Magnetic and magnetoelectric excitations in the multiferroic TbMnO_3 have been investigated at terahertz frequencies. Using different experimental geometries we can clearly separate the electro-active excitations (electromagnons) from the magneto-active modes, i.e. antiferromagnetic resonances (AFMR). Two AFMR resonances were found to coincide with electromagnons. This indicates that both excitations belong to the same mode and the electromagnons can be excited by magnetic ac-field as well. In external magnetic fields and at low temperatures distinct fine structure of the electromagnons appears. In spite of the 90^o rotation of the magnetic structure, the electromagnons are observable for electric ac-fields parallel to the a-axis only. Contrary to simple expectations, the response along the c-axis remains purely magnetic in nature.
In this work, we report the growth and functional characterizations of multiferroic TbMnO3 thin films grown on Nb-doped SrTiO3 (001) substrates using pulsed laser deposition. By performing detailed magnetic and ferroelectric properties measurements, we demonstrate that the multiferroicity of spin origin known in the bulk crystals can be successfully transferred to TbMnO3 thin films. Meanwhile, anomalous magnetic transition and unusual magnetoelectric coupling related to Tb moments are observed, suggesting a modified magnetic configuration of Tb in the films as compared to the bulk counterpart.…
Single-crystal synchrotron x-ray diffraction measurements in strong magnetic fields have been performed for magnetoelectric compounds GdMnO3 and TbMnO3. It has been found that the P || a ferroelectric phase induced by the application of a magnetic field at low temperatures is characterized by commensurate lattice modulation along the orthorhombic b axis with q = 1/2 and q = 1/4. The lattice modulation is ascribed to antiferromagnetic spin alignment with a modulation vector of (0 1/4 1). The change of the spin structure is directly correlated with the magnetic-field-induced electric phase trans…
This work addresses the effect of substituting Mn$^{3+}$ by Fe$^{3+}$ at the octahedral site of TbMnO$_3$ on the magnetic phase sequence, ferroelectric and magnetoelectric properties, keeping the Fe$^{3+}$ concentration below 5%. The temperature dependence of the specific heat, dielectric permittivity and electric polarization was studied as a function of Fe$^{3+}$ concentration and applied magnetic field. From the experimental results a strong decrease of the electric polarization with increasing Fe$^{3+}$ substitution is observed, vanishing above a concentration of 4%. However, within this r…
The magnetoelectric coupling, i.e., cross-correlation between electric and magnetic orders, is a very desirable property to combine functionalities of materials for next-generation switchable devices. Multiferroics with spin-driven ferroelectricity presents such a mutual interaction concomitant with magneto- and electro-active excitations called electromagnons. TbMnO3 is a paradigmatic material in which two electromagnons have been observed in the cycloidal magnetic phase. However, their observation in TbMnO3 is restricted to the cycloidal spin phase and magnetic ground states that can support…
Terahertz electromagnetic excitations in the multiferroic TbMnO3 at the field-induced magnetic transition are investigated for different orientations of the magnetic cycloid. In addition to the electromagnon along the a-axis, the detailed polarization analysis of the experimental spectra suggests the existence of an electro-active excitation for ac electric fields along the crystallographic c-axis. This excitation is possibly the electro-active eigenmode of the spin cycloid in TbMnO3, which has been predicted within the inverse Dzyaloshinskii-Moriya mechanism of magnetoelectric coupling.
