Magnetic anisotropy of a system of nanocrystalline BaO·6Fe2O3 particles

The anisotropy of a system of barium ferrite particles with an average diameter of 60 nm has been studied. The effective anisotropy constant has been determined in the temperature range from 4.2 K to T _c by the law governing approach to saturation magnetization. The observed deviation from the magnetocrystalline anisotropy constant is explained as due to a negative contribution of the “surface” anisotropy constant. An estimate is made of this contribution as a function of particle size. Fiz. Tverd. Tela (St. Petersburg) 40, 1894–1897 (October 1998)     

Photoionization of 3<Emphasis Type="Italic">d</Emphasis> electrons of Xe,Cs and Ba endohedral atoms: comparative analyses

We demonstrate rather interesting manifestations of co-existence of resonance features in characteristics of the photoionization of 3d-electrons in Xe, Cs and Ba endohedral atoms. It is shown that for all of the considered atoms the reflection by the fullerene shell of photoelectrons produced by the 3d subshell photoionization affects greatly partial photoionization cross-sections of 3d _5/2 and 3d _3/2 levels and respective angular anisotropy parameters, both dipole and non-dipole adding to all of them additional maximums and minimums. The results obtained demonstrate distinctive differences between the three atoms. The calculations are performed treating the 3/2 and 5/2 electrons as electrons of different kinds with their spins “up” and “down”. The effect of the C₆₀ shell is accounted for in the frame of the “orange” skin potential model. It is essential that in the considered photon frequency region the presented resonance features are not affected by the C₆₀polarization.      

Anisotropic ESR parameters of Cu(II) complexes in solutions and dynamics of solvent coordination: use of “minimum linewidths”

The “minimum linewidths” seen in the ESR linewidths against temperature plots, the dependence of line widths on the⁶³Cu nuclear magnetic quantum numbers and the Hubbard relation provide sufficient number of equations to determine the anisotropic ESR parameters in the case of axially symmetric Cu(II) complexes even when unresolved hyperfine structures make contributions to linewidths. After testing the method by reanalysing the literature data on Cu(II) bis-acetylacetonate, it has been used to obtain the anisotropic ESR parameters in the case of bis-salicylaldehydate of Cu(II). Linewidth contributions from unresolved hyperfine structures associated with the¹H of coordinating CHCl₃ inferred in these studies, were confirmed by comparing the widths in CHCl₃ and CDCl₃ under ideal conditions. The temperature dependence of this contribution and the estimate of rate constant at room temperature (∼ 10¹⁰ s⁻¹) suggest that the coordinating solvent exchange is diffusion controlled.     

Relaxation of quasi-transverse phonons in the Herring mechanism and ultrasound absorption in cubic crystals with positive and negative anisotropies of the second-order elastic moduli

The phonon relaxation and quasi-transverse ultrasound absorption in the course of Herring and Landau-Rumer anharmonic scattering processes in cubic crystals with positive (Ge, Si, diamond, InSb, LiF, MgO) and negative (KCl, NaCl, CaF₂) anisotropies of the second-order elastic moduli have been investigated. A new mechanism of transverse phonon relaxation, according to which the fusion of a transverse (slow or fast) phonon with a slow phonon generates a fast transverse phonon, has been considered in the long-wave-length approximation. This mechanism is similar to the Herring relaxation mechanism for longitudinal phonons. It has been demonstrated that, for crystals of the first group with a considerable anisotropy of the elastic energy (Ge, Si, InSb, LiF, MgO), “anomalous” relaxation processes in which the fusion of a slow transverse phonon with a fast phonon generates a slow transverse phonon are possible in contrast to the Herring relaxation mechanism for longitudinal phonons. These relaxation processes appear to be impossible for all crystals of the second group (KCl, NaCl, CaF₂), as well as for crystals of the first group with a small anisotropy of the elastic energy, such as diamond. The angular dependences of the ultrasound absorption coefficient for the Herring and Landau-Rumer mechanisms have been analyzed using the anisotropic-continuum model. It has been shown that, for the crystals of the first group under consideration, the contribution of the Herring mechanism to the long-wavelength ultrasound absorption is small compared to the contribution of the Landau-Rumer mechanism. However, for the KCl and NaCl crystals of the second group in directions of the [001] type, the contribution of the Herring mechanism can significantly exceed the contribution of the Landau-Rumer mechanism.     

