A simple theory of inhomogeneity linewidth broadening in MnxFe3−x,O4 ferrites

A simple theory of linewidth broadening due to thermal treatment is given. The theory is based on the assumption that the manganese-rich regions — clusters — with local tetragonal symmetry appear in the sample due to the alignment of tetragonally distorted Mn^{3 +} ions. This is a source of local anisotropy fields, leading to two-magnon scattering. The size of clusters and consequently their contribution to the linewidth depends on the thermal treatment. The function giving the dependence of the linewidth broadening on the cluster size is calculated using Schlömann's autocorrelation function. The recent experimental results are qualitatively discussed in terms of this theory. For the temperature dependence of the effect an effective compositionx = 1·8 inside the cluster is assumed, which gives a qualitative agreement with experiment. The discussion of the dependence of linewidth broadening on the composition has only an illustrative character and shows that the theory is compatible with experiment. A qualitative disagreement found for the angular dependence of (H) is believed to be a consequence of the high field approximation used.The author would like to express his thanks to Dr. S. Krupiçka for suggesting the problem and for many valuable discussions. Thanks are also du eto Dr. J. Loos for several discussions about the correlation problem, to Dr. Z. Smetana for information about experimental work and to Dr. C. Novák, who performed the numerical calculations.     

Calculation of nuclear spin-lattice relaxation rate due to two-magnon scattering in YBa2Cu3O6

YBa₂Cu₃O₆ is known to be an antiferromagnetic insulator with high Neel temperature (T_N≈400≈500 K). The nuclear spin-lattice relaxation rate 1/T₁ due to two-magnon scattering is calculated, using values of ecchange integrals and anisotropy gap published in literature. We found approximately quadratic dependence of relaxation rate 1/T₁ on temperature for temperatures above 100 K. The value of 1/T₁, determined by low-energy magnons, is found to be inversely proportional to magnitude of gap in magnon spectrum.     

Plasmon-magnon interaction in magnetic semiconductors

In appreciably doped semiconductors (e.g. EuO, CdCr₂S₄, etc.) plasmon and magnon energies are comparable. Therefore, there will be resonant interaction between these modes of excitations. On the basis of a new microscopic theory formulated for plasmon-magnon interaction, the effect of this interaction on the energies and lifetimes of plasmons and magnons has been calculated using the double-time Green’s function. The energy shifts are very small and the lifetimes of plasmons,τ ^p , and magnons,τ ^m , are of the order of 10⁻² and 10⁻³ sec respectively.     

Theory of infra-red and optical spectra of antiferromagnets

The contributions of magnons to the optical properties of antiferromagnets having the rutile structure are discussed. The properties considered are electric-dipole active two-magnon absorption in the infra-red, and magnon sidebands on sharp-line exciton transitions in the visible. The discussion is based on a thorough treatment of the properties of excitons and magnons in the antiferromagnetically ordered state. The site-group and space-group symmetries of the magnetic excitations are derived and the selection rules for electric and magnetic dipole transitions are determined. The occurrence of magnetic Davydov splittings of the excitons is investigated, and their symmetry properties throughout the Brillouin zone are derived. The functional dependences of exciton energy on wave vector are calculated. Applications of the theory are made to experimental results on excitons and magnons in MnF₂, FeF₂ and CoF₂.

The possible mechanisms for two-magnon and magnon-sideband absorption are discussed, and the influence of crystal symmetry on these mechanisms is described. The two-magnon state responsible for electric-dipole absorption is identified and selection rules for electric-dipole activity are presented. A spin Hamiltonian for the two-magnon process is set up and used to derive expressions for absorption coefficients for electric vector parallel and perpendicular to the crystal c-axis. Comparison with experiment for MnF₂ yields numerical values for the parameters of the basic coupling mechanism. The exciton-magnon states which give rise to magnon-sideband absorption are explicitly constructed and electric-dipole selection rules are derived for all possible types of sideband. Spin Hamiltonians for the various magnonsideband absorption processes are presented and used to derive expressions for sideband shapes. The results are applied to the experimental spectra for MnF₂ and FeF₂ and the sideband shapes in MnF₂ are calculated numerically. The sideband shapes observable in emission spectra are also briefly discussed.     

Magnetic Raman optical activity in FeF2

Raman optical activity (ROA) of magnons and phonons in antiferromagnetic FeF₂ (T_N=78 K) has been studied as a function of temperature and in applied magnetic field. For exciting light incident along the rutile-structure c-axis, ROA is observed for magnons but not phonons. In zero field, the small anisotropy-induced splitting (0.09 cm⁻¹) of the two acoustic-magnon branches is observed by light scattering for the first time. The splitting in applied magnetic field is found to reduce with increasing temperature in accordance with theory. No ROA was detected for two-magnon excitations.     

