Magnetic excitations in multiferroic TbMnO3: evidence for a hybridized soft mode

Non-equilibrium dynamics of spin-lattice coupling

Quantifying the dynamics of normal modes and how they interact with other excitations is of central importance in condensed matter. Spin-lattice coupling is relevant to several sub-fields of condensed matter physics; examples include spintronics, high-Tc superconductivity, and topological materials. However, experimental approaches that can directly measure it are rare and incomplete. Here we use time-resolved X-ray diffraction to directly access the ultrafast motion of atoms and spins following the coherent excitation of an electromagnon in a multiferroic hexaferrite. One striking outcome is the different phase shifts relative to the driving field of the two different components. This phase shift provides insight into the excitation process of such a coupled mode. This direct observation of combined lattice and magnetization dynamics paves the way to access the mode-selective spin-lattice coupling strength, which remains a missing fundamental parameter for ultrafast control of magnetism and is relevant to a wide variety of materials.

Elastic and magnetoelastic properties of TbMnO3single crystal by nanosecond time resolved acoustics and first-principles calculations

Time resolved pump and probe acoustics and first-principles calculations were employed to assess elastic properties of the TbMnO₃perovskite manganite having orthorhombic symmetry. Measuring sound velocities of bulk longitudinal and shear acoustic waves propagating along at least two different directions in the high symmetry planes (100), (010) and (001), provided a powerful mean to selectively determine the six diagonal elastic constantsC₁₁= 227 GPa,C₂₂= 349 GPa,C₃₃= 274 GPa,C₄₄= 71 GPa,C₅₅= 57 GPa,C₆₆= 62 GPa. Among the three remaining off-diagonal ones,C₂₃= 103 GPa was determined with a bissectrice direction. Density functional theory calculations with colinear spin-polarized provided complementary insights on their optical, elastic and magnetoelastic properties.

On Ferro- and Antiferro-Spin-Density Waves Describing the Incommensurate Magnetic Structure of NaYNiWO6

The incommensurate magnetic structure (0.47, 0, 0.49) of NaYNiWO₆ exhibits unconventional spin-density waves (SDWs) along the [100] direction, in which up and down spins alternate in each half-wave. This is in contrast to conventional SDWs, in which only one type of spin is present in each half-wave. We probed the formation of these unconventional SDWs by evaluating the spin exchanges of NaYNiWO₆ based on density functional theory calculations and analyzing the nature of the spin frustration in NaYNiWO₆ and by noting that a SDW is a superposition of two cycloids of opposite chirality. The unconventional SDWs along the [100] direction originate from the spin-frustrated antiferromagnetic chains of Ni²⁺ ions along that direction, leading to conventional SDWs along the [101] direction and unconventional SDWs along the [001] direction.

Observation of Magnon Polarons in a Uniaxial Antiferromagnetic Insulator

Magnon polarons, a type of hybridized excitations between magnons and phonons, were first reported in yttrium iron garnet as anomalies in the spin Seebeck effect responses. Here, we report an observation of antiferromagnetic (AFM) magnon polarons in a uniaxial AFM insulator Cr_{2}O_{3}. Despite the relatively higher energy of magnon than that of the acoustic phonons, near the spin-flop transition of ∼6  T, the left-handed magnon spectrum shifts downward to hybridize with the acoustic phonons to form AFM magnon polarons, which can also be probed by the spin Seebeck effect. The spin Seebeck signal is founded to be enhanced due to the magnon polarons at low temperatures.

Nonreciprocal thermal transport in a multiferroic helimagnet

Breaking of spatial inversion symmetry induces unique phenomena in condensed matter. In particular, by combining this symmetry with magnetic fields or another type of time-reversal symmetry breaking, noncentrosymmetric materials can be made to exhibit nonreciprocal responses, which are responses that differ for rightward and leftward stimuli. However, the effect of spatial inversion symmetry breaking on thermal transport in uniform media remains to be elucidated. Here, we show nonreciprocal thermal transport in the multiferroic helimagnet TbMnO₃ The longitudinal thermal conductivity depends on whether the thermal current is parallel or antiparallel to the vector product of the electric polarization and magnetization. This phenomenon is thermal rectification that is controllable with external fields in a uniform crystal. This discovery may pave the way to thermal diodes with controllability and scalability.

