Dispersion polaritons on metallized surfaces of optically uniaxial crystals

We have constructed a theory of dispersion polaritons (localized electromagnetic waves) on arbitrarily oriented metallized surfaces of optically uniaxial crystals. The domain of existence of polaritons is defined by the following inequalities for permittivities ε_o and ε_e of the crystal and the angle θ between the optical axis and the surface: ?ε_etan²θ < ε_o < 0. Thus, polaritons exist only in the range of wave frequencies ω ensuring negative values of ε_o(ω) for ε_e > 0. The frequency boundaries of this region are specified for the case when the ε_o(ω) dependence corresponds to the model of a single polar excitation. The azimuthal orientation φ of the optical axis projection onto the surface does not appear in the criterion for polariton existence, but affects (together with angle θ) its main dispersion characteristics, such as the refractive index and partial wave localization parameters. This effect is analytically described in detail. Anomalies in the behavior of polariton parameters are studied in the vicinity of the boundaries of the domain of its existence, where the wave fields are especially sensitive to variations in the angles θ and φ. It is shown that a polariton in the plane of propagation (sagittal plane) passing through the optical axis is transformed into a one-partial bulk wave satisfying the boundary conditions. Accordingly, the wave branch under investigation for close orientations (when the optical axis forms a small angle with the sagittal plane) describes deeply penetrating (quasi-bulk) polaritons.     

Dispersion of surface polaritons in uniaxial CdS

The dispersion of ordinary and extraordinary surface polaritons in uniaxial CdS has been measured using the ATR technique. The results have been compared with theoretical dispersion curves based on a classical oscillator model. The dielectric dispersion has also been generated. Comparison is made between the bulk phonons derived from Raman, infrared and from the surface mode data. Infrared measurements of small crystallites of CdS are in good agreement with the frequencies predicted for surface modes of small isolated spheres.     

Surface polaritons on semi-infinite anisotropic media

We have investigated the nature of polaritons which propagate on the surface of semi-infinite anisotropic dielectric and magnetic media and find that the surface polaritons are regular surface waves [i.e., the penetration constant α (ω) is real] only for special orientations of the wave vector k and of the normal to the surface n relative to the principal axes. In the case of biaxial crystals, regular surface polaritons occur when k and/or n is along a principal axis of the dielectric tensor ε(ω) for dielectric media [or the magnetic permeability tensor μ(ω) for magnetic media]. When k and n are both directed along principal axes, the surface polaritons are TM with E in the saggital plane for dielectric media. One finds that surface polaritons which are coupled photon-virtual surface dipole excitation modes can exist on “surface active” anisotropic media in addition to the familiar coupled photon-real surface dipole excitation modes. When neither k nor n are along principal axes, the surface polaritons that occur are, with the exception of special orientations, “generalized” surface waves [i.e., α(ω) is complex]. The Poynting vectors of the propagating surface polaritons are always in the plane of the surface but not, in general, along k. These results, which hold for uniaxial crystals, are also applicable to gyromagnetic media and to gyrodielectric media. This theory is also applicable to surface polaritons which propagate along the interface between two media, one or both of which is anisotropic, and with one or the other serving as the “surface active” medium.     

High temperature spin wave dynamics of the uniaxial antiferromagnets

In the framework of the spin operators diagram technique the dynamical properties of the easy-axis type antiferromagnets at high temperatures are considered. The diagonalization procedure generalizing the Bogoliubov u-v transformation on the spin operators is presented. The spin wave (SW) spectrum allowing for the temperature and the magnetic field dependence of the sublattice magnetizations at T～T_～ is obtained. The SW relaxation frequencies due to the processes of SW scattering on the thermal spin fluctuations are calculated. The latter are in agreement with the data obtained on MnF₂ near the spin-flop transition¹⁰.     

