Investigation of the 4f-electron-phonon-coupling in the ferromagnet LiTbF4 by inelastic scattering of light

The polarized Raman spectra of LiTbF₄ in an external magnetic field (B≦8 T) have been recorded in the wavenumber interval 0≦500 cm^?1 and at temperatures of 1.8 K and 4.2 K. We have studied effects of the 4f electron-phonon (magnetoelastic) coupling manifesting itself in the splitting of a twofold degenerate phonon mode and in anticrossing effects between phonons and electronic transitions. In the spectra probing the scattering tensor elements (xz) and (zy) this anticrossing shows an asymmetry with respect to the frequencies and scattering intensities of the quasi-degenerate components. These effects are discussed in detail and can be interpreted by the theory of magnetoelastic interaction and by taking into consideration the finite widths of the electronic and phonon components (“critical coupling”). Brillouin scattering has been used to determine the sound velocities in thea-direction. No effect of the magneto-elastic interaction could be detected in this case.     

Spin-flip Raman scattering from electrons in localized donor states in n-InSb

We report the first observation of spin-flip Raman scattering from electrons localized in shallow donor states in InSb. For a non-degenerate n-InSb sample (8×10¹³ cm^-3) measurements of the spin-flip Raman gain and the effective g-value as a function of the magnetic field show lineshapes and magnetic field dependences completely different to that of an InSb sample with the electron gas being in a degenerate regime (1.35×10¹⁵ cm^-3). For the 8×10¹³ cm^-3 InSb sample, at magnetic fields greater than 11.5 kG, a splitting of the spin-flip Raman line into two lines is observed which may be an indication that two shallow donor states with different effective g-values are concerned.     

Free carrier absorption in quantizing magnetic fields: Nonpolar optical phonon scattering

A quantum theory of free carrier absorption in nondegenerate semiconductors and in strong magnetic fields which was previously developed to treat the case when acoustic phonon scattering dominates the free carrier absorption process [1] is extended to treat the case when nonpolar optical scattering is important. When the electromagnetic radiation field is polarized parallel to the direction of the applied magnetic field, results are obtained which are similar to those when acoustic phonon scattering is dominant. The free carrier absorption is an oscillatory function of the magnetic field which on the average increases in magnitude with the magnetic field. However, more structure in the free carrier absorption occurs when nonpolar optical phonon scattering dominates. This is due to the fact that there are two periods in the oscillatory magnetic field dependence associated with the emission or the absorption of optical phonons during the intraband transitions. When the cyclotron frequency exceeds the sum of the photon and optical phonon frequencies, i.e. ω_c > θ + ω_o, the free carrier absorption is predicted to increase linearly with magnetic field when ?ω_c? k_BT. The magnetic field dependence of the free carrier absorption can be explained in terms of phonon-assisted transitions between the various Landau levels in a band involving the emission and absorption of optical phonons.     

Resonant magnon—optical phonon coupling in metamagnetic FeCl2·2H2O

The resonant coupling between magnons and optical phonons of symmetryB _g was observed in the Raman spectra at different magnetic fields in the antiferro-, ferri- and ferromagnetic phases of FeCl₂·2H₂O at 2K. The line positions of the coupled modes were calculated taking a field dependence of the coupling strength into account. Varying this strength and the frequencies of the uncoupled modes as parameters of this calculation a fit of the experimental data was obtained also at low fields where former interpretations were not satisfying. However, the field dependence of the coupling strength disagrees with a corresponding term of an appropriate microscopic coupling mechanism in which the local spins are disturbed by a modulation of the ctystal field via spin-orbit coupling. In accordance with the former results of the far infrared absorption measurements zero field splitting of the magnonlike mode was found to exist. In the AF-phase two magnonlike modes can be observed, but the Raman scattering cross section of one of these modes tends to zero at zero field corresponding to its vanishing phonon contributions responsible for the scattering cross sections of the coupled modes. The relationship between cross sections of the coupled modes and their phonon contributions was confirmed by analysing the field dependence of the mode intensities in the Raman spectra.A project of the Sonderforschungsbereich 65 Festkörperspektroskopie Darmstadt-Frankfurt, supported by the Deutsche Forschungsgemeinschaft     

Magnons and phonons in antiferromagnetic CeMg compound

The magnon dispersion curves in the antiferromagnetic phase and the acoustic phonon dispersion in the paramagnetic phase of CeMg compound have been investigated. The magnetic moment and the tetragonal distortion are measured versus temperature. Their variations are consistent with the occurrence of a highly magnetostrictive first-order transition at T_N = 19.5 K. Transverse magnetic excitations associated to transitions between two sublevels of the Г₈ crystal field ground state were measured along the main lines of the Brillouin zone. There is a large anisotropy of the dispersion depending whether the wavevector is parallel or perpendicular to the fourfold axis of the tetragonal cell. This dispersion can be well described by means of a dynamical susceptibility model in which only a few interactions occur.     