Hexagonal manganites: Strong coupling of ferroelectricity and magnetic orders

Hexagonal manganites belong to an exciting class of materials exhibiting strong interactions between a highly frustrated magnetic system, the ferroelectric polarization, and the lattice. The existence and mutual interaction of different magnetic ions (Mn and rare earth) results in complex magnetic phase diagrams and novel physical phenomena. A summary and discussion of the various properties, underlying physical mechanisms, the role of the rare earth ions, and the complex interactions in multiferroic hexagonal manganites are presented in this review.

Lattice and spin dynamics in multiferroic BiFeO3 and RMnO3

The multiferroic materials BiFeO₃ and RMnO₃ exhibit coexisting magnetic order and ferroelectricity, and provide exciting platforms for new physics and potentially novel devices, where intriguing interplay between phonons and magnons exists. In this review, we paint a complete picture of bulk BiFeO₃ together with orthorhombic and hexagonal RMnO₃ (R includes rare-earth elements and yttrium) by summarizing the dynamics of spin and lattice and their magnetoelectric coupling, as well as the methods of controlling these characteristics under non-equilibrium conditions, from experimental and simulation perspectives.

Electronic and Structural Factors Controlling the Spin Orientations of Magnetic Ions

Magnetic ions M in discrete molecules and extended solids form ML_n complexes with their first-coordinate ligand atoms L. The spin moment of M in a complex ML_n prefers a certain direction in coordinate space because of spin-orbit coupling (SOC). In this minireview, we examine the structural and electronic factors governing the preferred spin orientations. Elaborate experimental measurements and/or sophisticated computational efforts are required to find the preferred spin orientations of magnetic ions, largely because the energy scale of SOC is very small. The latter is also the very reason why one can readily predict the preferred spin orientation of M by analyzing the SOC-induced highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) interactions of the ML_n complexes in terms of qualitative perturbation theory. The strength of this HOMO-LUMO interaction depends on the spin orientation, which is governed by the selection rules based on the minimum |ΔL_z| value (i.e., the minimum difference in the magnetic quantum numbers) between the HOMO and LUMO. With the local z axis of ML_n chosen as its n-fold rotational axis, the preferred spin orientation is parallel to the z axis (∥z) when |ΔL_z| = 0 but perpendicular to the z axis (⊥z) when |ΔL_z| = 1.

Spin-Density Wave as a Superposition of Two Magnetic States of Opposite Chirality and Its Implications

A magnetic solid with weak spin frustration tends to adopt a noncollinear magnetic structure such as a cycloidal structure below a certain temperature and a spin-density wave (SDW) slightly above this temperature. The causes for these observations were explored by studying the magnetic structure of BaYFeO₄, which undergoes a SDW and a cycloidal phase transition below 48 and 36 K, respectively, in terms of the density functional theory calculations. We show that a SDW structure arises from a superposition of two magnetic states of opposite chirality, an SDW state precedes a chiral magnetic state because of the lattice relaxation, and whether a SDW is transversal or longitudinal is governed by the magnetic anisotropy of magnetic ions.

Study of crystal-field excitations and infrared active phonons in TbMnO3

The Tb³⁺ (4f ⁸) crystal-field (CF) excitations and the infrared phonons in TbMnO₃ are studied as a function of temperature and under an applied magnetic field. The phonon energy shifts reflect local displacement of the oxygen ions that contribute to the CF energy level shifts below 120 K and under magnetic field. The CF polarized transmission spectra provide interesting information about the debated nature of the excitations at 41, 65, 130 cm^-1. We also evaluate the contribution of the charge transfer mechanism to the magnetoelectric process in TbMnO₃ under magnetic field.

