The generation of monochromatic terahertz (THz) electromagnetic radiation remains a critical task for many current and future THz applications. Recently, we have demonstrated the emission of monochromatic sub-THz radiation by optical phonons in the dielectric material KY(MoO4)2. We are now extending our study to other materials in the MRe(MoO4)2 family, where Re stands for rare earth ions and M for an alkali ion.The layered crystallographic structure of these materials causes infrared-active lattice vibrations with the energies below 3.7 meV, corresponding to frequencies below 900 GHz, where solid-state monochromatic radiation sources are rare. Changing the Re3+ in the chemical composition enables more than 10 percent tunability of the optical phonon frequencies.After broadband excitations by 5 ps THz pulses, infrared active optical phonons in MRe(MoO4)2 emit narrowband sub-THz radiation as a time-varying dipole for tens of picoseconds, which is exceptionally long for oscillators with frequencies below 1 THz. Such a long coherent emission allows the detection of more than 50 periods of radiation at frequencies of 568 and 860 GHz. The remarkably long decay time, together with the chemical stability of materials used, suggest a variety of possible applications in THz technology.

The generation of monochromatic electromagnetic radiation in the terahertz (THz) frequency range has remained a challenging task for many decades. Here, the emission of monochromatic sub-THz radiation by optical phonons in the dielectric material KY(MoO4)2 is demonstrated. The layered crystal structure of KY(MoO4)2 causes infrared-active shear lattice vibrations to have energies below 3.7 meV, corresponding to frequencies lower than 900 GHz where solid-state-based monochromatic radiation sources are rare. Directly excited by a 5 ps long broadband THz pulse, infrared-active optical vibrations in KY(MoO4)2 re-emit narrowband sub-THz radiation as a time-varying dipole for tens of picoseconds, which is exceptionally long for oscillators with frequencies below 1 THz. Such a long coherent emission allows for the detection of more than 50 periods of radiation with frequencies of 568 and 860 GHz. The remarkably long decay time together with the chemical stability of the employed material suggests a variety of possible applications in THz technology.

The lack of both time-reversal and spatial inversion symmetry in polar magnets is a prerequisite for the occurrence of optical magnetoelectric effects such as nonreciprocal directional dichroism with the potential for the realization of optical diodes. In particular, antiferromagnetic materials with magnetic excitations in the THz range such as Fe2Mo3O8 are promising candidates for next-generation spintronic applications. In a combined experimental and theoretical effort we investigated the THz excitations of the polar honeycomb antiferromagnet Fe2Mo3O8 in external magnetic fields and their nonreciprocal directional dichroism, together with the temperature dependence of the electronic transitions in the mid- and near-infrared frequency range. Using an advanced single-ion approach for the Fe ions, we are able to describe optical excitations from the THz to the near-infrared frequency range quantitatively and successfully model the observed nonreciprocal directional dichroism in the THz regime.

The parameters of even and odd crystal fields acting on iron ions in tetrahedral and octahedral positions of the Fe2Mo3O8 crystal are calculated. The obtained energy level schemes of the lowest multiplets are discussed in the context of the available experimental data. By comparing the calculated intensities of magnetic and electric dipole transitions with experimental data, the parameters of the effective Hamiltonian of the interaction of 3d electrons with an electric field are refined. It is found that the main absorption lines at T < TN in the region of terahertz frequencies are due to excitations of iron ions and are not associated with collective oscillations of magnetic moments. The splitting of absorption lines upon application of an external magnetic field is a consequence of the difference in the orientations of the magnetic sublattices relative to the crystallographic axes.

The energy level schema of the ground term of the nickel ion in NiCr2O4 was calculated. The parameters of the interaction with the electric field were determined, and the distribution pattern of the electric dipole moments over different positions of nickel in the unit cell was calculated. The model of the NiCr2O4 magnetoelectric structure at T < Tc was constructed taking into account the data on neutron scattering and the results of the electric polarization measurements. The origin of the magnetodielectric effect was attributed to the peculiarities of the ground state of the nickel ion.

The effective Hamiltonians of the fine structure of Fe 2+ ( 5 D) 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 Fe 2+ ( 5 E) and Fe 2+ ( 5 T 2 ) 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.

Magnetization reversal in ferro- and ferrimagnets is a well-known archetype of non-equilibrium processes, where the volume fractions of the oppositely magnetized domains vary and perfectly compensate each other at the coercive magnetic field. Here, we report on a fundamentally new pathway for magnetization reversal that is mediated by an antiferromagnetic state. Consequently, an atomic-scale compensation of the magnetization is realized at the coercive field, instead of the mesoscopic or macroscopic domain cancellation in canonical reversal processes. We demonstrate this unusual magnetization reversal on the Zn-doped polar magnet Fe 2 Mo 3 O 8 . Hidden behind the conventional ferrimagnetic hysteresis loop, the surprising emergence of the antiferromagnetic phase at the coercive fields is disclosed by a sharp peak in the field-dependence of the electric polarization. In addition, at the magnetization reversal our THz spectroscopy studies reveal the reappearance of the magnon mode that is only present in the pristine antiferromagnetic state. According to our microscopic calculations, this unusual process is governed by the dominant intralayer coupling, strong easy-axis anisotropy and spin fluctuations, which result in a complex interplay between the ferrimagnetic and antiferromagnetic phases. Such antiferro-state-mediated reversal processes offer novel concepts for magnetization control, and may also emerge for other ferroic orders.