Morphic effects — III. Effects of an external magnetic field on the long wavelength optical phonons

The changes in the frequencies of the k ≈ 0 optical vibration modes on the application of a static, external magnetic field to a non-magnetic crystal are determined to first order in the field strength. Second order effects are equivalent to the effects of an electric field in second order and they are not considered here. It is shown that the frequency of a nondegenerate mode is not altered to first order in the magnetic field. In the case of the noncubic crystal structures it is found that the magnetic field must have a component along the axis of highest symmetry in order that the doubly degenerate modes at k ≈ 0 have their degeneracy lifted. In the case of the cubic structures a magnetic field applied in any direction can completely split the degeneracy of modes which are triply degenerate at k ≈ 0. Expressions are given for the field induced changes in the normal mode frequencies. The modes whose frequencies are shifted are found to be right or left circularly polarized. A brief discussion is given of spatial dispersion effects, that is, splitting of the mode degeneracy linear in the phonon wave-vector. Finally, a review of the symmetry aspects of acoustical activity and Faraday effects of acoustical phonons is presented.     

Polarization-modulated magnetoreflection in magnetic semiconductors: CdCr2S4 and EuSe

The polarization-modulated (PM) magnetoreflection technique has been used to study magnetic ordering effects in CdCr₂S₄ and EuSe. The energy gap for direct band-band transitions in CdCr₂S₄ has been measured to be E_G = 2.3 eV, and the exchange splitting of the valence band to be about 0.03 eV. Good agreement with thin film absorption measurements is obtained in the temperature dependence of spectral structure, observed at energies less than E_G, associated with crystal field and charge transfer transitions. No strongly blue-shifting peak is observed with magnetic order. PM magnetoreflection spectra of the E₁ peak of EuSe show a direct manifestation of the spin alignment from the ferrimagnetic to ferromagnetic state of this crystal at 2 K in external fields up to 16 kOe. An attempt is made to explain resonant Raman scattering in EuSe (observed by other workers) in terms of the field-induced shift of one of the polarized E₁ reflectivity components into coincidence with the 5145 Å argon-ion laser line.     

On the low-temperature properties of TmCo2Ge2

In this paper low-temperature magnetic properties of TmCo₂Ge₂ are reported. The compound was investigated by means of magnetic, electrical transport, heat capacity and neutron diffraction measurements. Clear anomalies were found in all of the bulk characteristics at the onset of antiferomagnetically ordered state below 2.4 K. According to neutron diffraction data, Tm magnetic moments are aligned along the c-axis, forming the AFI-type magnetic structure. In the paramagnetic state, the specific heat reveals a distinct Schottky contribution with the total crystal field splitting of about 150 K.     

Low-temperature thermal conductivity of terbium-gallium garnet

Thermal conductivity of paramagnetic Tb₃Ga₅O₁₂ (TbGG) terbium-gallium garnet single crystals is investigated at temperatures from 0.4 to 300 K in magnetic fields up to 3.25 T. A minimum is observed in the temperature dependence κ(T) of thermal conductivity at T _min = 0.52 K. This and other singularities on the κ(T) dependence are associated with scattering of phonons from terbium ions. The thermal conductivity at T = 5.1 K strongly depends on the magnetic field direction relative to the crystallographic axes of the crystal. Experimental data are considered using the Debye theory of thermal conductivity taking into account resonance scattering of phonons from Tb³⁺ ions. Analysis of the temperature and field dependences of the thermal conductivity indicates the existence of a strong spin-phonon interaction in TbGG. The low-temperature behavior of the thermal conductivity (field and angular dependences) is mainly determined by resonance scattering of phonons at the first quasi-doublet of the electron spectrum of Tb³⁺ ion.     