Electromagnon with Sensitive Terahertz Magnetochromism in a Room-Temperature Magnetoelectric Hexaferrite

An electromagnon in the magnetoelectric (ME) hexaferrite Ba_{0.5}Sr_{2.5}Co_{2}Fe_{24}O_{41} (Co_{2}Z-type) single crystal is identified by time-domain terahertz (THz) spectroscopy. The associated THz resonance is active on the electric field (E^{ω}) of the THz light parallel to the c axis (∥ [001]), whose spectral weight develops at a markedly high temperature, coinciding with a transverse conical magnetic order below 410 K. The resonance frequency of 1.03 THz at 20 K changes -8.7% and +5.8% under external magnetic field (H) of 2 kOe along [001] and [120], respectively. A model Hamiltonian describing the conical magnetic order elucidates that the dynamical ME effect arises from antiphase motion of spins which are coupled with modulating electric dipoles through the exchange striction mechanism. Moreover, the calculated frequency shift points to the key role of the Dzyaloshinskii-Moriya interaction that is altered by static electric polarization change under different H.

Control of Chiral Magnetism Through Electric Fields in Multiferroic Compounds above the Long-Range Multiferroic Transition

Polarized neutron scattering experiments reveal that type-II multiferroics allow for controlling the spin chirality by external electric fields even in the absence of long-range multiferroic order. In the two prototype compounds TbMnO_{3} and MnWO_{4}, chiral magnetism associated with soft overdamped electromagnons can be observed above the long-range multiferroic transition temperature T_{MF}, and it is possible to control it through an electric field. While MnWO_{4} exhibits chiral correlations only in a tiny temperature interval above T_{MF}, in TbMnO_{3} chiral magnetism can be observed over several kelvin up to the lock-in transition, which is well separated from T_{MF}.

Non-collinear magnetism in multiferroic perovskites

We present an overview of the current interest in non-collinear magnetism in multiferroic perovskite crystals. We first describe the different microscopic mechanisms giving rise to the non-collinearity of spins in this class of materials. We discuss, in particular, the interplay between non-collinear magnetism and ferroelectric and antiferrodistortive distortions of the perovskite structure, and how this can promote magnetoelectric responses. We then provide a literature survey on non-collinear multiferroic perovskites. We discuss numerous examples of spin cantings driving weak ferromagnetism in transition metal perovskites, and of spin-induced ferroelectricity as observed in the rare-earth based perovskites. These examples are chosen to best illustrate the fundamental role of non-collinear magnetism in the design of multiferroicity.

Critical slowing down near the multiferroic phase transition in MnWO4

By using broadband dielectric spectroscopy in the radio frequency and microwave range, we studied the magnetoelectric dynamics in the multiferroic chiral antiferromagnet MnWO_{4}. Above the multiferroic phase transition at T_{N2}≈12.6  K we observe a critical slowing 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 1, which is expected for magnetic second-order phase transition scenarios. Therefore, the investigated dynamics have to be interpreted as the softening of an electrically active magnetic excitation, an electromagnon.

Magnetic susceptibility and heat capacity measurements of single crystal TbMnO3

Measurements of the magnetic susceptibility χ and heat capacity C on single crystals of the multiferroic TbMnO3 are presented. A non-magnetic isostructural compound, LaGaO3, was used to isolate the magnetic component of the heat capacity. An anisotropic magnetic susceptibility, deviations from Curie-Weiss behaviour and a significant magnetic entropy above the antiferromagnetic ordering temperature TN1 = 41 K are attributed to a combination of crystal-field effects and short-range order between the Mn moments. Heat capacity in a magnetic field applied along the a axis confirms the saturation of Tb(3+) moments in 90 kOe. A hyperfine contribution from the Tb and Mn nuclear moments that may be convolved with a contribution from low-lying Tb crystal-field levels leads to a low-temperature rise in C(T)/T.