The field-induced multiferroic transition in TbMnO3 has been studied by neutron scattering. Apart strong hysteresis, the magnetic transition associated with the flop of electronic polarization exhibits a memory effect: after a field sweep, TbMnO3 does not exhibit the same phase as that obtained by zero-field cooling. The strong changes in the magnetic excitations across the transition perfectly agree with a rotation of the cycloidal spiral plane indicating that the inverse Dzyaloshinski-Moriya coupling causes the giant magnetoelectric effect at the field-induced transition. The analysis of the…
We have performed Raman measurements on TbMnO3 single crystal under magnetic field along the three crystallographic directions. The flip of the spin spiral plane creates an electromagnon excitation. In addition to the electromagnons induced by the Heisenberg coupling, we have detected the electromagnon created by the Dzyaloshinskii-Moriya interaction along the c axis. We have identified all the vibrational modes of TbMnO3. Their temperature dependences show that only one phonon observed along the polarization axis is sensitive to the ferroelectric transition. This mode is tied to the Tb3+ ion …
We have investigated the role of the 4$f$ moment on the magnetoelectric (ME) effect of orthorhombic $R$MnO$_{3}$ ($R$=rare earth ions). In order to clarify the role of the 4$f$ moment, we prepared three samples: (Eu,Y)MnO$_{3}$ without the 4$f$ moment, TbMnO$_{3}$ with the anisotropic 4$f$ moment, and (Gd,Y)MnO$_{3}$ with the isotropic 4$f$ moment. The ferroelectric behaviors of these samples are different from each other in a zero magnetic field. (Eu,Y)MnO$_{3}$ and (Gd,Y)MnO$_{3}$ show the ferroelectric polarization along the a axis in the ground state, while TbMnO$_{3}$ shows it along the c…
The magnetic excitations in multiferroic TbMnO3 have been studied by inelastic neutron scattering in the spiral and sinusoidally ordered phases. At the incommensurate magnetic zone center of the spiral phase, we find three low-lying magnons whose character has been fully determined using neutron-polarization analysis. The excitation at the lowest energy is the sliding mode of the spiral, and two modes at 1.1 and 2.5meV correspond to rotations of the spiral rotation plane. These latter modes are expected to couple to the electric polarization. The 2.5meV-mode is in perfect agreement with recent…
We present measurements of the thermal conductivity $κ$ and the thermal expansion $α$ of NdMnO$_3$ and TbMnO$_3$. In both compounds a splitting of the $4f$ multiplet of the $R^{3+}$ ion causes Schottky contributions to $α$. In TbMnO$_3$ this contribution arises from a crystal-field splitting, while in NdMnO$_3$ it is due to the Nd-Mn exchange coupling. Another consequence of this coupling is a strongly enhanced canting of the Mn moments. The thermal conductivity is greatly suppressed in both compounds. The main scattering process at low temperatures is resonant scattering of phonons between di…
We calculate spectra of magnetic excitations in the spin-spiral state of perovskite manganates. The spectra consist of several branches corresponding to different polarizations and different ways of diffraction from the static magnetic order. Goldstone modes and opening of gaps at zero and non-zero energies due to the crystal field and the Dzyaloshinski-Moriya anisotropies are discussed. Comparing results of the calculation with available experimental data we determine values of effective exchange parameters and anisotropies. To simplify the spin-wave calculation and to get a more clear physic…
We provide a detailed study of the reflectivity of multiferroic TbMnO_3 for wave numbers from 40 cm^{-1} to 1000 cm^{-1} and temperatures 5 K < T < 300 K. Excitations are studied for polarization directions E || a, the polarization where electromagnons are observed, and for E || c, the direction of the spontaneous polarization in this material. The temperature dependencies of eigenfrequencies, damping constants and polar strengths of all modes are studied and analyzed. For E || a and below the spiral ordering temperature of about 27 K we observe a transfer of optical weight from phonon excitat…
Spin excitations of magnetoelectric LiNiPO$_4$ are studied by infrared absorption spectroscopy in the THz spectral range as a function of magnetic field through various commensurate and incommensurate magnetically ordered phases up to 33\,T. Six spin resonances and a strong two-magnon continuum are observed in zero magnetic field. Our systematic polarization study reveals that some of the excitations are usual magnetic-dipole active magnon modes, while others are either electromagnons, electric-dipole active, or magnetoelectric, both electric- and magnetic-dipole active spin excitations. Field…