Spin dynamics of layered triangular antiferromagnets with uniaxial anisotropy

The spin dynamics of the semiclassical Heisenberg model with uniaxial anisotropy, on the layered triangular lattice with antiferromagnetic coupling for both intralayer nearest neighbor interaction and interlayer interaction is studied both in the ordered phase and in the paramagnetic phase, using the Monte Carlo-molecular dynamics technique. The important quantities calculated are the full dynamic structure function S(q,ω)$S(\mathbf{q},\omega )$, the chiral dynamic structure function _Schi(ω)$S_{\mathrm{chi}}(\omega )$, the static order parameter and some thermodynamic quantities. Our results show the existence of propagating modes corresponding to both S(q,ω)$S(\mathbf{q},\omega )$ and _Schi(ω)$S_{\mathrm{chi}}(\omega )$ in the ordered phase, supporting the recent conjectures. Our results for the static properties show the magnetic ordering in each layer to be of coplanar 3-sublattice type deviating from 120^°${120}^{°}$ structure. In the presence of magnetic trimerization, however, we find the 3-sublattice structure to be weakened along with the tendency towards non-coplanarity of the spins, supporting the experimental conjecture. Our results for the spin dynamics are in qualitative agreement with those from the inelastic neutron scattering experiments performed recently.     

Macroscopic magnetic fields of antiferromagnets

The macroscopic magnetic fields arising in the space outside or in the bulk of an antiferromagnet in the absence of external currents are a result of surface magnetization. The general problem of determining these fields is formulated. It is shown that the field distribution near special lines on the surface is monopolar. An experimental study of the field makes it possible to determine the surface magnetization on the faces of an antiferromagnetic crystal. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 724–728 (10 May 1996)     

Surface polaritons in semi-infinite crystals

Recent progress in the field of optical surface modes in semi-infinite crystals is reviewed. The basic equations for surface polaritons originating from phonons, plasmons, excitons and magnons are given. Their observation by ATR, the resulting information and possible applications are discussed.     

Heisenberg antiferromagnets with uniaxial exchange and cubic anisotropies in a field

Classical Heisenberg antiferromagnets with uniaxial exchange anisotropy and a cubic anisotropy term in a field on simple cubic lattices are studied with the help of ground state considerations and extensive Monte Carlo simulations. Especially, we analyze the role of non-collinear structures of biconical type occurring in addition to the well-known antiferromagnetic and spin-flop structures. Pertinent phase diagrams are determined, and compared to previous findings.     

Single-oscillation two-dimensional solitons of magnetic polaritons

The propagation of bulk polaritons in ferromagnetic slab is considered through a short-wavelength approximation. Neither the damping nor the demagnetizing field do affect essentially the propagation and stability of the line soliton. The stable line soliton may be destroyed by background instability: the latter is suppressed in a narrow strip. The unstable line soliton decays into lumps, which can be described both numerically and through a variational approach. Lump interactions are mentioned.     

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.     

Nonlinear surface magnetic polaritons in a nonuniform magnetic field

High-frequency surface magnetic polaritons of finite amplitude propagating along the interface between a ferrite and a nonlinear insulator in a weakly nonuniform, shaft-shaped external magnetic field are investigated theoretically. The analysis is based on employment of the variational method together with bilinear relations having the form of Lorentz’s lemma. It is shown that the wave dispersion and the transverse profile of a wave along the field nonuniformity depend significantly on the amplitude of the wave. Zh. Tekh. Fiz. 68, 92–95 (September 1998)     

Surface plasmon polaritons in metallo-dielectric meander-type gratings

The optical properties of a gold film deposited on a quartz substrate with periodic grooves were investigated theoretically. The main peculiarities of the spectra are due to the excitation of the surface plasmon polaritons (SPPs). It is shown that the empty lattice approximation (ELA) for the SPPs is well applicable for the structure of interest. Two different approaches for deriving the air-gold SPP dispersion curves are compared. Our special attention is focused on the wavelength region approaching the d-band in gold, where the dielectric function is of a strongly non-Drude-type.     

Crystalline anisotropy energy of uniaxial antiferromagnets evaluated from low field torque data

The influence of the magnetocrystalline anisotropy energy on the static torque of uniaxial antiferromagnets is investigated. It is shown that this influence provides a method for accurate determination of the first anisotropy constant K₁ of most uniaxial antiferromagnets. Experimental results are shown from measurements on the hexagonal polymorph of FeGe.     

