Magnetostriction and thermal expansion of HoAl3(BO3)4

The magnetostriction and thermal expansion of rare-earth aluminoborate HoAl₃(BO₃)₄ have been studied theoretically. The calculated field and temperature dependences of the multipole moments of the Ho³⁺ ion in HoAl₃(BO₃)₄ made it possible to describe the known experimental data and to predict possible anomalies of thermal expansion. It has been shown that, for the direction of the field B ‖ c, the nonmonotonic character of magnetostriction along the axis a is determined by the multipole moments, the main of which is β _J 〈O ₄ ⁰ 〉. For B ‖ a and B ‖ b, the maximum moments are β _J 〈O ₄ ² 〉and α _J 〈O ₂ ² 〉; their variation with the field and temperature explain well the form of magnetostriction. It has been established that the greater value of magnetostriction Δa/a for B ‖ b than for B ‖ a and the greater value of magnetostriction for the field in the basal plane than for B ‖ c are caused by greater variations in the field of actual multipole moments.     

Features of the magnetic and magnetoelectric properties of HoAl3(BO3)4

The main features of the magnetic and record magnetoelectric properties of a HoAl₃(BO₃)₄ aluminoborate single crystal have been studied experimentally and theoretically. It has been found that the electric polarization that was previously detected in HoAl₃(BO₃)₄ and is record for multiferroics is significantly larger, ΔP _ba (B _a ) ≈ ?5240 μC/m², with an increase in the magnetic field to 9 T at T = 5 K. The measured magnetic properties and revealed features have been interpreted within a united theoretical approach based on the molecular field approximation and on calculations in the crystal field model for a rare-earth ion. The experimental temperature (from 3 to 300 K) and field (up to 9 T) dependences of the magnetization have been described. The parameters of the crystal field of trigonal symmetry for a Ho³⁺ ion in HoAl₃(BO₃)₄ have been determined from the interpretation of the experimental data.     

Vibrational spectra and elastic,piezoelectric, and magnetoelectric properties of HoFe3(BO3)4 and HoAl3(BO3)4 crystals

Raman spectra of light are obtained for HoFe₃(BO₃)₄ and HoAl₃(BO₃)₄ crystals at various temperatures and are used for determining the frequencies of crystal lattice vibrations at the center of the Brillouin zone. It is also found that the HoFe₃(BO₃)₄ crystal exhibits a phase transition at T _c ≈ 366 K. The magnetoelectric effect in the paramagnetic phase of these compounds is studied experimentally. The lattice vibration frequencies, elastic and piezoelectric moduli, Born dynamic charges, and the high-frequency permittivity are calculated using the density functional method. A peculiar behavior of the transverse acoustic vibration branch is observed in the Γ → Z direction of the Brillouin zone of the HoFe₃(BO₃)₄ crystal. The electric polarization induced by an external field is estimated using the calculated values of piezoelectric moduli and experimental values of magnetostriction.     

Spectroscopy of phonon and vibronic states of YbAl3(BO3)4 single crystal

The polarized Raman and reflection spectra of a single crystal YbAl₃(BO₃)₄ at room temperature were studied. Raman active vibrational modes A ₁, E _TO, and E _LO are identified. In the Raman spectrum, we detected an intense line at a frequency of 1018 cm⁻¹, which refers to internal vibrations of the BO₃ group and is known to be promising for use in amplifiers based on stimulated Raman scattering. From the simulation of reflection spectra by the method of dispersion analysis the frequencies of A ₂ vibrational modes were determined. Intense bands observed in the low-temperature transmission spectra in the range of f-f transitions in the Yb³⁺ ion are attributed to electron-phonon transitions. The Raman lines are compared with electron-phonon lines in the transmission spectrum.     

Specific heat of YFe3(BO3)4, Y0.5Gd0.5Fe3(BO3)4, and GdFe3(BO3)4

The specific heat was measured in the range 0.4–300 K in YFe₃(BO₃)₄, Y_0.5Gd_0.5Fe₃(BO₃)₄, and GdFe₃(BO₃)₄ single crystals. Sharp anomalies were found at temperatures of first-order structural, second-order antiferromagnetic, and first-order spin-reorientational transitions. A Néel temperature of about 37 K was found to be virtually independent of presence of rare-earth ions, indicating rather weak coupling of Gd and Fe subsystems. The contribution of the magnetic system to specific heat was separated through the scaling procedure allowing determination of the magnetic entropy of Fe and Gd subsystems. At the lowest temperatures, the specific heat in GdFe₃(BO₃)₄ exhibits a Schottky-type anomaly, which is due to Gd³⁺ eightfold degenerate ground-level splitting by the internal magnetic field of the Fe subsystem of about 7 T. The text was submitted by the authors in English.     