We investigated the spin excitations of magnetoelectric $\text{LiFePO}_4$ by THz absorption spectroscopy in magnetic fields up to 33$\,$T. By studying their selection rules, we found not only magnetic-dipole, but also electric-dipole active (electromagnons) and magnetoelectric resonances. The magnetic field dependence of four strong low-energy modes is reproduced well by our four-sublattice spin model for fields applied along the three orthorhombic axes. From the fit, we refined the exchange couplings, single-ion anisotropies, and the Dzyaloshinskii-Moriya interaction parameters. Additional sp…
We have studied spin excitations in a single-domain crystal of antiferromagnetic LiCoPO4 by THz absorption spectroscopy. By analyzing the selection rules and comparing the strengths of the absorption peaks in the different antiferromagnetic domains, we found electromagnons and magnetoelectric spin resonances besides conventional magnetic-dipole active spin-wave excitations. Using the sum rule for the magnetoelectric susceptibility we determined the contribution of the spin excitations to all the different off-diagonal elements of the static magnetoelectric susceptibility tensor in zero as well…
We investigate the demagnetization dynamics of the cycloidal and sinusoidal phases of multiferroic TbMnO$_3$ by means of time-resolved resonant soft x-ray diffraction following excitation by an optical pump. Using orthogonal linear x-ray polarizations, we suceeded in disentangling the response of the multiferroic cycloidal spin order from the sinusoidal antiferromagnetic order in the time domain. This enables us to identify the transient magnetic phase created by intense photoexcitation of the electrons and subsequent heating of the spin system on a picosecond timescale. The transient phase is…
The intrinsic noncollinear spin patterns in rare-earth pyrochlore are physically interesting, hosting many emergent properties, e.g. spin ice and monopole-type excitation. Recently, the magnetic monopole excitation of spin ice systems was predicted to be magnetoelectric active, while rare experimental works have directly confirmed this scenario. In this work, we performed systematic experimental investigation on the magnetoelectricity of Dy$_2$Ti$_2$O$_7$ by probing the ferroelectricity, spin dynamics, and dielectric behaviors. Two ferroelectric transitions at $T_{c1}$=25 K and $T_{c2}$=13 K h…
The spectra of far-infrared transmission in Tb3Fe5O12 magnetoelectric single crystals have been studied in the range between 15 and 100 cm-1, in magnetic fields up to 10 T, and for temperatures between 5 and 150 K. We attribute some of the observed infrared-active excitations to electric-dipole transitions between ligand-field split states of Tb3+ ions. Anticrossing between the magnetic exchange excitation and the ligand-field transition occurs at the temperature between 60 and 80 K. The corresponding coupling energy for this interaction is 6 cm-1. Temperature-induced softening of the hybrid I…
Multiferroics are those materials with more than one ferroic order, and magnetoelectricity refers to the mutual coupling between magnetism and electricity. The discipline of multiferroicity has never been so highly active as that in the first decade of the twenty-first century, and it has become one of the hottest disciplines of condensed matter physics and materials science. A series of milestones and steady progress in the past decade have enabled our understanding of multiferroic physics substantially comprehensive and profound, which is further pushing forward the research frontier of this…
Magnetic skyrmions, vortex-like swirling spin textures characterized by a quantized topological invariant, realized in chiral-lattice magnets are currently attracting intense research interest. In particular, their dynamics under external fields is an issue of vital importance both for fundamental science and for technical application. Whereas observations of magnetic skyrmions had been limited to metallic magnets so far, their realization was discovered also in a chiral-lattice insulating magnet Cu2OSeO3 in 2012. Skyrmions in the insulator turned out to exhibit multiferroic nature with spin-i…
An effective model is developed to explain the phase diagram and the mechanism of magnetoelectric coupling in multiferroics, $RMn_2O_5$. We show that the nature of magnetoelectric coupling in $RMn_2O_5$ is a coupling between two Ising-type orders, namely, the ferroelectric order in the b axis, and the coupled magnetic order between two frustrated antiferromagnetic chains. The frustrated magnetic structure drives the system to a commensurate-incommensurate phase transition, which can be understood as a competition between a collinear or col-plane order stemming from the `order by disorder' mech…
The origin of electromagnon excitations in cycloidal \textit{R}MnO$_3$ is explained in terms of the Heisenberg coupling between spins despite the fact that the static polarization arises from the much weaker Dzyaloshinskii-Moriya (DM) exchange interaction. We present a model that incorporates structural characteristics of this family of manganites that is confirmed by far infrared transmission data as a function of temperature and magnetic field and inelastic neutron scattering results. A deep connection is found between the magnetoelectric dynamics of the spiral phase and the static magnetoel…
