Controlled generation of coherent spin waves with highest possible frequencies and shortest possible wavelengths is a cornerstone of spintronics and magnonics. Here, using Heisenberg antiferromagnet RbMnF3, we demonstrate that laser-induced THz spin dynamics corresponding to pairs of mutually coherent counter-propagating spin waves with the wavevectors up to the edge of the Brillouin zone cannot be understood in terms of magnetization and antiferromagnetic (Néel) vectors, conventionally used to describe spin waves. Instead, we propose to model such spin dynamics using the spin correlation function. We derive a quantum-mechanical equation of motion for the latter and emphasize that unlike the magnetization and antiferromagnetic vectors the spin correlations in antiferromagnets do not exhibit inertia.

The coupling between antiferromagnetic spins and infrared-active phonons in solids is responsible for many intriguing phenomena and is a field of intense research with extensive potential applications in the modern devices based on antiferromagnetic spintronics and phononics. Insulating rutile antiferromagnetic crystal CoF$_2$ is one of the model materials for studying nonlinear magnetophononics due to the strong spin-lattice coupling as a result of the orbitally degenerate ground state of Co$^{2+}$ ions manifested in the plethora of static and induced piezomagnetic effects. Here we report results on the complete infrared spectroscopy study of lattice and magnetic dynamics in CoF$_2$ in a wide temperature range and their careful analysis. We observed that infrared-active phonons demonstrate frequency shifts at the antiferromagnetic ordering. Furthermore, using first-principles calculations, we examined the lattice dynamics and disclosed that these frequency shifts are rather due to the spin-phonon coupling than geometrical lattice effects. Next we found that the low-frequency dielectric permittivity demonstrates distinct changes at the antiferromagnetic ordering due to the spontaneous magnetodielectric effect caused by the behavior of infrared-active phonons. In addition, we have observed magnetic excitations in the infrared spectra and identified their magnetodipole origin. To strengthen our conclusions, we analyze the theoretical phonon-magnon coupling overall phonons at the $\Gamma$ point. We conclude that the largest effect comes from the $A_{1g}$ and $B_{2g}$ Raman-active modes. As such, our results establish a solid basis for further investigations and more deeper understanding of the coupling of phonons with spins and magnetic excitations in antiferromagnets.

Abstract Understanding spin-lattice interactions in antiferromagnets is a critical element of the fields of antiferromagnetic spintronics and magnonics. Recently, coherent nonlinear phonon dynamics mediated by a magnon state were discovered in an antiferromagnet. Here, we suggest that a strongly coupled two-magnon-one phonon state in this prototypical system opens a novel pathway to coherently control magnon-phonon dynamics. Utilizing intense narrow-band terahertz (THz) pulses and tunable magnetic fields up to μ 0 H ext = 7 T, we experimentally realize the conditions of magnon-phonon Fermi resonance in antiferromagnetic CoF2. These conditions imply that both the spin and the lattice anharmonicities harvest energy from the transfer between the subsystems if the magnon eigenfrequency f m is half the frequency of the phonon 2f m = f ph. Performing THz pump-infrared probe spectroscopy in conjunction with simulations, we explore the coupled magnon-phonon dynamics in the vicinity of the Fermi-resonance and reveal the corresponding fingerprints of nonlinear interaction facilitating energy exchange between these subsystems.