Magnetic anisotropy of antiferromagnet (CH3)4NMnCl3

The parameters of the electron paramagnetic resonance (EPR) spectra of S ion pairs in diamagnetic crystals are analyzed. A relation between the spin Hamiltonian constants is established for solitary ions and pairs for (CH₃)₄NCdCl₃: Mn²⁺ crystals. In contrast to solitary ions, an additional contribution (which is a linear function of the exchange field) to the “single-ion” spin Hamiltonian constants appears in the case of pairs. It is shown that anisotropic exchange mechanisms do not play a significant part in the formation of the axial constant of the spin Hamiltonian for this crystal. Some aspects of the method of studying “single-ion” anisotropy predicted by the two-ion model are developed with the help of an isostructural diamagnetic analog with impurity concentration of the paramagnetic ions of a magnetically concentrated substance sufficiently high for observing the EPR spectrum of the pairs. It is found that the microscopic quantities determined partially from the EPR spectra for pairs and solitary Mn²⁺ ions in (CH₃)₄NCdCl₃ are in accord with the experimental value of the effective field for the (CH₃)₄NMnCl₃ crystal anisotropy which can be described primarily by the dipole and “single-ion” mechanisms of the exchange origin.     

Uniaxial magnetic anisotropy of rhombohedral CoCO3 crystals at T = 0 K

A method for calculating the contribution of exchange interaction to uniaxial anisotropy with the use of g’ factors has been worked out using CoCO₃ crystals as an example. The calculated contribution of dipole-dipole interactions to the anisotropy of CoCO₃ is 0.93 cm^?1. The sum of the contributions to the anisotropy constant of CoCO₃ with the inclusion of the dipole-dipole interactions is 36.1 cm^?1.     

Giant magnetoresistance in Hg<Subscript>1−x−y</Subscript>Mn<Subscript>x</Subscript>Fe<Subscript>y</Subscript>Te crystals

Giant magnetoresistance in Hg _1−x−y Mn _x Fe _y Te crystals is caused by clusters with “antiferromagnetic” (Mn-Te-Mn-Te, Mn-Te-Fe-Te) and “ferromagnetic” (Fe-Fe-Fe) ordering. The effect is due to the fact that the charge carriers taking part in electric current interact with the “ferromagnetic” cluster subsystem (Fe-Fe-Fe) magnetized to saturation and become spin-polarized. These spin-polarized charge carriers are strongly scattered by the “antiferromagnetic” Mn-Te-Mn-Te and Mn-Te-Fe-Te clusters, because the magnetic moments inside the clusters and resultant moments of clusters have chaotic orientations. Investigations of kinetic coefficients of Hg _1−x−y Mn _x Fe _y Te crystals before and after thermal treatment show that there is no marked correlation between the giant magnetoresistance and charge-carrier concentration, mobility, and band parameters of crystals. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 28–33, October, 2007.     

Effects of interaction of nanoparticles in a highly anisotropic ferrimagnet

This paper reports on a study of the field and temperature dependences of the parameters of the particle magnetic interaction in a densely packed system of nanocrystals of the highly anisotropic hexagonal ferrite BaFe₁₂O₁₉ with the particles distributed in diameter within the range 10—100 nm and having volumes satisfying the criterion of “small Stoner—Wohlfarth particles.” It is shown that the resultant particle interaction in the temperature range 300 K≤T≤640 K has a negative sign, whereas for T>640 K, it is positive. The maximum values of the parameter Δm allow classification of the interaction as moderate in strength. The temperature dependences of the interaction parameters are found to correlate with manifestation of the size and surface effects in the system, which are characteristic of small particles (transition to the superparamagnetic state, “surface” anisotropy, and reduced exchange interaction in a structurally defective near-surface layer of particles).     

The structure of the distortion free-energy density in nematics: Second-order elasticity and surface terms

Summary By means of a phenomenological approach, we demonstrate that the mixed splay-bend elastic constantK ₁₃ in the free energy density of nematic liquid crystals must be considered zero, unless the bulk contributions of the squares of the distortion second-order derivatives are taken into account, together with the squares of the first-order derivatives times the second-order derivatives, and with the fourth powers of the first-order derivatives. Such contributions just reduce to one in the presence of—and close to—a threshold. Furthermore, the saddle-splayK ₂₄-term instead is shown always to play an essential role, as the bulk first-order elasticity, in determining the distortion free energy of nematics with weak anchoring subjected to spatial deformations. Finally, the new surfacelike elastic constants are shown to have a nilpotent character: thus they behave as well asK ₂₄ from the point of view of the variational calculus. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