Chirality, i.e., the right- and left-handedness of structure, is one of the key concepts in many fields of science including biology, chemistry and physics, and its manipulation is an issue of vital importance. The electron spins in solids can form chiral configurations. In perovskite manganites RMnO3 (R=Tb, Dy,...etc), the Mn-spins form a cycloidal structure, which induces ferroelectric polarization (P) through the relativistic spin-orbit interaction. This magnetism-induced ferroelectricity (multiferroics) and associated infrared-active spin waves (electromagnons) open a promising route to co…
The phenomenological theory of ferroelectricity in spiral magnets presented in [M. Mostovoy, Phys. Rev. Lett. 96, 067601 (2006)] is generalized to describe consistently states with both uniform and modulated-in-space ferroelectric polarizations. A key point in this description is the symmetric part of the magnetoelectric coupling since, although being irrelevant for the uniform component, it plays an essential role for the non-uniform part of the polarization. We illustrate this importance in generic examples of modulated magnetic systems: longitudinal and transverse spin-density wave states a…
We propose a model for the pair of electromagnon excitations observed in the class of multiferroic materials {\it R}MnO$_3$ ({\it R} is a rare-earth ion). The model is based on a harmonic cycloid ground state interacting with a zone-edge magnon and its twin excitation separated in momentum space by two times the cycloid wave vector. The pair of electromagnons is activated by cross coupling between magnetostriction and spin-orbit interactions. Remarkably, the spectral weight of the twin electromagnon is directly related to the presence of a magnetically induced oscillatory polarization in the g…
Inelastic neutron scattering (INS) experiments were performed to investigate the spin dynamics in magnetoelectric effect (ME) LiCoPO$_4$ single crystals. Weak dispersion was detected in the magnetic excitation spectra along the three principal crystallographic axes measured around the (0 1 0) magnetic reflection. Analysis of the data using linear spin-wave theory indicate that single-ion anisotropy in LiCoPO$_4$ is as important as the strongest nearest-neighbor exchange coupling. Our results suggest that Co$^{2+}$ single-ion anisotropy plays an important role in the spin dynamics of LiCoPO$_4$…
Magnetodielectric materials are characterized by a strong coupling of magnetic and dielectric properties and in rare cases simultaneously exhibit both, magnetic and polar order. Among other multiferroics, TbMnO3 and GdMnO3 reveal a strong magneto-dielectric (ME) coupling and as a consequence fundamentally new spin excitations exist: Electro-active magnons, or electromagnons, i. e. spin waves which can be excited by ac electric fields. Here we show that these excitations appear in the phase with an incommensurate (IC) magnetic structure of the manganese spins. In external magnetic fields this I…
We investigate magnetic excitations in an $S=3/2$ Heisenberg model representing two-dimensional antiferromagnet ${\rm Ba_2CoGe_2O_7}$. In terahertz absorption experiment of the compound, Goldstone mode as well as novel magnetic excitations, conventional magnetic resonance at 2 meV and both electric- and magnetic-active excitation at 4 meV, have been observed. By introducing a hard uniaxial anisotropy term $Λ(S^z)^2$, three modes can be explained naturally. We also indicate that, via the spin-dependent metal-ligand hybridization mechanism, the 4 meV excitation is an electric-active mode through…
Magnetic order and excitations in multiferroic DyMnO3 were studied by neutron scattering experiments using a single crystal prepared with enriched 162Dy isotope. The ordering of Mn moments exhibits pronounced hysteresis arising from the interplay between Mn and Dy magnetism which possesses a strong impact on the ferroelectric polarization. The magnon dispersion resembles that reported for TbMnO3. We identify the excitations at the magnetic zone center and near the zone boundary in the b direction, which can possess electromagnon character. The lowest frequency of the zone-center magnons is in …
Spin-phonon coupling, the interaction of spins with surrounding lattice is a key parameter to understand the underlying physics of multiferroics and engineer their magnetization dynamics. Elementary excitations in multiferroic materials are strongly influenced by spin-phonon interaction, making Raman spectroscopy a unique tool to probe these coupling(s). Recently, it has been suggested that the dielectric and magnetic properties of 15R-type hexagonal BaMnO3 are correlated through the spin-lattice coupling. Here, we report the observation of an extensive renormalization of the Raman spectrum of…