The copper metaborate CuB2O4 2 O 4 with a unique noncentrosymmetric crystal structure and the two structurally nonequivalent 4b b and 8d d magnetic subsystems of Cu2+ 2 + ions are characterized by several commensurate and incommensurate magnetic phases below the N & eacute;el temperature of T N = 20 K. Transitions between them can be induced by varying the sample temperature or the applied magnetic field. High-resolution optical spectroscopy of the Frenkel exciton states is used to probe the magnetic phase transitions. The absorption spectra are measured in the temperature range from 4.3 K up to T N and in magnetic fields up to 2 T. The exciton transitions are observed in the range of 1.405-1.407 . 405-1 . 407 eV and are related to the lowest-energy electronic transition in the 4b b magnetic subsystem of Cu2+ 2 + ions, thus allowing us to monitor the behavior of this particular subsystem. The exciton lines show abrupt changes of intensity and energy splitting, which can be unambiguously attributed to the magnetic phase transitions in the 4b b subsystem. The magnetic phase diagram reconstructed from the spectroscopic experiments on the 4b b subsystem is compared with those from magnetic measurements, which reflect the magnetic behavior of both the 4b b and 8d d subsystems. The suggested spectroscopic approach enables separate monitoring of the temperature and magnetic field behavior of different magnetic subsystems in structurally and magnetically complex compounds.

Rare-earth orthoferrites are a promising platform for antiferromagnetic spintronics with a rich variety of terahertz spin and lattice dynamics phenomena. For instance, it has been experimentally demonstrated that the light-driven optical phonons can coherently manipulate macroscopic magnetic states via nonlinear magnetophononic effects. Here using TbFeO3 as an example, we reveal the origin of the mode mixing between the LO and TO phonons, which is important for understanding of nonlinear phononics. We performed a comprehensive study of the lattice dynamics of the TbFeO3 single crystal by polarized infrared and Raman scattering spectroscopic techniques, and experimentally obtained and carefully analyzed the spectra of anisotropic complex dielectric functions in the far-infrared spectral range. This allowed us to reliably identify the symmetries and parameters of most infrared- and Raman-active phonons. Next, the experimental studies were supplemented by the lattice dynamics calculations which allowed us to propose the normal mode assignments. We reveal that the relation between LO and TO polar phonons is complex and does not strictly follow the "LO-TO rule" due to the strong mode mixing. We further analyze how displacements of different ions contribute to phonon modes and reveal that magnetic Fe ions are not involved in Raman-active phonons, thus shedding light on a lack of spin phonon coupling for such phonons. The obtained results establish a solid basis for further in-depth experimental research in the field of nonlinear phononics and magnetophononics in rare-earth orthoferrites.

The copper metaborate ${\mathrm{CuB}}_{2}{\mathrm{O}}_{4}$ with a unique noncentrosymmetric crystal structure and the two structurally nonequivalent $4b$ and $8d$ magnetic subsystems of ${\mathrm{Cu}}^{2+}$ ions are characterized by several commensurate and incommensurate magnetic phases below the N\'eel temperature of ${T}_{\mathrm{N}}=20$ K. Transitions between them can be induced by varying the sample temperature or the applied magnetic field. High-resolution optical spectroscopy of the Frenkel exciton states is used to probe the magnetic phase transitions. The absorption spectra are measured in the temperature range from 4.3 K up to ${T}_{\mathrm{N}}$ and in magnetic fields up to 2 T. The exciton transitions are observed in the range of $1.405--1.407$ eV and are related to the lowest-energy electronic transition in the $4b$ magnetic subsystem of ${\mathrm{Cu}}^{2+}$ ions, thus allowing us to monitor the behavior of this particular subsystem. The exciton lines show abrupt changes of intensity and energy splitting, which can be unambiguously attributed to the magnetic phase transitions in the $4b$ subsystem. The magnetic phase diagram reconstructed from the spectroscopic experiments on the $4b$ subsystem is compared with those from magnetic measurements, which reflect the magnetic behavior of both the $4b$ and $8d$ subsystems. The suggested spectroscopic approach enables separate monitoring of the temperature and magnetic field behavior of different magnetic subsystems in structurally and magnetically complex compounds.

