The magnetic and ferroelectric properties of the multiferroic system Mn$_{1-x}$Co$_x$WO$_4$ (x=0.135, 0.15, and 0.17) are studied in magnetic fields $H_c$ oriented along the monoclinic $c$-axis. Mn$_{0.85}$Co$_{0.15}$WO$_4$, which is right at the phase boundary between two helical spin structures, exhibits a spontaneous sign change of the ferroelectric polarization when cooled in fields $H_c>$ 25 kOe. The origin of the ferroelectric polarization is studied and two magnetic exchange interactions contributing to the polarization are identified. In Mn$_{0.85}$Co$_{0.15}$WO$_4$ domains of the characteristic helical spin structures, known for x$<$0.15 and x$>$0.15, coexist and form domain boundaries. The contributions of the different domains to the global polarization are determined. The polarization reversal in Mn$_{0.85}$Co$_{0.15}$WO$_4$ can be explained by a combination of various contributions to the polarization and a strong correlation between magnetic domains of different helical spin orders resulting in a smooth transition across the domain walls which preserves the chirality of the spin spiral.
The low-temperature ferroelectric polarization of multiferroic $YMn_2O_5$ is completely reversed at a critical pressure of 10 kbar and the phase transition from the incommensurate to the commensurate magnetic phase is induced by pressures above 14 kbar. The high-pressure data correlate with thermal expansion measurements indicating a significant lattice strain at the low-temperature transition into the incommensurate phase. The results support the exchange striction model for the ferroelectricity in multiferroic $RMn_2O_5$ compounds and they show the importance of magnetic frustration as well …
Terahertz (THz) radiation has been observed from multiferroic BiFeO$_3$ thin films via ultrafast modulation of spontaneous polarization upon carrier excitation with illumination of femtosecond laser pulses. The radiated THz pulses from BiFeO$_3$ thin films were clarified to directly reflect the spontaneous polarization state, giving rise to a memory effect in a unique style and enabling THz radiation even at zero-bias electric field. On the basis of our findings, we demonstrate potential approaches to ferroelectric nonvolatile random access memory with nondestructive readability and ferroelect…
The unusual magnetoelectric effects observed in the multiferroic phase arising below TN=6.7K in Ba2CoGe2O7 (BCG) are related to the spontaneous toroidal moment existing in this compound. The transition to the multiferroic state, which involves spontaneous magnetization, polarization and toroidal moment gives rise to spontaneous toroidic effects. These effects produce specific contributions to the spontaneous polarization and magnetization under applied magnetic or electric fields which provide indirect indications of the existence and role of the toroidal moment in multiferroic materials. The …
In multiferroic TbMn$_2$O$_5$, the behavior of the terbium ions forms a crucial part of the magneto-electric coupling. The result is a magnetically induced reversal of the electric polarization at 2 T. In this article we present the first direct measurement of the terbium magnetic structure under applied magnetic fields. Contrary to the current interpretation of the magnetic properties of \tmo, we show that upon the electric polarization reversal the terbium sub-lattice adopts a canted antiferromagnetic structure with a large component of magnetic moment parallel to the \textit{a}-axis. Furthe…
By an electrical-pump--optical-probe technique we show that the electric-field-induced reversal of the magnetic order parameter in multiferroic MnWO$_4$ occurs on the time scale of milliseconds and maintains a rigid coupling of the magnetization to the magnetically induced electric polarization. The temporal progression of the spatially resolved domain structure was imaged with nanosecond resolution by optical second harmonic generation and compared to the quasi-static domain reversal. A qualitative model gives an estimate of why the magnetoelectric order-parameter reversal in the magnetically…
Three independent contributions to the magnetically induced spontaneous polarization of multiferroic TbMn2O5 are uniquely separated by optical second harmonic generation and an analysis in terms of Landau theory. Two of them are related to the magnetic Mn3+/4+ order and are independent of applied fields of up to 7 T. The third contribution is related to the long-range antiferromagnetic Tb3+ order. It shows a drastic decrease upon the application of a magnetic field and mediates the change of sign of the spontaneous electric polarization in TbMn2O5. The close relationship between the rare-earth…
The ground-state structural and electronic properties of ferroelectric BiFeO$_3$ are calculated using density functional theory within the local spin-density approximation and the LSDA+U method. The crystal structure is computed to be rhombohedral with space group $R3c$, and the electronic structure is found to be insulating and antiferromagnetic, both in excellent agreement with available experiments. A large ferroelectric polarization of 90-100 $μ$C/cm$^2$ is predicted, consistent with the large atomic displacements in the ferroelectric phase and with recent experimental reports, but differi…