Effects of the interaction between R and Fe modes of the magnetic resonance in RFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> rare-earth iron borates

Resonance modes that are due to magnetic excitations in the exchange-coupled subsystems of rare-earth ions (R = Nd³⁺, Sm³⁺, and Gd³⁺) and Fe³⁺ ions have been detected in submillimeter transmission spectra (0.1–0.6 THz) of RFe₃(BO₃)₄ iron borate-multiferroic single crystals. The strong interaction between spin oscillations of the Fe and R subsystems has been revealed, which determines the behavior of the modes depending on the anisotropy of the exchange splitting of the ground doublet of the R ion. It has been shown that the intensities of coupled modes (contributions to the magnetic permeability) depend strongly on the difference between the g factors of Fe and R ions. This dependence makes it possible to determine the sign of the latter g factor. In particular, a noticeable intensity of exchange Nd modes in NdFe₃(BO₃)₄ is due to an increase in their contribution at g _{⊥, ‖}^Nd < 0, while in GdFe₃(BO₃)₄ with g _Gd ≈ g _Fe ≈ 2, the Fe and Gd contributions compensate each other and the exchange (Gd) mode is not observed. In spite of the weak interaction of Sm ions with the magnetic field, SmFe₃(BO₃)₄ exhibits resonance modes, which are attributed to the excitation of Sm ions through the Fe subsystem.     

Anisotropy of the vortex structure and resistivity in the basal plane of YBa<Subscript>2</Subscript>Cu<Subscript>4</Subscript>O<Subscript>8</Subscript> single crystals

The vortex lattice of the YBa₂Cu₄O₈ high-temperature superconductor is studied in the basal plane of monocrystalline samples using the decoration technique in a field interval of 40–600 Oe. Vortex lattice anisotropy (field-independent “compression” of a regular hexagonal vortex cell in the poorly conducting direction by a factor of about 1.3) is detected. Resistivity anisotropy ρ _a /ρ _b measured at temperatures from T _c to room temperature is 16–9. Possible reasons for the discrepancy between our results and the available data are discussed.     

Surface effects in nanoparticles: application to maghemite -Fe O

We present a microscopic model for nanoparticles, of the maghemite (-Fe₂O₃) type, and perform classical Monte Carlo simulations of their magnetic properties. On account of M?ssbauer spectroscopy and high-field magnetisation results, we consider a particle as composed of a core and a surface shell of constant thickness. The magnetic state in the particle is described by the anisotropic classical Dirac-Heisenberg model including exchange and dipolar interactions and bulk and surface anisotropy. We consider the case of ellipsoidal (or spherical) particles with free boundaries at the surface. Using a surface shell of constant thickness ( nm) we vary the particle size and study the effect of surface magnetic disorder on the thermal and spatial behaviors of the net magnetisation of the particle. We study the shift in the surface “critical region” for different surface-to-core ratios of the exchange coupling constants. It is also shown that the profile of the local magnetisation exhibits strong temperature dependence, and that surface anisotropy is responsible for the non saturation of the magnetisation at low temperatures. Received 1 September 1999 and Received in final form 3 November 1999     

Physical reasons for the emergence of jumps during rotation of the magnetization of a two-sublattice ferrimagnet at low temperatures

It is shown that the contribution of the intersublattice exchange interaction to the magnetic anisotropy energy of a two-sublattice ferrimagnet can come only from higher order constants satisfying the condition 2K₂+3K₃+?>0. For this reason, for different signs of the first anisotropy constants of the sublattices, this contribution may cause a spontaneous spin-reorientation second-order transition, but not first-order transitions and jumps during magnetization rotation, which are associated with such a transition. Such jumps can appear only when the opposite inequality is satisfied, and the corresponding contribution to anisotropy can be ensured only by a fairly strong magnetoelastic interaction.     

Periodic domain structures obtained by growth of LiNbO<Subscript>3</Subscript> crystals doped with gadolinium

The growth of a periodic domain structure in LiNbO₃ crystals doped with gadolinium (Gd, 0.44 wt %) was investigated by special electron beam surface charging in a scanning electron microscope and on a atomic force microscope. Ferroelectric domain boundaries with “tail-to-tail” and “head-to-head” P _s orientations were comparatively analyzed. The domain boundaries had different forms and differed by their physical properties. Micron-size surface crystal regions close to the “tail-to-tail” boundaries were charged slower by electron irradiation and had modified elastic properties. This region was detected by using the lateral force mode of atomic force microscopy. The observed morphology and property features were supposed to be due to different concentration gradients of the Gd impurity and different width of its distribution close to the domain boundaries of different types.     