The Mössbauer effect and magnetic phase transitions

The Mössbauer effect provides a direct method for identifying the spin axis in magnetic crystals and observing magnetic phase transitions. The order of the transition may be inferred from the Mössbauer spectrum. Phase changes can occur as a function of temperature (e.g. when the anisotropy fieldB _A changes sign) or as a function of applied magnetic field. In an antiferromagnet a field ?(2B _E B _A)^1/2 along the spin axis whereB _E is the exchange field causes the spin-flop transition which is normally first order (sharp) whereas the transition to the paramagnetic phase which occurs at higher fields?2B _E is second order (continuous). In quasi-one-dimensional crystals Mössbauer spectra show that the spin-flop transition is first order locally but occurs over a range of fields throughout the crystal, so that the first order character is masked in a conventional magnetization measurement. In fields applied at a finite angle>B _A/2B _E to the spin axis the transition becomes second order, i.e. a continuous rotation of the spins occurs. In canted antiferromagnets (or weak ferromagnets) the spin-flop transition is also continuous; in addition a “screw” re-orientation may be induced by fields applied perpendicular to the spin axis and arises from antisymmetric exchange. For crystals with lowT _N the hyperfine field changes when a magnetic field is applied and has a minimum at a phase transition; this may be used to map out the magnetic phase diagram.     

Raman spectroscopy of very small Cd1−xCoxS quantum dots grown by a novel protocol: direct observation of acoustic‐optical phonon coupling

Glass‐embedded Cd_1−xCo_xS quantum dots (QDs) with mean radius of R ≈ 1.70 nm were successfully synthesized by a novel protocol on the basis of the melting‐nucleation synthesis route and herein investigated by several experimental techniques. Incorporation of Co²⁺ ions into the QD lattice was evidenced by X‐ray diffraction and magnetic force microscopy results. Optical absorption features with irregular spacing in the ligand field region confirmed that the majority of the incorporated Co²⁺ ions are under influence of a low‐symmetry crystal field located near to the Cd_1−xCo_xS QD surface. Electron paramagnetic resonance data confirmed the presence of Co²⁺ ions in a highly inhomogeneous crystal field environment identified at the interface between the hosting glass matrix (amorphous) and the crystalline QD. The acoustic‐optical phonon coupling in the Cd_1−xCo_xS QDs (x ≠ 0.000) was directly observed by Raman measurements, which have shown a high‐frequency shoulder of the longitudinal optical phonon peak. This effect is tuned by the size‐dependent sp‐d exchange interaction due to the magnetic doping, causing variations in the coupling between electrons and longitudinal optical phonon. Copyright © 2013 John Wiley & Sons, Ltd.     

Polarized Raman scattering and low frequency infrared study of hydroxyapatite

A detailed investigation of the polarized Raman spectrum of monoclinic hydroxyapatite (OHAp) and a careful study of the low frequency infrared spectrum of polycrystalline OHAp, is reported. Most of the spectral details of Raman scattering are consistent with the local pseudo-hexagonal C₆ factor group symmetry of OHAp. However, some features, for example the absence of TO-LO splitting for particular E₁ phonon geometries and the splitting of the lowest frequency Raman line, are a reflection of the centrosymmetric monoclinic lattice of OHAp. Between 0 and 50cm^?1, a temperature-dependent background, having E₁ symmetry, and probably associated with OH^? disordering flucuations, was observed in OHAp. Both OHAp and FAp displayed low frequency Raman lines which softened with decreasing temperature. However, no evidence for a phase transition was found in either OHAp or FAp in the 12–295 K temperature range.     

Level splitting in semimagnetic semiconductors under spin-magnetophonon resonance conditions

The splitting of electronic levels in quantum wells of semimagnetic semiconductors typically characterized by large effective g factors is analyzed theoretically. They are found to be capable of supporting resonance, provided the Zeeman spin-level splitting is equal to the energy of the longitudinal optical phonon ?ω_‖. The resonance condition can be written as ?ω_‖ = gμ_B B. This condition can be satisfied by choosing the magnetic field Bsuch that the sum of the energies of the lowest spin level and the optical phonon coincides with the energy of the highest level. It is shown that these two degenerate energy levels should experience mutual repulsion. The magnitude of the corresponding splitting depends on both the electron-phonon and spin-orbit interactions in semiconductors; moreover, it turns out substantially lower than the Zeeman energy gμ_B B. Resonant passage of light through and its reflection from a quantum well are considered as one of possible ways to observe this energy level splitting.     

Ab initio study of phonons in the rutile structure of TiO2

The local-density approximation is used to find the phonon dispersion relations, total and partial phonon density of states for TiO₂ crystal of rutile structure. For that the Hellmann-Feynman forces were computed and direct method applied. Some thermodynamic quantities are also presented. Calculated results are analyzed and compared with the experimental neutron scattering and optic data. Good agreement has been achieved. A giant LO/TO splitting is observed for A_2u and E_u modes.     