Despite remarkable progress in developing multifunctional materials, spin-driven ferroelectrics featuring both spontaneous magnetization and electric polarization are still rare. Among such ferromagnetic ferroelectrics are conical spin spiral magnets with a simultaneous reversal of magnetization and electric polarization that is still little understood. Such materials can feature various multiferroic domains that complicates their study. Here we study the multiferroic domains in ferromagnetic ferroelectric Mn$_{2}$GeO$_{4}$ using neutron diffraction, and show that it features a double-Q conica…
A theoretical description of the sequence of magnetic phases in Co3TeO6 is presented. The strongly first-order character of the transition to the commensurate multiferroic ground state, induced by coupled order parameters corresponding to different wavevectors, is related to a large magnetoelastic effect with an exchange energy critically sensitive to the interatomic spacing. The monoclinic magnetic symmetry C2' of the multiferroic phase permits spontaneous polarization and magnetization as well as the linear magnetoelectric effect. The existence of weakly ferromagnetic domains is verified exp…
We describe the design of a new magnetic ferroelectric with large spontaneous magnetization and polarization using first-principles density functional theory. The usual difficulties associated with the production of robustly-insulating ferromagnets are circumvented by incorporating the magnetism through {\it ferri-}magnetic behavior. We show that the the ordered perovskite \BFCO will have a polarization of $\sim$80 $μ$C/cm$^2$, a piezoelectric coefficient of 283 $μ$C/cm$^{2}$, and a magnetization of $\sim$160 emu/cm$^3$ (2 $μ_B$ per formula unit), far exceeding the properties of any known mult…
Synthesis and extensive structural, pyroelectric, magnetic, dielectric and magneto-electric characterizations are reported for polycrystalline Co4Nb2O9 towards unraveling the multiferroic state especially in reference to the magnetic spin flop transition. Magnetic measurements confirm the Co4Nb2O9 becomes antiferromagnetic (AFM) at around 28 K but no clear evidence for spin-flop effect was found. Associated with the magnetic phase transition, a sharp peak in pyroelectric current indicates the appearance of the strong magneto-electric coupling below Neel temperature (TN) with a large coupling c…
The electric-field control of $d$-electron magnetism in multiferroic transition metal oxides is attracting widespread interest for the underlying fundamental physics and for next generation spintronic devices. Here, we report an extensive study of the $3d$ magnetism in magnetoelectric Ga$_{0.6}$Fe$_{1.4}$O$_3$ (GFO) epitaxial films by polarization dependent x-ray absorption spectroscopy. We found a non-zero integral of the x-ray magnetic circular dichroism, with a sign depending upon the relative orientation between the external magnetic field and the crystallographic axes. %By reliably enlarg…
First-principles electronic structure calculations have been performed for the double perovskite Bi$_2$CoMnO$_6$ in its non-centrosymmetric polar state using generalized gradient approximation plus Hubbard U approach. We find that while Co is in a high spin state, Mn is in an intermediate spin state. The calculated dynamical charge tensors are anisotropic reflecting a low-symmetry structure of the compound. Magnetic structure dependent phonon frequencies indicate the presence of spin-phonon coupling. Using Berry phase method, we obtain a spontaneous electronic polarization of 5.88 $μC/cm^2$ wh…
We study adatom-covered single layers of CrSiTe$_3$ and CrGeTe$_3$ using first-principles calculations based on hybrid functionals. We find that the insulating ground state of a monolayer of La (Lu) deposited on single-layer CrSiTe$_3$ (CrGeTe$_3$) carries spontaneously generated current loops around the Cr sites, These "flux states" induce antiferromagnetically ordered orbital moments on the Cr sites and are also associated with nontrivial topological properties. The calculated Chern numbers for these systems are predicted to be $\pm 1$ even in the absence of spin-orbit coupling, with sizable…
We report the magnetic and electric properties of Ba$_3$NiNb$_2$O$_9$, which is a quasi-two-dimensional spin-1 triangular lattice antiferromagnet (TLAF) with trigonal structure. At low $T$ and with increasing magnetic field, the system evolves from a 120 degree magnetic ordering phase (A phase) to an up-up-down ($uud$) phase (B phase) with a change of slope at 1/3 of the saturation magnetization, and then to an "oblique" phase (C phase). Accordingly, the ferroelectricity switches on at each phase boundary with appearance of spontaneous polarization. Therefore, Ba$_3$NiNb$_2$O$_9$ is a unique T…
We report the discovery of a complete suppression of ferroelectricity in $MnWO_4$ by 10 % iron substitution and its restoration in external magnetic fields. The spontaneous polarization in $Mn_{0.9}Fe_{0.1}WO_4$ arises below 12 K in external fields above 4 T. The magnetic/ferroelectric phase diagram is constructed from the anomalies of the dielectric constant, polarization, magnetization, and heat capacity. The observations are qualitatively described by a mean field model with competing interactions and strong anisotropy. We propose that the magnetic field induces a non-collinear inversion sy…
Breaking of spatial inversion symmetry (SIS) induces unique phenomena in condensed matter. Besides the classic examples such as natural optical activity and piezoelectricity, the spin-orbit interaction further enriches the effect of SIS breaking, as exemplified by the Rashba effect. In particular, by combining this symmetry with magnetic fields or another type of time-reversal symmetry (TRS) breaking, noncentrosymmetric materials can be made to exhibit nonreciprocal responses, which are responses that differ for rightward and leftward stimuli. For example, resistivity becomes directionally dep…