Calculation of X-ray natural circular dichroism

A method is presented to calculate the natural circular dichroism recently discovered in the X-ray range (XNCD). The basic formula represents XNCD as an odd second-rank tensor and leads to a sum rule that relates XNCD to the mixing of odd and even orbitals in the ground state. A multiple-scattering theory of XNCD is presented, and calculated spectra for the L-edges of iodine in LiIO₃ compare favorably with the experiments. Received: 20 October 1997 / Revised: 18 February 1998 / Accepted: 31 March 1998     

X-ray natural circular dichroism in copper metaborate

The local electronic structure of copper ions in a copper metaborate CuB₂O₄ crystal is studied on the ESRF synchrotron using X-ray absorption polarization-dependent spectroscopy. The X-ray natural circular dichroism near the K absorption edge of copper is measured in the direction that is perpendicular to crystal axis c. The data obtained indicate the presence of hybridized p–d electronic states of copper. Theoretical calculations are used to separate the contributions of the two crystallographically nonequivalent positions of copper atoms in the unit cell of CuB₂O₄ to the absorption and X-ray circular dichroism spectra of the crystal.     

Antiferromagnetic resonance and magnetic anisotropy in single crystals of the YFe3(BO3)4-GdFe3(BO3)4 system

The antiferromagnetic resonance in single crystals of the YFe₃(BO₃)₄-GdFe₃(BO₃)₄ system is studied in the frequency range 25–140 GHz and the temperature range 4.2–50.0 K. It is established that the YFe₃(BO₃)₄ crystal containing only the magnetic subsystem of Fe³⁺ ions is an antiferromagnet with an easy anisotropy plane. The temperature dependences of the gaps in the antiferromagnetic resonance spectra of GdFe₃(BO₃)₄ and Y _x Gd_{1 ? x} Fe₃(BO₃)₄ are used to calculate the contributions of the Fe³⁺ and Gd³⁺ subsystems to the magnetic anisotropy of these crystals. The contributions are found to be close in magnitude and have opposite signs. This leads to a relatively weak uniaxial anisotropy field in the crystals under investigation. Since the exchange interaction between the Gd³⁺ and Fe³⁺ ions magnetizes the magnetic subsystem of gadolinium, both subsystems start to contribute simultaneously at the Néel temperature of the iron subsystem.     

Magnetic properties of HoFe3(BO3)4

The magnetic properties of an antiferromagnet with trigonal symmetry, namely, HoFe₃(BO₃)₄, have been investigated theoretically. The calculations have been performed in the molecular field approximation and in the framework of the crystal field model for the rare-earth subsystem. Extensive experimental data on the magnetic properties of HoFe₃(BO₃)₄ have been interpreted and good agreement between theory and experiment has been achieved using the obtained theoretical dependences. The spontaneous spin-reorientation transition and the spin-reorientation transition induced by a magnetic field B ‖ a from the easy-axis to easy-plane state, as well as the spin-flop transition in a magnetic field B ‖ c, have been described. It has been shown that the spontaneous spin-reorientation transition is a magnetic analog of the Jahn-Teller effect. The temperature dependences of the initial magnetic susceptibility at temperatures ranging from 2 to 300 K, the nonlinear curves of magnetization for B ‖ c and B ⊥ c in a magnetic field up to 1.2 T (which indicate the occurrence of first-order phase transitions), and their evolution with variations in the temperature have been described, as well as the temperature and field dependences of the magnetization in a magnetic field up to 9 T. The parameters of the trigonal crystal field for the rare-earth ion Ho³⁺ and the parameters of the Fe-Fe and Ho-Fe exchange interactions have been determined in the course of interpretation of the experimental data.     

Magnetic circular dichroism of the phonon-assisted exciton transitions in GaP

Magnetic circular dichroism is measured for the excitonic absorption in GaP. Their signs and intensities are explained using selection rules for the phonon-assisted transitions; and the hole forming the free exciton is found to have a g-value g_h ? 1.0.     