Wärmewiderstand durch Spinwellen —Spinwellenstreuung in einem Ferromagnetikum

The heat conduction by spin waves is obtained using the Boltzmann equation and considering only magnon-magnon scattering. In contrast to the case of phonons with a linear energy-momentum relationship, Umklapp processes need not be considered to obtain a non-vanishing collision-term in the Boltzmann equation for magnons. In a spin system with a Hamiltonian consisting of exchange and anisotropy energies the temperature dependence of the thermal resistivity isa+bT ^3/2 within the spin wave approximation.     

Fission and the ion-ion interaction

A fission theory based on a preformation probability and the decay of the daughter pair through their associated ion-ion potential is presented. The preformation probability is estimated to be 10⁻⁵. The nuclear component of ion-ion potential is determined in a sudden approximation by superposing the ground state densities of the daughter pair and is found to be 60–70 MeV deep. Using observed kinetic energies, absolute lifetimes are calculated for both symmetric and asymmetric fission of U²³⁴, Pu²⁴⁰, Cm²⁴⁴, and Cf²⁴⁸ with good results. In addition, the absolute lifetimes associated with the decay of Pu²⁴⁰ into a series of other modes are presented. The relevance of this theory to the isotopic dependence of lifetimes, prompt neutron fission, and subthreshold fission is discussed in qualitative terms. Thus the nuclear fission seems to be a sudden process.     

Nature of the temperature dependence of the absorption coefficient in the remote wing of the 4.3 μm CO2 band

The complex nature of the temperature dependence of the absorption coefficient beyond the edge of the CO₂ 4.3 m band — the change of the sign of the derivative of the absorption coefficient with respect to the temperature near the edge and in the remote wing of the band — is explained on the basis of the theory of spectrum line wings. The first change in the sign is due to the temperature dependence of the classical potential of intermolecular interaction; the second depends mainly on the difference in the quantum energies of molecule interaction. Therefore, a study of the dependence of the absorption coefficient on the temperature in the band wings provides information about the nature of the terms of the interacting molecules.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 42–45, December, 1987.     

Magnetic excitations in solids

This article presents a review of low to moderate frequency magnetic excitations, termed magnons or spin waves, in magnetically ordered materials. The emphasis is on intuitive behavior rather than analytical theory. Topics include spin waves, magnetostatic modes, dipole-exchange modes, surface anisotropy, dispersion properties, nonlinear effects, and relaxation. These phenomena are illustrated with experimental examples based on magnon light scattering results as well as conventional microwave techniques.     

Quantum Bocce: Magnon–magnon collisions between propagating and bound states in 1D spin chains

The dynamics of two magnons in a Heisenberg spin chain under the influence of a non-uniform magnetic field is investigated by means of a numerical wave-function-based approach using a Holstein–Primakoff transformation. The magnetic field is localized in space such that it supports exactly one single-particle bound state. We study the interaction of this bound mode with an incoming spin wave and the interplay between transmittance, energy and momentum matching. We find analytic criteria for maximizing the interconversion between propagating single-magnon modes and true propagating two-magnon states. The manipulation of bound and propagating magnons is an essential step towards quantum magnonics.     

Influence of magnetic dipolar interaction on one- and two-magnon scattering of light in ferromagnets

It is shown that the presence of magnetic dipolar interaction in a ferromagnetic medium changes the polarization selection rules of light scattered by magnons. In addition it provides a new mechanism for two-magnon scattering.     

On the two-magnon scattering of light and neutrons

The effect of magnon-magnon interaction on the two-magnon scattering of light and neutrons has been calculated at finite temperatures. Neglecting life-time effects the temperature dependence of the magnetization and that of the spin wave energy as well as the Bose functions for the magnon occupation number have been taken into account. In the low temperature region, where this spin wave approximation is valid, we have gotten a shift of the two-magnon peak toward smaller energies with increasing temperature, which scales with the temperature dependence of the magnon energy and a broadening of the peak as well. These features are in agreement with the result of optical experiments.     