Electric field control of terahertz polarization in a multiferroic manganite with electromagnons

All-electrical control of a dynamic magnetoelectric effect is demonstrated in a classical multiferroic manganite DyMnO3, a material containing coupled antiferromagnetic and ferroelectric orders. Because of intrinsic magnetoelectric coupling with electromagnons a linearly polarized terahertz light rotates upon passing through the sample. The amplitude and the direction of the polarization rotation are defined by the orientation of ferroelectric domains and can be switched by static voltage. These experiments allow the terahertz polarization to be tuned using the dynamic magnetoelectric effect.

Paramagnetic collective electronic mode and low temperature hybrid modes in the far infrared dynamics of orthorhombic NdMnO₃

We report on the far- and mid-infrared reflectivity of NdMnO3 from 4 to 300 K. Two main features are distinguished in the infrared spectra: active phonons in agreement with expectations for the orthorhombic [Formula: see text]-Pbnm (Z = 4) space group remaining constant down to 4 K and a well defined collective excitation in the THz region due to eg electrons in a d-orbital fluctuating environment. We trace its origin to the NdMnO3 high-temperature orbital disordered intermediate phase not being totally dynamically quenched at lower temperatures. This results in minute orbital misalignments that translate into randomized non-static eg electrons within orbitals yielding a room-temperature collective excitation. Below TN ∼ 78 K, electrons gradually localize, inducing long-range magnetic order as the THz band condenses into two modes that emerge pinned to the A-type antiferromagnetic order. They harden simultaneously down to 4 K, obeying power laws with TN as the critical temperature and exponents β ∼ 0.25 and β ∼ 0.53, as for a tri-critical point and Landau magnetic ordering, respectively. At 4 K they match known zone center spin wave modes. The power law dependence is concomitant with a second order transition in which spin modes modulate orbital instabilities in a magnetoelectric hybridized orbital-charge-spin-lattice scenario. We also found that phonon profiles also undergo strong changes at TN ∼ 78 K due to magnetoelasticity.

Hexagonal Manganites—(RMnO3): Class (I) Multiferroics with Strong Coupling of Magnetism and Ferroelectricity

Hexagonal manganites belong to an exciting class of materials exhibiting strong interactions between a highly frustrated magnetic system, the ferroelectric polarization, and the lattice. The existence and mutual interaction of different magnetic ions (Mn and rare earth) results in complex magnetic phase diagrams and novel physical phenomena. A summary and discussion of the various properties, underlying physical mechanisms, the role of the rare earth ions, and the complex interactions in multiferroic hexagonal manganites, are presented in this paper.

Molecular-spin dynamics study of electromagnons in multiferroic RMn2O5

We investigate the electromagnon in magnetoferroelectrics RMn(2)O(5) using combined molecular-spin dynamics simulations. We confirm that the origin of the electromagnon modes observed in the optical spectra is due to the exchange-striction interaction between the magnons and the phonons, and the dielectric step at the magnetic phase transition is due to the appearance of the electromagnon in the low-temperature phase in these materials. The magnetic anisotropy breaks the rotational symmetry of the magnetic structures and, as a result, the electromagnon splits into three modes in RMn(2)O(5). We find that the electromagnon frequencies are very sensitive to the magnetic wavevector along the a direction q(x). Therefore, the electromagnon frequencies of TmMn(2)O(5) (q(x) ~ 0.467) are expected to be much higher than those of other materials of the family, such as R= Tb, Y, Ho, etc (q(x) ~ 0.48). We further calculate the electromagnons in the magnetic field, and find a new mode appearing in the magnetic field. Although the modes' frequencies change significantly under magnetic field, the total static dielectric constant contributed from the electromagnons does not change much in the magnetic field, suggesting that the colossal magnetodielectric effects in these materials may not be caused by the electromagnons.

Dynamical magnetoelectric effects in multiferroic oxides

Multiferroics with coexistent ferroelectric and magnetic orders can provide an interesting laboratory to test unprecedented magnetoelectric (ME) responses and their possible applications. One such example is the dynamical and/or resonant coupling between magnetic and electric dipoles in a solid. As examples of such dynamical ME effects, (i) the multiferroic domain wall dynamics and (ii) the electric dipole active magnetic responses are discussed with an overview of recent experimental observations.