The parameters of the interaction of 3d electron states with an electromagnetic wave, as well as the probabilities of magnetic and electric dipole transitions between states of the ground term of an iron ion, which is split by the crystal field, exchange interaction, and spin–orbit coupling, have been calculated. The dependences of the absorption lines on the magnitude and direction of the applied magnetic field have been determined. It has been shown that the optical diode effect discovered in [Sh. Yu, B. Gao, J. W. Kim, S.-W. Cheong, M. K. L. Man, J. Madeo, K. M. Dani, and D. Talbayev, Phys. Rev. Lett. 120, 037601 (2018)] can be explained by the interference of magnetic and electric dipole transitions.

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<TN. 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.

A FeCr 2 O 4 single crystal with the spinel structure is grown by the zone melting method with optical heating. The critical temperatures of establishing the orbital ordering T OO = 138 K, the formation of the collinear ferrimagnetic state T N = 65 K, and the formation of the spiral modulation of the magnetic structure T s = 38 K are determined from the temperature dependences of the heat capacity and magnetic susceptibility. An anomaly of the susceptibility at T ~ 21 K, below which the hysteresis curves become butterfly-like is probably caused by a change in the magnetic anisotropy. It is established that the magnetic resonance spectrum in the microwave X-band (~9.4 GHz) at T = 30 K changes under the reversal of the direction of the external magnetic field (nonreciprocity phenomenon). Magnetic and induced electric dipole transitions are considered theoretically. The detected nonreciprocity is explained by the interference of these transitions.

Within the framework of the quantum mechanical approach, the available experimental data are analyzed to identify the electronic structure of the multiferroic FeCr 2 O 4 . The relative values of the key contributions to the parameters of even and odd crystal fields acting on the 3 d electrons of the Fe 2+ ion are determined. Data on local lattice distortions are systematized. The parameter of the electron-deformation interaction of the ground term Fe 2+ ( 5 E ) is determined considering lattice distortions, and the parameters of binding of the spins of Fe 2+ and Cr 3+ to the electric field are estimated. The calculation results are compared with the available experimental data on the magnetic and structural characteristics of FeCr 2 O 4 , the critical temperature of the transition to an orbitally ordered state, optical conductivity data, the Mössbauer effect study, and measurements of spontaneous electric polarization.

Within the framework of the quantum mechanical approach, the microscopic theory for magnetoelectric coupling and spin-canting in the spin ordered FeCr2O4 is discussed. We describe two possible mechanisms of magnetoelectric coupling caused by the combined action of the odd crystal field from the tetrahedral environment of the iron ions, the spin-orbit interaction and the exchange field acting on the 3d iron electrons from the chromium spins. We also consider sources of spin-canting. The first one is DM interaction which induces an angle-canting about 2 degrees, the second is a new one due to the common action of the Jahn-Teller and spin-orbit couplings, which yields up to the 50 degrees

We report on the low-frequency optical excitations in the multiferroic ground state of polycrystalline FeCr2S4 in the frequency range 0.3-3 THz and their changes upon applying external magnetic fields up to 7 T. In the ground state below the orbital-ordering temperature T-OO = 9 K we observe the appearance of several new modes. By applying the external magnetic field parallel and perpendicular to the propagation direction of the THz radiation, we can identify the strongest absorptions to be of predominantly electric-dipole origin. We discuss these modes as the low-energy electronic excitations of the Fe2+ ions (3d(6), S = 2) in an tetrahedral S2- environment. The eigenfrequencies and relative intensities of these absorption lines are satisfactorily reproduced by our calculation assuming an effective exchange field of 12.8 cm(-1) at the Fe2+-ions sites. The direction of the exchange field is found to be slightly tilted out of the ab plane. With our approach we can also describe previously reported results from Mossbauer studies and the order of magnitude of the electric polarization induced by orbital and noncollinear spin ordering.

Analytical expressions are obtained for the interaction between orbitally doubly degenerate states of ions through the strain field in weak-anisotropy cubic crystals. The arrangement of interacting pairs may be arbitrary. The energy of cooperative orbital ordering of the states of Fe 2+ ions in FeCr 2 O 4 crystal is calculated with regard to the local Jahn–Teller and the quadrupole–quadrupole interactions. It is found that the main contribution to the cooperative Jahn–Teller effect is made by the interaction through the strain field. The estimated critical phase transition temperature corresponds in order of magnitude to experimental data.

An explicit expression for the energy of interaction between two spherically symmetric particles via the strain field in cubic crystals is obtained with an accuracy up to quadratic terms with respect to the anisotropy parameter d = c 11 – c 12 – 2 c 44 . The diagrams depicting the regions of attraction and repulsion between particles projected onto the xy plane are drawn. It is found that at d < 0, the attraction regions are formed mostly along the x and y axes. At d > 0, the directions preferable for the attraction in the linear approximation with respect to the anisotropy parameter d are diagonals. However, each such direction becomes “split” into two directions if the nonlinear corrections are taken into account. In passing, we reveal the errors and misprints in the earlier papers based on the isotropic medium approximation ( d = 0) and on the linear approximation with respect of parameter d .