Rotational state distribution of NO molecules scattered from surfaces

Quantum mechanical calculations of final rotational state distributions are carried out for a simple model of the scattering of NO from surfaces. The dependence of the results on parameters of the potential such as sign and size of the anisotropy and asymmetry, the well depth etc. is discussed. Certain difficulties in explaining experimental results for NO scattered from Ag (111) are pointed out. The dependence of the results on an initial rotational temperature is discussed also. Its main effect — which is well known from the literature — is to average out the quantum oscillations of the cross sections around the rainbow structures. The oscillations may become visible at rotational temperatures slightly lower than used up to now.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Angular dependence of magnetoresistivity in c-oriented MgB thin film

The anisotropy of MgB₂ is still under debate: its value, strongly dependent on the kind of sample and on the measuring method, ranges between 1.2 and 13. In this work we present our results on MgB₂ c-oriented superconducting thin film. To evaluate the anisotropy, we followed two different approaches. Firstly, magnetoresistivity was measured as a function of temperature at selected magnetic fields applied both parallel and perpendicular to the c-axis; secondly, we measured magnetoresistivity at selected temperatures and magnetic fields, varying the angle θ between the magnetic field and the c-axis. The anisotropy estimated from the ratio between the upper critical fields parallel and perpendicular to the c-axis and the one obtained in the framework of the scaling approach within the anisotropic Ginzburg-Landau theory are different but show a similar trend in the temperature dependence. Some differences in the upper critical field and in its anisotropy of our film with respect to single crystals are emphasized: some of these aspects can be accounted for by an analysis of upper critical fields within a two-band model in presence of disorder and/or crystallographic strain. Received 12 July 2002 / Received in final form 17 September 2002 Published online 29 November 2002     

Low temperature nuclear orientation of nuclei far from beta stability Spin — Facility at JINR

The experimental facility for the study of the decay of oriented nuclei in a broad range of atomic and mass number and half-lives based on hyperfine interactions at ultralow temperatures — the SPIN facility at JINR — is described. High cooling power top loading 3He-4He dilution refrigerator of the system is capable of fast cooling of the sample inserted into the mixing chamber to the base temperature 10 mK for about 1–2 h. Detection system is designed for the study of angular distribution and temperature dependence of the anisotropy of gamma rays, linear polarisation of gamma rays and NMR/ON studies. Some results of nuclear orientation studies in off-line mode of radioactive nuclei with the half-live down to 1 h produced by spallation reaction with 660 MeV protons are presented. The project of nuclear orientation system on-line to the mass-separator and the new 600 MeV Dubna proton phasotron is described.     

Analytic properties of scattering amplitudes in two variables in general quantum field theory

It is shown that scattering amplitudes have analytic properties as functions of momentum transfer not only for physical, but also for complex energies. This follows from local relativistic field theory for all reactions for which an ordinary dispersion relation can be proved.It is further shown that such amplitudes are boundary values of analytic functions of the two variables energy and momentum transfer. A domain of holomorphy — which is however not best possible — is given explicitly. It follows then that partial waves can be analytically continued to complex energies.     

Raman scattering studies of hexagonal rare‐earth RMnO3 (R = Tb,Dy, Ho,Er) thin films

We have studied the rare‐earth (R) dependence of the phonon and magnon scattering in hexagonal RMnO₃ (R = Tb, Dy, Ho, Er) thin films using Raman scattering spectroscopy. We found, as the ionic radius of R decreases from Tb to Er, the phonons shift to higher energies. Our results indicate that both the lattice constants a and c of hexagonal RMnO₃ would decrease when the ionic radius of R decreases, and the lattice constant c would have a weaker R dependence. The magnons also shift to higher energies when the radius of the R ion decreases, and they show faster upshift than the phonons. In addition, the Néel temperature also shows a systematic increasing behavior when the radius of the R ion decreases. The dependence of the rare‐earth R on the magnons and the Néel temperature can be explained by the rapid increase of the spin‐exchange integral when the Mn–Mn distance decreases. Copyright © 2011 John Wiley & Sons, Ltd.     

The coefficient of surface stiffness for a pinned interface

We derive nonperturbatively — within the meanfield version of the Landau-Ginzburg-Wilson theory — the expressions for the constrained order parameter, for the coefficient of surface stiffness, and for the effective interface potential of a fluctuating interface in the presence of a flat substrate. The derived expressions display the typical dependence on the distancel between the interface and the substrate; the exponentially decaying contributions are multiplied by polynomials inl. We show that the expressions for the coefficient of surface stiffness and for the effective interface potential have identical form as those proposed recently by Jin and Fisher (Phys. Rev.B 47, 7365 (1993)).Dedicated to Herbert Wagner on the occasion of his 60th birthday