The observation of strongly coupled lattice and spin dynamics in altermagnet CoF$_2$ is reported. On the background of the expected spin-phonon interaction leading to renormalization of all phonons at the Neel temperature an additional strong coupling between one-magnon excitation and the lowest frequency Raman-active phonon of B1g symmetry was observed and manifested an anomaly in its energy, full width, and intensity at temperature T*=23 K precisely where the frequency of the phonon becomes exactly twice the frequency of the magnon. We assigned this effect to unique magnon-phonon coupling in the form of a two-magnons-one-phonon interaction. The consistent experimental data clearly demonstrate that there is an intrinsic coupling that does not require coherent excitation.

A Study of THz spin dynamics was performed in a single crystal of antiferromagnetic TbFeO3. Terbium orthoferrite exhibits magnetic phase transition of the Jahn-Teller type resulting in simultaneous rotation of both iron spins and terbium orbital moments and even leading to the emergence of a multiferroic state. A single-cycle THz pulse, generated in the LiNbO3 crystal, is used as a driven torque. The temperature-dependent measurements, across the phase transition region, revealed, that apart from the expected coexistence of two well-distinguished modes of antiferromagnetic resonance at 650 GHz and 450 GHz, near the phase transition temperature, the lower frequency mode bandwidth widens significantly with a subsequent increase of the spectral weight. The widening effect, revealed near the transition temperature, is due to the strong interaction between Tb-Fe sublattices. The interaction is increasing at lower temperatures so that the dynamics, detected in the Fe-sublattice, are mainly governed by the Tb-sublattice. Surprisingly, near the transition point, even lover frequency modes (~150 GHz), assigned to the impurity modes, were observed.

Ultrafast photo-induced phase transitions occurring under the impact of femtosecond laser pulses provide versatile opportunities for switching solids between distinctly-different crystalline, electronic, and magnetic states and thus modify their functional properties in a significant way. In this paper, we report on the laser-induced spin reorientation and Verwey phase transitions in a single crystalline ferrimagnetic magnetite Fe3O4. Using femtosecond optical and magneto-optical pump-probe techniques, we define the range of the initial sample temperatures and laser fluences when partial or complete photo-induced phase transitions occur from a monoclinic insulating to a cubic metallic state with concomitant switching of magnetic anisotropy from the uniaxial to the cubic one. We thus reveal a connection between these phase transitions when driven by femtosecond laser pulses. Using transient linear and quadratic magneto-optical effects, we examine magnetization dynamics launched the switching of the magnetic anisotropy axis. We unveil the presence of the domains undergoing the laser-induced phase transitions even below the established threshold fluence for the transitions, as well as when the material is initially in the cubic phase. This is the manifestation of the first order of these both laser-induced phase transitions beyond the range of thermodynamic equilibrium.

Understanding spin-lattice interactions in antiferromagnets is one of the most fundamental issues at the core of the recently emerging and booming fields of antiferromagnetic spintronics and magnonics. Recently, coherent nonlinear spin-lattice coupling was discovered in an antiferromagnet which opened the possibility to control the nonlinear coupling strength and thus showing a novel pathway to coherently control magnon-phonon dynamics. Here, utilizing intense narrow band terahertz (THz) pulses and tunable magnetic fields up to 7 T, we experimentally realize the conditions of the Fermi magnon-phonon resonance in antiferromagnetic $CoF_{2}$. These conditions imply that both the spin and the lattice anharmonicities harvest energy transfer between the subsystems, if the magnon eigenfrequency $f_{m}$ is twice lower than the frequency of the phonon $2f_{m}=f_{ph}$. Performing THz pump-infrared probe spectroscopy in conjunction with simulations, we explore the coupled magnon-phonon dynamics in the vicinity of the Fermi-resonance and reveal the corresponding fingerprints of an impulsive THz-induced response. This study focuses on the role of nonlinearity in spin-lattice interactions, providing insights into the control of coherent magnon-phonon energy exchange.

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 TN = 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.