Magnetic excitations in the low-temperature ferroelectric phase of multiferroic YMn2O5 using inelastic neutron scattering

We studied magnetic excitations in a low-temperature ferroelectric phase of the multiferroic YMn(2)O(5) using inelastic neutron scattering (INS). We identify low-energy magnon modes and establish a correspondence between the magnon peaks observed by INS and electromagnon peaks observed in optical absorption [A. B. Sushkov et al., Phys. Rev. Lett. 98, 027202 (2007).]. Furthermore, we explain the microscopic mechanism, which results in the lowest-energy electromagnon peak, by comparing the inelastic neutron spectral weight with the polarization in the commensurate ferroelectric phase.

Magnetic field induced dehybridization of the electromagnons in multiferroic TbMnO₃

We have studied the impact of the magnetic field on the electromagnon excitations in TbMnO₃ crystal. Applying a magnetic field along the c axis, we show that the electromagnons transform into pure antiferromagnetic modes, losing their polar character. Entering in the paraelectric phase, we are able to track the spectral weight transfer from the electromagnons to the magnon excitations and we discuss the magnetic excitations underlying the electromagnons. We also point out the phonons involved in the phase transition process. This reveals that the Mn-O distance plays a key role in understanding the ferroelectricity and the polar character of the electromagnons. Magnetic field measurements along the b axis allow us to detect a new electromagnon resonance in agreement with a Heisenberg model.

Magnetic and magnetoelectric excitations in multiferroic manganites

We review the recent experimental findings concerning the magnetic and magnetoelectric excitations in multiferroic manganites with special focus on orthorhombic RMnO(3) (R = rare earth). The dynamics of these materials has attracted special attention recently due to the existence of novel magnetoelectric excitations which were termed electromagnons. In addition to the strong electric activity of the electromagnons, a series of other excitations of magnetic and magnetoelectric nature is observed in the same frequency range as the electromagnons. We summarize the systematics of the existing modes and the current understanding of the underlying mechanisms.

The splitting of the electromagnon mode in conically spiral multiferroic magnets

In this paper, we study conically spiral multiferroic magnets with coupled magnetic and ferroelectric orders. By generalizing the spin-current model, we study spin wave excitations and electromagnons. We find that the electromagnon mode will split into two branches with different dispersions in an (external or internal) magnetic field. We apply our theory to some multiferroic materials and find that the results qualitatively agree with recent experiments. We also make predictions for new experiments.

A phenomenological Landau theory for electromagnons in cubic spinel multiferroic CoCr₂O₄

Non-anisotropic free energy is considered which under minimization yields two magnetic phases: a conical spin density wave and a low temperature conical cycloid. Using equations of motion, the excitation spectrum is studied. Knowing the nature of these excitations, the dielectric function as well as the fluctuation specific heat is computed and compared with the experimental spectrum. Due to the electromagnon going soft, the dielectric function (imaginary part) as well as the specific heat capacity show peaks at the temperature where ferroelectricity appears in the system.

Theory of electromagnons in the multiferroic Mn perovskites: the vital role of higher harmonic components of the spiral spin order

We study theoretically the electromagnon and its optical spectrum (OS) of the terahertz-frequency regime in the magnetic-spiral-induced multiferroic phases of the rare-earth-metal (R) Mn perovskites, RMnO3, taking into account the spin-angle modulation or the higher harmonics of the spiral spin configuration, which has been missed so far. A realistic spin Hamiltonian, which gives phase diagrams in agreement with experiments, resolves a puzzle, i.e., the double-peak structure of the OS with a larger low-energy peak originating from magnon modes hybridized with the zone-edge state. We also predict the magnon branches associated with the electromagnon, which can be tested by neutron-scattering experiment.