Competing magnetic exchange interactions often result in non-collinear magnetic states, such as spin spirals, which break the inversion symmetry and induce ferroelectric polarization. The resulting strong interactions between magnetic and dielectric degrees of freedom lead to a technologically important possibility to control magnetic order by electric fields and to electromagnons, magnetic excitations that can be excited by an electric dipole of the electromagnetic field. Here we study the effects of chiral domain walls on magnetoelectric properties of spiral magnets. We use a quasi-1D model …
We have investigated the directional dichroism of magnetic resonance spectra in the polar ferromagnet GaV$_4$S$_8$. While four types of structural domains are energetically degenerated under zero field, the magnetic resonance for each domain is well separated by applying magnetic fields due to uniaxial magnetic anisotropy. Consequently, the directional dichroism as large as 20 % is clearly observed without domain cancellation. The present observation therefore demonstrates that not only magnetoelectric mono-domain crystals but also magnetoelectric multi-domain specimens can be used to realize …
The spin-wave excitations of the multiferroic $\rm MnWO_4$ have been measured in its low-temperature collinear commensurate phase using high-resolution inelastic neutron scattering. These excitations can be well described by a Heisenberg model with competing long-range exchange interactions and a single-ion anisotropy term. The magnetic interactions are strongly frustrated within the zigzag spin chain along c axis and between chains along the a axis, while the coupling between spin along the b axis is much weaker. The balance of these interactions results in the noncollinear incommensurate spi…
Competing interactions in the so-called spin-ice compounds stabilize a frustrated ground-state with finite zero-point entropy and, interestingly, emergent magnetic monopole excitations. The properties of these monopoles are at the focus of recent research with particular emphasis on their quantum dynamics. It is predicted that each monopole also possesses an electric dipole moment, which allows to investigate their dynamics via the dielectric function ε(ν). Here, we report on broadband spectroscopic measurements of ε(ν) in Dy2Ti2O7 down to temperatures of 200mK with a specific focus on the cri…
We present a study of terahertz frequency magnetoelectric effect in ferrimagnetic pyroelectric CaBaCo$_4$O$_7$ and its Ni-doped variants. The terahertz absorption spectrum of these materials consists of spin excitations and low-frequency infrared-active phonons. We studied the magnetic-field-induced changes in the terahertz refractive index and absorption in magnetic fields up to 17 T. We find that the magnetic field modulates the strength of infrared-active optical phonons near 1.2 and 1.6 THz. We use the Lorentz model of the dielectric function to analyze the measured magnetic-field dependen…
We present a theory of magnetoelectric magnon-photon coupling in cavities hosting noncentrosymmetric magnets. Analogously to nonreciprocal phenomena in multiferroics, the magnetoelectric coupling is time-reversal and inversion asymmetric. This asymmetry establishes a means for exceptional tunability of magnon-photon coupling, which can be switched on and off by reversing the magnetization direction. Taking the multiferroic skyrmion-host Cu$_2$OSeO$_3$ with ultralow magnetic damping as an example, we reveal the electrical activity of skyrmion eigenmodes and propose it for magnon-photon splittin…
We investigate the possible types of coupling between ferroelectricity and magnetism for the zig-zag spin chain multiferroic LiCu2O2 compound. We construct a multi-order parameter phenomenological model for the material based on a group theoretical analysis. From our calculation we conclude that a coupling involving the inter-chain magnetic structure and ferroelectricity is necessary to understand the experimental results of Park et.al. Our proposed model is able to account for the electric polarization flop in the presence of an externally applied magnetic field. Furthermore, based on our the…
Right- and left-handed circularly polarized light interact differently with electronic charges in chiral materials. This asymmetry generates the natural circular dichroism and gyrotropy, also known as the optical activity. Here we demonstrate that optical activity is not a privilege of the electronic charge excitations but it can also emerge for the spin excitations in magnetic matter. The square-lattice antiferromagnet Ba$_2$CoGe$_2$O$_7$ offers an ideal arena to test this idea, since it can be transformed to a chiral form by application of external magnetic fields. As a direct proof of the f…