Interfaces in heavy metal (HM) - antiferromagnetic insulator (AFI) heterostructures have recently become highly investigated and debated systems in the effort to create spintronic devices that function at terahertz frequencies. Such heterostructures have great technological potential because AFIs can generate sub-picosecond spin currents which the HMs can convert into charge signals. In this work we demonstrate an optically induced picosecond spin transfer at the interface between AFIs and Pt using time-domain THz emission spectroscopy. We select two antiferromagnets in the same family of fluoride cubic perovskites, KCoF 3 and KNiF 3 , whose magnon frequencies at the centre of the Brillouin zone differ by an order of magnitude. By studying their behaviour with temperature, we correlate changes in the spin transfer efficiency across the interface to the opening of a gap in the magnon density of states below the Néel temperature. Our observations are reproduced in a model based on the spin exchange between the localized electrons in the antiferromagnet and the free electrons in Pt. Through this comparative study of selected materials, we are able to shine light on the microscopy of spin transfer at picosecond timescales between antiferromagnets and heavy metals and identify a key figure of merit for its efficiency: the magnon gap. Our results are important for progressing in the fundamental understanding of the highly discussed physics of the HM/AFI interfaces, which is the necessary cornerstone for the designing of femtosecond antiferromagnetic spintronics devices with optimized characteristics.

In the last two decades copper metaborate CuB 2 O 4 with a unique noncentrosymmetric crystal structure has become the subject of active research due to its unusual magnetic and optical properties. We consider the propagation and absorption of light in CuB 2 O 4 based on the solution of Maxwell’s equations. We present an overview of the main results on the investigation of the phonon spectrum using infrared and Raman spectroscopy. Studies in the region of electronic transitions in Cu 2+ ions in the crystal field have allowed the separation of contributions to the optical absorption from copper ions in inequivalent positions. A splitting of zero-phonon absorption lines in a magnetic field has been detected, and these results have received a theoretical explanation in terms of the exciton model. A rich structure of exciton–magnon states has been observed in the photoluminescence spectra. We have carried out a spectroscopic study of the optical second harmonic generation in the region of excitonic transitions, which has allowed the contribution of the toroidal moment and the Fano resonance to the observed signals to be revealed.

Excitation, detection, and control of coherent THz magnetic excitation in antiferromagnets are challenging problems that can be addressed using ever shorter laser pulses. We study experimentally excitation of magnetic dynamics at THz frequencies in an antiferromagnetic insulator CoF2by sub-10 fs laser pulses. Time-resolved pump-probe polarimetric measurements at different temperatures and probe polarizations reveal laser-induced transient circular birefringence oscillating at the frequency of 7.45 THz and present below the Néel temperature. The THz oscillations of circular birefringence are ascribed to oscillations of the magnetic moments of Co2+ions induced by the laser-driven coherentEgphonon mode via the THz analogue of the transverse piezomagnetic effect. It is also shown that the same pulse launches coherent oscillations of the magnetic linear birefringence at the frequency of 3.4 THz corresponding to the two-magnon mode. Analysis of the probe polarization dependence of the transient magnetic linear birefringence at the frequency of the two-magnon mode enables identifying its symmetry.

Orthorhombic PbMnBO4 is a rare example of an insulating ferromagnet in which the magnetic properties, in particular the strong magnetic anisotropy, are determined by the Mn3+ Jahn-Teller ion. Here, we report on the detailed investigation of magnetic excitations in the subterahertz and terahertz frequency ranges, as well as lattice excitations in the terahertz range. Using polarized azimuthally resolved Raman spectroscopy, four branches of magnetic excitations were observed and assigned to one acoustic and three optical one-magnon modes. The coupling between ferromagnetic ordering at T-c = 31 K and the Jahn-Teller distortions of [MnO6] octahedra due to the spin-phonon interaction was directly observed for some specific phonon modes involved in these distortions. A spin-wave Hamiltonian was developed that allowed us to determine a unique set of exchange and effective anisotropy parameters. The intensity ratio of the anti-Stokes to Stokes acoustic magnon peaks is found to be anomalous and directly indicates the involvement of the magneto-optical parameters in the magnetic Raman scattering process.