Longitudinal magnetoresistance in the Extreme Quantum Limit in nonparabolic semiconductors

We calculate the Longitudinal Magnetoresistance in the Extreme Quantum Limit (?Ω_c ? k_BT) for a nondegenerate n-type InSb sample at low temperatures when the dominant energy and momentum loss mechanisms are the el-acoustic phonon and the el-ionized impurity interactions. The magnetic field dependence of the effective mass which is due to the nonparabolic nature of the conduction band as well as the energy and magnetic field dependence of the relaxation time are incorporated in the analysis. Analytical results are presented for both nondegenerate and degenerate samples when individual scattering mechanisms are operative. In general nonparabolicity causes an enhancement in the Longitudinal Magnetoresistance and changes the nature of its magnetic field dependence as compared to the case of a parabolic conduction band.     

Magnetic field dependent splitting of doubly degenerate phonon states in anhydrous cerium-trichloride

The Raman spectra of single crystals of hexagonal CeCl₃ have been investigated atT=2K in external magnetic fieldsB up to 6 T. The crystal field states of the 4f ¹(² F _5/2)-configuration of Ce³⁺ show a linear Zeeman-splitting. Two degenerate phonon states (197 cm^–1(E _1g), 109 cm^–1(E _2g)) also split in the magnetic field. ForB parallel to the optic axisZ the field dependence of the splitting is similar to the behaviour reported earlier for Ce F₃ and NdF₃ (linear splitting at low fields, which is followed by a saturation at high fields). ForBZ a splitting of the same phonons proportional toB ² is observed in CeCl₃, which was not found in the other compounds. The linewidths of the electronic transitions and of the split phonon components are reduced with increasing magnetic fieldstrength.The field- and temperature dependences of the phonon energies can be explained quantitatively using results of the theory of the 4f-electron-phonon interaction as developed for the cooperative Jahn-Teller-effect or for the magneto-elastic interaction. The experimental results forBZ require an interaction Hamiltonian which is bilinear in the electronic and phonon operators, respectively. The conclusions are supported by group theoretical considerations.The experiments described here have been performed at the Technische Hochschule Darmstadt, Institut für Festkörperphysik II, Fachgebiet Technische Physik as a project of the Sonderforschungsbereich Festkörperspektroskopie SFB65, supported by the Deutsche Forschungsgemeinschaft     

Mesoscopic mixing of spin orientation phases in particles with Ising ions: Holmium: Yttrium iron garnets in strong magnetic fields

The paper presents a theoretical analysis of macroscopic quantum tunneling phenomena in small particles of a cubic ferromagnet of the Ho_xY_3?xFe₅O₁₂ type with strongly anisotropic (Ising) impurity ions present in a low concentration x ? 1 in the region of strong magnetic fields, at which many orientation phase transitions related to the competition of external and exchange field actions on the spin subsystem are observed. The theory of path integrals for the magnetic subsystem was used to calculate the instanton contributions to interphase tunneling amplitudes in the vicinity of first-order transitions for three principal orientations of an external magnetic field in a cubic crystal. It was shown that low-energy barriers separating angular phases could result in anomalously large mesoscopic volumes at which macroscopic spin tunneling effects could appear in the energy spectra of particles. The special features of spectral splitting caused by the mixing of azimuthally degenerate angular phases and phases with different polar angles of magnetization orientation were revealed.     

Magnetic-field-induced changes in the photorefractive sensitivity of lithium niobate

The effect of a magnetic field on the average photorefractive sensitivity of an undoped LiNbO₃ crystal is studied by phase-mismatched second-harmonic generation. The experimental data obtained show the photorefractive sensitivity to reverse sign as the external magnetic field exceeds B ₁=?0.38±0.04 T. The magnetic field is oriented perpendicular to the crystal optical axis and to the plane of laser radiation polarization. The variation of the photorefractive sensitivity is associated with paramagnetic iron centers, whose photoionization probability depends on the direction of their magnetic moment relative to the optical axis.     

Splitting of transverse optical phonon modes localized in GaAs quantum wires on a faceted (311)A surface

The energy splitting of fundamental localized transverse optical (TO1) phonon modes in GaAs/AlAs superlattices and quantum wires grown by molecular-beam epitaxy on a faceted (311)A GaAs surface is observed by Raman spectroscopy. The form of the Raman scattering tensor makes it possible to observe the TO_x and TO_y modes separately, using different scattering geometries the y and x axes are the directions of displacement of the atoms and are directed parallel and transverse to the facets on the (311)A surface). Enhancement of the splitting of the TO1_x and TO1_y modes is observed as the average thickness of the GaAs layers is decreased from 21 to 8.5 Å. The splitting is probably due to the effect of the corrugation of the GaAs/AlAs (311)A hetero-interface on the properties of localized phonon modes. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 1, 45–48 (10 July 1997)