The coexisting magnetic and ferroelectric orders in multiferroic materials give rise to a handful of novel magnetoelectric phenomena, such as the absorption difference for the opposite propagation directions of light called the non-reciprocal directional dichroism (NDD). Usually these effects are restricted to low temperature, where the multiferroic phase develops. In this paper we report the observation of NDD in the paramagnetic phase of Sr2CoSi2O7 up to temperatures more than ten times higher than its Néel temperature (7 K) and in fields up to 30 T. The magnetically induced polarization and…
By using broadband dielectric spectroscopy in the radiofrequency and microwave range we studied the magnetoelectric dynamics in the multiferroic chiral antiferromagnet MnWO$_4$. Above the multiferroic phase transition at $T_{N2} \approx 12.6$ K we observe a critical slowing down of the corresponding magnetoelectric fluctuations resembling the soft-mode behavior in canonical ferroelectrics. This electric field driven excitation carries much less spectral weight than ordinary phonon modes. Also the critical slowing down of this mode scales with an exponent larger than one which is expected for m…
Spin excitations were studied by absorption spectroscopy in CaBaCo4O7 which is a type-I multiferroic compound with the largest magnetic-order induced ferroelectric polarization (ΔP=17mC/m2) reported, so far. We observed two optical magnon branches: a solely electric dipole allowed one and a mixed magnetoelectric resonance. The entangled magnetization and polarization dynamics of the magnetoelectric resonance gives rise to unidirectional light absorption, i.e. that magnon mode absorbs the electromagnetic radiation for one propagation direction but not for the opposite direction. Our systematic …
The quadruple Calcium manganite (CaMn7O12) is a multiferroic material that exhibits a giant magnetically-induced ferroelectric polarization which makes it very interesting for magnetoelectric applications. Here, we report the Raman spectroscopy study on this compound of both the phonon modes and the low energy excitations from 4 K to room temperature. A detailed study of the Raman active phonon excitations shows that three phonon modes evidence a spin-phonon coupling at TN2 = 50 K. In particular, we show that the mode at 432 cm-1 associated to Mn(B)O6 (B position of the perovskite) rotations a…
We have determined the terahertz spectrum of the chiral langasite Ba$_3$NbFe$_3$Si$_2$O$_{14}$ by means of synchrotron-radiation measurements. Two excitations are revealed that are shown to have a different nature. The first one, purely magnetic, is observed at low temperature in the magnetically ordered phase and is assigned to a magnon. The second one persits far into the paramagnetic phase and exhibits both an electric and a magnetic activity at slightly different energies. This magnetoelectric excitation is interpreted in terms of atomic rotations and requires a helical electric polarizati…
We report the magnetic field dependence of the THz absorption and non-reciprocal directional dichroism spectra of BiFeO$_3$ measured on the three principal crystal cuts for fields applied along the three principal directions of each cut. From the systematic study of the light polarization dependence we deduced the optical selection rules of the spin-wave excitations. Our THz data, combined with small-angle neutron scattering results showed that i) an in-plane magnetic field rotates the $\mathbf{q}$ vectors of the cycloids perpendicular to the magnetic field, and ii) the selection rules are mos…
High resolution inelastic neutron scattering reveals that the elementary magnetic excitations in multiferroic MnWO4 consist of low energy dispersive electromagnons in addition to the well-known spin-wave excitations. The latter can well be modeled by a Heisenberg Hamiltonian with magnetic exchange coupling extending to the 12th nearest neighbor. They exhibit a spin-wave gap of 0.61(1) meV. Two electromagnon branches appear at lower energies of 0.07(1) meV and 0.45(1) meV at the zone center. They reflect the dynamic magnetoelectric coupling and persist in both, the collinear magnetic and parael…
The $J_1$-$J_2$ quantum spin sawtooth chain is a paradigmatic one-dimensional frustrated quantum spin system exhibiting unconventional ground-state and finite-temperature properties. In particular, it exhibits a flat energy band of one-magnon excitations accompanied by an enhanced magnetocaloric effect for two singular ratios of the basal interactions $J_1$ and the zigzag interactions $J_2$. In our paper, we demonstrate that one can drive the spin system into a flat-band scenario by applying an appropriate electric field, thus overcoming the restriction of fine-tuned exchange couplings $J_1$ a…
Clusters of single spins form the relevant spin entities in the formation of long-range magnetic order in spin cluster Mott insulators. Such type of spin order bears resemblance to molecular crystals, and we therefore may expect a prototypical spin wave spectrum which can be divided into low-energy external and high-energy internal cluster spin wave modes. Here, we study high-energy spin cluster excitations in the spin cluster Mott insulator Cu$_{2}$OSeO$_{3}$ by means of spontaneous Raman scattering. Multiple high-energy optical magnon modes are observed, of which the Raman-activity is shown …