Dipole contribution of Fe3+ ions in 12k positions to the anisotropy energy constant of the BaFe12O19 hexaferrite

The anisotropy of local fields on ⁵⁷Fe nuclei of Fe³⁺ ions located in the 12k positions of the BaFe₁₂O₁₉ ferrite is studied at low temperatures. The contributions of the anisotropy of the dipole and hyperfine fields to the anisotropy of local fields are separated. The contribution of Fe³⁺ ions in the 12k positions to the anisotropy energy constant K ₁ is calculated in the case of the interionic magnetic dipole-dipole interaction. This contribution comprises more than one-half the experimental K ₁ value.     

Scales in nuclear matter: Chiral dynamics with pion nucleon form factors<Superscript>⋆</Superscript>

A systematic calculation of nuclear matter is performed which includes the long-range correlations between nucleons arising from one- and two-pion exchange. Three-body effects from 2π exchange with excitations of virtual Δ(1232)-isobars are also taken into account in our diagrammatic calculation of the energy per particle ˉ(k _f). In order to eliminate possible high-momentum components from the interactions we introduce at each pion-baryon vertex a form factor of monopole type. The empirical nuclear matter saturation point, ρ₀ ≃ 0.16fm^-3, ˉ₀ ≃ - 16MeV, is well reproduced with a monopole mass of Λ ≃ 4πf _π ≃ 1.16GeV. As in the recent approach based on the universal low-momentum NN potential V _low-k, the inclusion of three-body effects is crucial in order to achieve saturation of nuclear matter. We demonstrate that the dependence of the pion exchange contributions to ˉ(k _f) on the “resolution” scale Λ can be compensated over a wide range of Λ by counterterms with two “running” contact couplings. As a further application we study the in-medium chiral condensate 〈ˉq〉(ρ) beyond the linear density approximation. For ρ ⩽ 1.5ρ₀ we find small corrections from the derivative dˉ(k _f)/dm _π, which are stable against variations of the monopole regulator mass Λ.     

Spin wave dispersion of FeBO3 at small wavevectors

Brillouin scattering from thermally excited magnons and ferromagnetic resonance are used to determine the spin wave dispersion of the low-frequency spin wave branch in FeBO₃, a transparent weak ferromagnet. In addition to the dominant exchange and Zeeman contributions, the investigation takes into account magnetic dipole and magnetoelastic interactions. Due to the antisymmetric exchange enhancement the material exhibits a broad spin wave band and a large gap energy at small magnetic fields. Competing directional dependences of the dipole and the exchange energy produce a degeneracy of spin waves with a certain magnitude of the wavevector propagating in different directions. The gap energy is shown to be due to magnetoelastic coupling, whereas the contribution of the anisotropy in the easy plane is negligible atT=300 K.     

晶场二级效应与交换作用对PrF3晶体磁性及磁光性质的影响

研究了晶场二级效应在PrF₃晶体中的作用，发现该效应可使Pr³⁺离子的晶场单态与其他态混合，对PrF₃晶体磁化率产生明显影响.进一步研究了晶体内的交换作用有效场，其形式为H_in=(1.9-0.02556T)×10^-5M，在100—300 K的温度范围内，以此计算的PrF₃晶体的倒数磁化率和Verdet常数的倒数与实验值符合较好.结果表明，在PrF₃晶体中，晶场二级效应与离子间的交换作用都不能忽略. 关键词： 晶场二级效应 交换作用有效场 Verdet常数 3晶体')" href="#">PrF₃晶体     

Magnetostatic volume waves in exchange-coupled ferrite films

The influence of exchange coupling of layers on the propagation of magnetostatic dipole volume waves in normally and tangentially magnetized two-layer epitaxial ferrite structures is investigated. It is shown that the indicated influence is manifested in the form of dynamic spin pinning effects on the interlayer boundary and formation of a common dipole-exchange wave spectrum for the entire structure. In this case, at the synchronism frequencies of the dipole and exchange waves the losses of the dipole waves grow and anomalous segments appear in the dispersion. In films magnetized in the “hard” direction relative to the axis of normal uniaxial surface anisotropy the magnetostatic dipole volume waves can interact resonantly with the surface spin waves supported by the boundaries with pinned spins. Zh. Tekh. Fiz. 68, 97–110 (July 1998)