Employing polarization sensitive terahertz (THz) transmission spectroscopy, we explored how the waveform of initially single-cycle linearly polarized THz pulses changes upon propagation through a thick antiferromagnetic crystal of CoF2. The changes upon propagation through CoF2 are found to depend strongly on both the incoming polarization and temperature. In particular, the ellipticity and polarization rotation acquired by initially linearly polarized light are quantified and explained in terms of magnetic linear birefringence and dichroism. Although the magneto-optical effects are often considered to be relatively weak, our experiments reveal that the polarization of the THz pulse substantially changes along the pulse duration. The pulse shape is further complicated by features assigned to the formation of magnon-polaritons. The findings clearly show the importance of accounting for propagation effects in antiferromagnetic spintronics and magnonics.

The detailed Raman scattering investigation of the lattice and spin dynamics of a single crystal of the Fe3BO6 antiferromagnet is reported. Azimuthally resolved polarization measurements provided an unambiguous determination of the symmetry of observed excitations. Low-temperature experiments at T=4.2 K allowed us to reduce anharmonic contribution and deconvolute several overlapping phonon modes. Low-frequency measurements have made it possible to find two excitations at 13.1 and 16.6 cm−1, which were assigned to quasi-ferromagnetic and quasi-antiferromagnetic magnon excitations, respectively. The magnetic field applied along the hard-magnetization axis causes energy shifts of these excitations, but no spin-flip transition was observed up to B=30 T.

The piezomagnetic effect manifests itself in emergence of a net magnetic moment in a mechanically-stressed magnetically ordered material. Up to now, this effect was theoretically analyzed and experimentally studied for the case of static or low frequency deformations of antiferromagnets, and in our brief overview we present the recent progress in exploring the piezomagnetic effect at the THz frequencies. We discuss particular lattice distortions in the model piezomagnetic antiferromagnets MnF2 and CoF2 that are associated with the Raman-active phonons. We show that the phonons of the Eg and B2g symmetry should support emergence of a dynamic magnetic moment oscillating at the corresponding THz phonon frequencies. We further analyze conditions for coherent excitations of these modes by using ultrashort laser pulses via the mechanism of impulsive stimulated Raman scattering. We show that observation of transverse piezomagnetic effect is, in principle, feasible for the Eg phonon. We also discuss experimental results demonstrating laser-induced excitation of coherent Eg phonon in MnF2 and CoF2, as well as speculate about possibilities to detect piezomagnetic effect at the THz frequencies.

The optical spectra of antiferromagnetic copper metaborate CuB_2O_4 are characterized by an exceptionally rich structure of narrow absorption lines due to electronic transitions within the magnetic Cu^2+ ions, but their unambiguous identification and behavior in magnetic field remain far from being fully understood. We studied the polarized magneto-absorption spectra of this tetragonal antiferromagnet with a high spectral resolution in the range of 1.4055-1.4065 eV in magnetic fields up to 9.5 T and temperatures from 1.6 up to T_N = 20 K. We observed a set of eight absorption lines at T=1.6 K in magnetic fields exceeding 1.4 T which we identified as arising from Frenkel excitons related to the ground and the first excited state of Cu^2+ ions. The number of these excitons is defined by the presence of the four Cu^2+ ions with the doubly-degenerate spin state S = 1/2 at the 4b positions in the crystallographic unit cell. The energies of these excitons are determined the exchange interaction of 0.5 meV of Cu^2+ ions in the excited state with 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 developed a theoretical model of Frenkel excitons in magnetic field that accounts for specific features of the spin structure and exchange interactions in CuB_2O_4. The model was used for fitting the experimental data and evaluation of Frenkel exciton parameters, such as the Davydov splitting, the molecular exchange energy, and the g-factors of the ground and excited states of the Cu^2+ ions.