Evidence for electroactive excitation of the spin cycloid in TbMnO3

Terahertz electromagnetic excitations in the multiferroic TbMnO3 single crystals are investigated across the magnetic field induced rotation of the magnetic spin cycloid. In addition to the electromagnon along the a axis, the detailed polarization analysis of the experimental spectra suggests the existence of an electroactive excitation for ac electric fields of the electromagnetic wave along the crystallographic c axis. This excitation is possibly the electroactive eigenmode of the spin-cycloid in TbMnO3, which has been predicted within the inverse Dzyaloshinskii-Moriya mechanism of magnetoelectric coupling.

Unconventional ferroelectric transition in the multiferroic compound TbMnO3 revealed by the absence of an anomaly in c-polarized phonon dispersion

TbMnO(3) exhibits a spontaneous electric polarization along c concomitantly with a spiral spin ordering modulated along b below T_{C} = 28 K. We have performed inelastic x-ray scattering measurements on a single crystal of TbMnO(3) to clarify whether phonon anomalies related to the ferroelectricity exist. We measured transverse modes, especially the Mn-O-Mn bending mode polarized along c and propagating along b, which we expect is most relevant to the ferroelectricity. However, no anomaly was found in the phonon dispersion below 50 meV across T_{C}. The present result suggests that the mechanism of ferroelectricity in TbMnO(3) is different from that of a conventional displacive-type ferroelectric. The weak coupling between electric polarization and lattice in TbMnO(3) strongly suggests that the ferroelectricity is mainly derived from the spiral spin ordering.

Flop of electric polarization driven by the flop of the Mn spin cycloid in multiferroic TbMnO3

Using in-field single-crystal neutron diffraction, we have determined the magnetic structure of TbMnO(3) in the high field P parallel a phase. We unambiguously establish that the ferroelectric polarization arises from a cycloidal Mn spin ordering, with spins rotating in the ab plane. Our results demonstrate directly that the flop of the ferroelectric polarization in TbMnO(3) with applied magnetic field is caused from the flop of the Mn cycloidal plane.

Magnetic and magnetoelectric excitations in TbMnO3

Magnetic and magnetoelectric excitations in the multiferroic TbMnO3 have been investigated at terahertz frequencies. Using different experimental geometries we can clearly separate the electroactive excitations (electromagnons) from the magnetoactive modes, i.e., antiferromagnetic resonances. Two antiferromagnetic resonances were found to coincide with electromagnons. This indicates that both excitations belong to the same mode and the electromagnons can be excited by a magnetic ac field as well. In spite of the 90 degrees rotation of the magnetic cycloid in external magnetic fields, the electromagnons are observable for electric ac fields parallel to the a axis only.

Evidence for an electric-dipole active continuum band of spin excitations in multiferroic TbMnO3

The wide range optical spectra on a multiferroic prototype TbMnO3 have been investigated to clarify the origin of spin excitations observed in the far-infrared region. We elucidate the full band structure, whose high energy edge (133 cm;{-1}) exactly corresponds to twice of the highest-lying magnon energy. Thus the origin of this absorption band is clearly assigned to two-magnon excitation driven by the electric field of light. There is an overlap between the two-magnon and phonon energy ranges, where the strong coupling between them is manifested by the frequency shift and transfer of oscillator strength of the phonon mode.

Possible observation of cycloidal electromagnons in BiFeO3

We unravel the magnon spectra of BiFeO3 by means of low-energy inelastic light scattering. We show the existence of two species of magnons corresponding to spin wave excitations in and out of the cycloidal plane. These excitations might be interpreted as electromagnon modes. The present observations present an unique opportunity to study the competition between ferroelectric and magnetic orders.

Spin phonon coupling in hexagonal multiferroic YMnO3

Inelastic neutron scattering measurements have been performed on YMnO3, aiming to study the interplay between spin and lattice degrees of freedom in this hexagonal multiferroic material. Our study provides evidence for a strong coupling between magnons and phonons, evidenced by the opening of a gap below T(N) in the dispersion of the transverse acoustic phonon mode polarized along the ferroelectric axis. The resulting upper phonon branch is found to lock on one of the spin-wave modes. These findings are discussed in terms of a possible hybridization between the two types of elementary excitations.