Surface plasmon-phonon polaritons of hexagonal zinc oxide

The anisotropy of surface plasmon-phonon polaritons of the first and second types in hexagonal zinc oxide is investigated at various electron concentrations and orientations of the C axis of the crystal relative to its surface. It is shown that surface plasmon-phonon polaritons of a third type are generated when the electron concentration in ZnO is greater than 2×10¹⁸ cm⁻³ and the orientation corresponds to K⊥C and xy⊥C. The spectrum of the surface plasmon-phonon polaritons of the third type are calculated, and the conditions for the existence of surface plasmon-phonon polaritons of the third type in ZnO single crystals are determined. Zh. Tekh. Fiz. 68, 58–62 (January 1998)     

Surface plasmon polaritons based optical directional coupler

As a basic optical device, the optical directional coupler (ODC) is basically used as optical splitters, optic switches and so on. A novel ODC employing surface plasmon polaritons (SPPs) is proposed for high integration. The finite difference time domain (FDTD) method is adopted to simulate and analyze its properties. Results show that the ODC proposed here follows the general regulations of a conventional dielectric ODC, but its transverse size is of nanoscale, which improves the optical integration greatly. For 1550 nm and 1310 nm input wavelengths, when the coupling region length (L) equals half of its coupling length, the Excess Loss is respectively 0.57 dB and 0.56 dB, which is practical in applications. So the research on the present ODC is of some practical importance.     

The magnetic order of two-dimensional anisotropic antiferromagnets

We study the two-dimensional quantum Heisenberg antiferromagnet on the square lattice with easy-axis exchange anisotropy by means of Green’s function approach within random phase and Callen’s approximations. The Néel temperature T_N, energy gap w₀ and staggered magnetization m are calculated. The theoretical predictions of T_N and w₀ for K₂NiF₄, Rb₂MnF₄, K₂MnF₄, Rb₂MnCl₄ and (CH₃NH₃)₂MnCl₄ fit well to the measured values. The power law behavior of is also investigated. The exponents β and ν for K₂NiF₄ are in excellent agreement with the experimental results.     

Theory of itinerant antiferromagnets in magnetic fields

In this contribution, we develop a theory of an itinerant antiferromagnet, which is a generalization of previous theories by taking into account more general band structures and homogeneous magnetic fields. As a result we obtain several phase transitions at finite magnetic fields, and also other thermodynamic properties are changed compared with these previous theories.     

Surface polaritons at the magnetized semiconductor-dielectric interface

Conditions for the existence of a surface polariton at the semiconductor-dielectric interface have been analyzed. With allowance for the gyrotropy and the resonance frequency dispersion of the semiconductor, which manifests itself in an external magnetic field, the dispersion relation, the characteristic frequencies determining the existence region of a surface polariton, the wave fields, and the energy flux distribution in each of the interfacing media have been obtained. A numerical analysis of the influence of the external field and absorption, which lead to the manifestation of nonreciprocal properties of the polariton and to a substantial reconstruction of the spectrum, has been performed.     

Surface plasmon polaritons on square-lattice arrays of three-fold symmetric nanostructures

The influence of the geometry of three-fold symmetric rotor shaped nanostructures arranged as a two-dimensional square-lattice on the excitation of surface plasmon polaritons (SPPs) is studied numerically. We consider SPP-related extrema of the far-field reflectivity R(α) as a function of the polarization angle α of the incident light. In agreement with recent experimental work, it is observed that these extrema shift away from α=0° and α=90°, where they are found for rotationally invariant nanostructures. The polarization angle corresponding to the most efficient SPP excitation is found to be independent of the shape of the individual nanostructures. We further investigate the influence of the shape and size of the nanostructures and discuss consequences for optical near- and far-field properties.     

The influence of magnetic impurities on thermodynamic characteristics of antiferromagnets

The thermodynamic behaviour of an impurity spin interacting with both one and another sublattice of an antiferromagnet with the “easy axis” anisotropy type is considered in the framework of phenomenological theory. The direct interaction between impurity magnetic moments is assumed to be negligible. The ground (pure Neel) state of the host lattice is shown to become unstable in the presence of an impurity. At this condition a local magnetic distortion being “frozen” in the vicinity of an impurity takes place and gives rise to appearance of a local ferromagnetism vector perpendicular to the anisotropy axis. Such phenomenon may be described as a local phase transition within the host lattice.