Making use of index theorem and spin Chern Simons theory, we construct an effective topological field theory of strongly correlated topological insulators coupling to a nonabelian gauge field $ SU(N) $ with an interaction constant $ g $ in the absence of the time-reversal symmetry breaking. If $ N $ and $ g $ allow us to define a t'Hooft parameter $ λ$ of effective coupling as $ λ= N g^{2} $, then our construction leads to the fractional quantum Hall effect on the surface with Hall conductance $ σ_{H}^{s} = \frac{1}{4λ} \frac{e^{2}}{h} $. For the magnetoelectric response described by a bulk ax…
Recently, oxide multiferroics have attracted much attention due to their large magnetoelectric effect which allows the tuning of magnetic properties with electric field and vice versa and open new venues for future spintronic applications such as multiple-state memory devices with dual magnetic and electric control. BiFeO$_3$ (BFO) belongs to this new class of materials and shows both ferroelectric and antiferromagnetic orders at room temperature with a large electric polarizationassociated with a cycloidal spiral magnetic ordering. The incommensurate magnetic order induces magnon zone folding…
Low-energy magnon excitations in magnetoelectric LiFePO$_4$ have been investigated by high-frequency high-field electron spin resonance spectroscopy in magnetic fields up to B = 58 T and frequencies up to f = 745 GHz. For magnetic fields applied along the easy magnetic axis, the excitation gap softens and vanishes at the spin-flop field of BSF = 32 T before hardening again at higher fields. In addition, for B smaller than BSF we observe a resonance mode assigned to excitations due to Dzyaloshinskii-Moriya (DM)-interactions, thereby evidencing sizable DM interaction of approx 150 micro eV in Li…
The spin wave excitations of the geometrically frustrated triangular lattice antiferromagnet (TLA) $\rm CuFeO_2$ have been measured using high resolution inelastic neutron scattering. Antiferromagnetic interactions up to third nearest neighbors in the ab plane (J_1, J_2, J_3, with $J_2/J_1 \approx 0.44$ and $J_3/J_1 \approx 0.57$), as well as out-of-plane coupling (J_z, with $J_z/J_1 \approx 0.29$) are required to describe the spin wave dispersion relations, indicating a three dimensional character of the magnetic interactions. Two energy dips in the spin wave dispersion occur at the incommens…
Magnetic excitations are investigated for a hexagonal polar magnet Fe2Mo3O8 by terahertz spectroscopy. We observed magnon modes including an electric-field active magnon, electromagnon, in the collinear antiferromagnetic phase with spins parallel to the c axis. We unravel the nature of these excitations by investigating the correlation between the evolution of the mode profile and the magnetic transition from antiferromagnetic to ferrimagnetic order induced by magnetic field or Zn-doping. We propose that the observed electromagnon mode involves the collective precession of the spins with oscil…
Understanding ultrafast magnetization dynamics on the microscopic level is of strong current interest due to the potential for applications in information storage. In recent years, the spin-lattice coupling has been recognized to be essential for ultrafast magnetization dynamics. Magnetoelectric multiferroics of type II possess intrinsic correlations among magnetic sublattices and electric polarization (P) through spin-lattice coupling, enabling fundamentally coupled dynamics between spins and lattice. Here we report on ultrafast magnetization dynamics in a room-temperature multiferroic hexafe…
Using a combination of first-principles and magnetization-dynamics calculations, we study the effect of the intense optical excitation of phonons on the magnetic behavior in insulating magnetic materials. Taking the prototypical magnetoelectric \CrO\ as our model system, we show that excitation of a polar mode at 17 THz causes a pronounced modification of the magnetic exchange interactions through a change in the average Cr-Cr distance. In particular, the quasi-static deformation induced by nonlinear phononic coupling yields a structure with a modified magnetic state, which persists for the du…
We predict the phenomenon of antiferroelectric resonance (AFER), in which an ac electric field causes magnetic ions located at noncentrosymmetric positions in a multi-sublattice magnet to undergo magnetic transitions corresponding to exchange collective excitations of the system. We construct a theory of such resonances, and show that in magnets with collinear magnetic structures AFER is caused by relativistic and exchange-relativistic magnetoelectric interactions, while in the noncollinear magnets a significant contribution can also come from the exchange magnetoelectric interaction. We predi…
