The optical spectra of antiferromagnetic copper metaborate ${\mathrm{CuB}}_2{\mathrm{O}}_4$ are characterized by an exceptionally rich structure of narrow absorption lines due to electronic transitions within the magnetic ${\mathrm{Cu}}^{2+}$ ions, but their unambiguous identification and behavior in magnetic fields have remained far from being fully understood. We study the polarized magnetoabsorption spectra of this tetragonal antiferromagnet with high spectral resolution across the energy range of $1.4055–1.4065$ eV in magnetic fields up to 9.5 T for temperatures from 1.6 up to the Néel temperature $T_N=20$ K. We observe a set of eight absorption lines at $T=1.6$ K in magnetic fields exceeding 1.4 T, which we identify as arising from Frenkel excitons related to the ground and first excited states of the ${\mathrm{Cu}}^{2+}$ ions. The number of these excitons is defined by the presence of the four ${\mathrm{Cu}}^{2+}$ ions with doubly degenerate spin state $S=1/2$ at the $4b$ positions in the crystallographic unit cell. The energies of these excitons are determined by the exchange interaction of 0.5 meV of the ${\mathrm{Cu}}^{2+}$ ions in the excited state with the surrounding ions and by the Davydov splitting of 0.12 meV. In large magnetic field the observed Zeeman splitting is controlled by the anisotropic $g$-factors of both the ground and excited states. We develop a theoretical model of Frenkel excitons in the magnetic field that accounts for specific features of the spin structure and exchange interactions in ${\mathrm{CuB}}_2{\mathrm{O}}_4$. The model is used for fitting the experimental data and evaluation of the Frenkel exciton parameters, such as the Davydov splitting, the molecular exchange energy, and the $g$-factors of the ground and excited states of the ${\mathrm{Cu}}^{2+}$ ions.

In the last decade, Fe₂Mo₃O₈ was recognized for a giant magnetoelectric effect, the origin of which is still not clear. In the present paper, we contribute to the microscopic theory of the magnetoelectric coupling in this compound. Using crystal field theory and the molecular field approximation, we calculated the low-lying energy spectrum for iron ions and their interaction with electric and magnetic fields. Classical ionic contribution to the electric polarization related to the ionic shifts is also estimated. It is found that the electronic and ionic contributions to the electric polarization are comparable and these mechanisms support each other at $T<T_N$. The suggested electronic mechanism provides insight into the nature of huge jumps in polarization upon phase transitions from paramagnetic (PM) to antiferromagnetic (AFM) and then to ferrimagnetic (FRM) states under an applied external magnetic field as well as the large differential magnetoelectric coefficient.

The change in the absorption spectra due to reversal of the direction of light propagation (nonreciprocity of absorption) is a consequence of a simultaneous violation of both time-reversal and spatial-inversion symmetries. Here, we report on a high-resolution spectroscopic study of absorption nonreciprocity in the noncentrosymmetric multiferroic CuB₂O₄ below the antiferromagnetic transition temperature T_N = 21 K in the commensurate phase in magnetic fields up to 0.5 T. The study was performed in a broad spectral region covering several exciton transitions, which all are followed by an anomalously rich structure due to the multiple exciton-magnon-phonon satellites. Two components were resolved for the spectral line near 1.4 eV corresponding to the exciton transition between the ground and the first excited state. A quantitative theory of the optical absorption and nonreciprocity at this line was developed. The theory takes into account the interference between the electric and magnetic dipole contributions to the absorption and gives an adequate explanation of the relevant effects.

The effective Hamiltonians of the fine structure of Fe²⁺ (⁵D) terms are derived using the methods of operator perturbation theory taking into account covalent bonds between iron and oxygen ions. The energy operators of coupling of magnetic and electric dipole moments with the electric field are obtained for states of multiplets Fe²⁺ (⁵E) and Fe²⁺ (⁵T₂) with minimal sets of parameters. The energy spectra of low-lying states, the magnetic anisotropy parameters, and the distribution of quadrupole and induced electric dipole moments over all positions in the unit cell are calculated. The results of calculations are compared with available experimental data.