eff =H _K exp(–2a ₀ ² . The theoretical deductions are conformed by experiment.Translated from Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 75–81, July, 1987.     

The influence of surface roughness in X-ray resonant magnetic reflectivity experiments

We present simulations of X-ray resonant magnetic reflectivity (XRMR) spectra of the surface magnetic dead layer in La_1−x Sr _x MnO₃ (LSMO) films that take in account the effect of different forms of roughness that can be encountered experimentally. The results demonstrate a method to distinguish between surface (morphological) roughness, and two generic kinds of magnetic roughness at the buried interface between the surface dead layer and the fully magnetic bulk part of the film. We show that the XRMR technique can distinguish between different types of magnetic roughness at the dead layer/bulk interface only if the sample surface is nearly atomically flat (the morphological roughness is one unit cell or less). Furthermore, to distinguish between the two types of magnetic roughness, the simulations show that fitting of XRMR spectra out to very high incidence angles must be performed. In the specific case of LSMO films with a dead layer with average thickness of 4 unit cells, this corresponds to an incidence angle > 50^∘.     

Temperature dependences of Raman scattering in different types of GaN epilayers

First-order Raman scatterings of hexagonal GaN layers deposited by the hydride vapour phase epitaxy and by metal-organic chemical vapour deposition on SiC and sapphire substrates are studied in a temperature range between 303 K and 503 K. The temperature dependences of two GaN Raman modes (A₁ (LO) and E₂ (high)) are obtained. We focus our attention on the temperature dependence of E₂ (high) mode and find that for different types of GaN epilayers their temperature dependences are somewhat different. We compare their differences and give them an explanation. The simplified formulas we obtained are in good accordance with experiment data. The results can be used to determine the temperature of a GaN sample.     

Calculation of nuclear resonant scattering spectra of magnetic multilayers

We report on calculations of the angle- and time-dependent photon reflectivity of multilayers using the technique of characteristic matrices. Spectra of⁵⁶Fe/⁵⁷Fe and Cr/Fe multilayers are calculated under various conditions. The parameters of the multilayers are optimized for suitable test samples of reflectometry measurements.     

Depth magnetization profile of a perpendicular exchange coupled system by soft-x-ray resonant magnetic reflectivity

The magnetic profile across the interface of a perpendicular exchange coupled [NiO/CoO]3/Pt-Co/Pt(111) system is investigated. The magneto-optic Kerr effect reveals a strong coupling between the antiferromagnetic (AFM) oxide and the ferromagnetic (FM) Pt-Co layer, by an increasing coercivity and a rotation of the easy magnetization axis of the FM layer along the AFM spins. Soft x-ray resonant magnetic reflectivity is used to probe the spatial distribution of the out-of-plane magnetization inside the oxide above its ordering temperature. It extends over 1 nm and exhibits a change of sign.     

Some angular| dependences of the ion-electron emission coefficient

In the cases when primary ion beam direction is aligned with close-packed planes the dependences of the reduced coefficient of ion-electron emission on various angles has been studied. It was found that there are such ranges of azimuthal angle and angle of incidence of primary ion beam within which the reduced coefficient is determined mainly by the angle between the primary ion beam and close-packed plane only.     

Creation of the ordering of angular momenta of particles in strong electric and magnetic fields

It is shown that strong magnetic and electric fields can create ordered states of angular momenta, which manifests itself in the interconversion of the polarizations of radiation.     

Forced ferromagnetic ordering in systems with magnetic ions of two types

The distribution of magnetization in domain walls of ferromagnetic (FM) crystals with two order parameters interacting with each other—F_1z and F_2z, is considered. In one case the interaction is represented as (F_1zF_2z) and in another—(F_1z²F_2z²). It is shown that in the former case the magnetization distribution has space amplitude modulation, and in latter case appears space frequency modulation. Changes of the paramagnetic-ferromagnetic phase transition temperature in view of interaction of two FM subsystems have been studied.     

Effect of cubic magnetic anisotropy on angular dependences of the resonance field in (111)-oriented films

The angular dependences of the ferromagnetic resonance (FMR) field in (111)-oriented films are analyzed with the use of resonance relations and the conditions for equilibrium orientation of the magnetization. Based on the results obtained, an FMR method is proposed for determining the sign of the cubic anisotropy and the position of the crystallographic axes. Zh. Tekh. Fiz. 68, 118–120 (November 1998)     

Types of the jump phenomenon in the angular dependence of the noncollinear exchange bias

Based on the principle of minimal energy and the coherent rotation model, two types of the jump phenomena, complete and incomplete jump phenomenon, are proved to exist in the angular dependence of the exchange bias with noncollinear unidirectional and uniaxial anisotropies. It is found that the transition between complete and incomplete jump phenomena occurs on condition that the exchange-coupling constant exceeds a critical value. Additionally, two different modes of the magnetization rotation, the whole-plane rotation, and the half-plane rotation are present in the magnetization reversal process, and they are dependent on the direction of the external field. Furthermore, the equations of the critical angle, at which orientation the exchange bias field reaches a maximum value and the coercivity disappears, are also derived in this paper. The numerical calculations in this paper are consistent with the relevant experimental observations, indicating that our method to study the angular dependence of the exchange bias as well as the magnetization reversal behaviors is valid. Our discussion about the jump phenomenon, the critical angle, and the modes of the magnetization reversal can explain the observed differences in results between different experiments.     

Effect of the intersite Coulomb interaction on chiral superconductivity at the noncollinear spin ordering

We investigate the effect of the intersite Coulomb interaction in a planar system with the triangular lattice on the structure of chiral order parameter Δ(p) in the phase of coexisting superconductivity and noncollinear 120° magnetic ordering. It has been established that the Coulomb correlations in this phase initiate the state where the quasi-momentum dependence Δ(p) can be presented as a superposition of the chiral invariants corresponding to the \({d_{{x^2} - {y^2}}} + i{d_{xy}}\) and p _x + ip _y symmetry types. It is demonstrated that the inclusion of the Coulomb interaction shifts the Δ(p) nodal point positions and, thereby, changes the conditions for a quantum topological transition.