Phase transitions and crystal-field and exchange interactions in TbFe3(BO3)4 as seen via optical spectroscopy

High-resolution polarized broadband (1800-23?000?cm(-1)) optical absorption spectra of Tb(3+) in TbFe(3)(BO(3))(4) single crystals are studied between room temperature and 4.2?K. The spectral signatures of the structural (R32-P3(1)21, T(S )?=?192?K) and magnetic (T(N )?=?41?K) phase transitions are found and analyzed. Energies and symmetries of the Tb(3+) crystal-field (CF) levels were determined for both the high-temperature R32 and the low-temperature P3(1)21 structures of TbFe(3)(BO(3))(4) and compared with the calculated ones. It follows unambiguously from the spectral data that the ground state is the Γ(1)?+?Γ(2) quasi-doublet of the local D(3) point symmetry group for Tb(3+) in the R32 high-temperature structure. The CF calculations revealed the CF parameters and wavefunctions for Tb(3+) in TbFe(3)(BO(3))(4). The value of the Tb-Fe exchange integral and of the effective magnetic field created by the ordered Fe subsystem were estimated as J(fd)?=?0.26?K and B(eff)?=?3.92?T, using the observed splitting Δ?=?32?cm(-1) of the Tb(3+) ground quasi-doublet at the temperature 5?K. The reliability of the obtained parameters was proven by modeling the literature data on the magnetic susceptibility of TbFe(3)(BO(3))(4). Lattice distortions below T(S) were evidenced by the observed changes of probabilities of the forced electric dipole transitions of Tb(3+).     

High-temperature heat capacity of YFe3(BO3)4

The molar heat capacity of YFe₃(BO₃)₄ has been measured using differential scanning calorimetry in the temperature range 339–1086 K. It has been found that the dependence C _p = f(T) exhibits an extremum at a temperature of 401 K due to the structural transition.     

Structural form of vibronic intensities in vibronic induced transitions

A general method for calculating the overall shape of the spectrum of vibronic induced transitions in transition-metal ion systems is developed. The vibronic structure is expressed in terms of a weighted sum of medium induced lorentzian lines located at the frequencies of the fundamental odd vibrations of the complex. Each of these lines is followed by a series of vibronic lines assigned to the combination frequencies with one or more even vibrations. The relative intensities of these combination lines are determined by the values of an intramolecular distribution which includes both the effects of geometry and frequency changes of the modes involved in the transition. Values of the linear and the quadratic parameter for the molecule can be estimated from a fit to the experimental spectra.     

High-temperature heat capacity of TbFe3(BO3)4

The molar heat capacity of TbFe₃(BO₃)₄ in the temperature range of 346–1041 K has been measured by differential scanning calorimetry. It has been found that the C _p = f(T) curve does not show extremes. The thermodynamic properties of the oxide compound have been determined from the experimental data.     

Comparison of the Absorption Spectra of Nd3+ Ions in the NdFe3(BO3)4, Nd0.5Gd0.5Fe3(BO3)4, and Ho0.75Nd0.25Fe3(BO3)4 Crystals

Physics of the Solid State - The polarized optical absorption spectra in the region of a series of the f–f  transitions of Nd3+ ions in the Ho0.75Nd0.25Fe3(BO3)4,...     

Mechanisms of the generation of circular dichroism of singlet-triplet transitions

Possible mechanisms of the generation of circular dichroism of singlet-triplet transitions localized in achiral chromophores are investigated in this work. The estimates show that the spin-orbit interaction of the optical electrons in the field of the electrons and nuclei of the perturbing groups (the externall-s interaction) makes a contribution comparable in order of magnitude to the internal.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 7–10, July, 1981.     

6 MHz BAW resonators fabricated using new piezoelectric crystals PrCa4O(BO3)3 and NdCa4O(BO3)3

Thickness shear mode Bulk Acoustic Wave (BAW) resonators with frequency of 6 MHz, were fabricated using monoclinic piezoelectric crystals PrCa₄O(BO₃)₃ (PrCOB) and NdCa₄O(BO₃)₃ (NdCOB). Zero temperature coefficient of frequency (TCF) characteristics were achieved over the temperature range of –140 °C to 200 °C for (YXt)–1.5° cut PrCOB and (YXt)15° cut NdCOB, with the turnover temperature at 20 °C. The electromechanical coupling factor k₂₆ and the piezoelectric coefficient d₂₆ were determined to be 30.2% and 15.8 pC/N for PrCOB, 29.0% and 15.1 pC/N for NdCOB resonators, respectively. The temperature independent frequency behavior, large coupling factor, high piezoelectric coefficient, together with noticeable mechanical quality factors (Q > 2,500), make PrCOB and NdCOB crystals good candidates for sensing applications with expanded temperature usage range. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)