We report $α$-Cu$_2$V$_2$O$_7$ to be an improper multiferroic with the simultaneous development of electric polarization and magnetization below $T_C$ = 35 K. The observed spontaneous polarization of magnitude 0.55 $μ$Ccm$^{-2}$ is highest among the copper based improper multiferroic materials. Our study demonstrates sizable amount of magneto-electric coupling below $T_C$ even with a low magnetic field. The theoretical calculations based on density functional theory (DFT) indicate magnetism in $α$-Cu$_2$V$_2$O$_7$ is a consequence of {\em ferro-orbital} ordering driven by polar lattice distort…
The magnon and optical phonon spectrum of an incommensurate multiferroic such as BiFeO3 is considered in the framework of a phenomenological Landau theory. The resulting spin wave spectrum is quite distinct from commensurate substances due to soft mode anisotropy and magnon zone folding. The former allows electrical control of spin wave propagation via reorientation of the spontaneous ferroelectric moment. The latter gives rise to multiple magneto-dielectric resonances due to the coupling of optical phonons at zero wavevector to magnons at integer multiples of the cycloid wavevector. These res…
Anisotropic multiferroic properties of SrMnGe2O6 pyroxene single crystals were systematically investigated by means of magnetization, heat capacity, pyroelectric current measurement and elastic and inelastic neutron scattering experiments. Single crystal neutron diffraction allows us to unambiguously reveal the presence of two incommensurate magnetic orderings: a non-polar amplitude-modulated collinear sinusoidal magnetic structure emerges at TN1=4.36(2)K followed by a polar elliptical cycloidal spin structure below TN2=4.05(2)K. Pyroelectric current measurements on single crystal confirm the …
In this article, the collective response of the spins is explored through low field bulk magnetic measurement for the series YMn$_{2-x}$Cr$_x$O$_5$ (x= 0.0, 0.05). Low field ac susceptibility and dc magnetization of YMn$_2$O$_5$ shows multiple transition in analogy to those observed in electrical measurement of the compound. Using various time dependent magnetization protocols it has been observed that the behavior of spins in commensurate and incommensurate phase are drastically different. YMn$_{1.95}$Cr$_{0.05}$O$_5$ undergoes a ferrimagnetic ordering with an enhanced magnetic ordering tempe…
Frustration-induced multiferroicity in hauerite MnS2
Leibniz Institute for Solid State and Materials Research Dresden（德累斯顿莱布尼茨固体与材料研究所）；University of Salzburg（萨尔茨堡大学）；Zernike Institute for Advanced Materials, University of Groningen（格罗宁根大学泽尔尼克先进材料研究所）；Technische Universität Dresden（德累斯顿工业大学）
We study the dynamical interplay between ferroelectricity and magnetism in a multiferroic with a helical magnetic order. We show that the dynamical exchange-striction induces a biquadratic interaction between the spins and transverse phonons resulting in quantum fluctuations of the spontaneous ferroelectric polarization $\mathbf{P}$ in the ferroelectric phase. The hybridization between the spin wave and the fluctuation of the electric polarization leads to low-lying transverse phonon modes. Those are perpendicular to $\mathbf{P}$ and to the helical spins at small wave vector but then turn para…
Phase transitions involving spontaneous time-reversal symmetry breaking are studied on the honeycomb lattice at finite hole-doping with next-nearest-neighbor repulsion. We derive an exact expression for the mean-field equation of state in closed form, valid at temperatures much less than the Fermi energy. Contrary to standard expectations, we find that thermally induced intraband particle-hole excitations can create and stabilize a uniform metallic phase with broken time-reversal symmetry as the temperature is "raised" in a region where the groundstate is a trivial metal.
The dielectric properties of the prototypical frustrated ferromagnetic spin-chain compound PbCuSO$_4$(OH)$_2$ known as linarite, are studied across its strongly anisotropic magnetic phase diagram in single crystal samples. The ferroelectric character of the principal low-field spin spiral phase is confirmed. The measured polarization is fully consistent with the previously proposed magnetic structure. Spontaneous polarization is also detected in two other field-induced phases but in some cases is incompatible with previously suggested models for the spin arrangement.
We introduce a microscopic model for collinear multiferroics capable to reproduce, as a consequence of magnetic frustration and easy-axis anisotropy, the so-called "uudd" (or antiphase) magnetic ordering observed in several type II multiferroic materials. The crucial role of lattice distortions in the multiferroic character of these materials is entered into the model via an indirect magnetoelectric coupling, mediated by elastic degrees of freedom through a pantograph mechanism. Long range dipolar interactions set electric dipoles in the antiferroelectric order. We investigate this model by me…
We report experimental evidence of a remarkable spontaneous time reversal symmetry breaking in two dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P $δ-$layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, pro…
We report for the first time, that Fe3Se4 is a room temperature, type-II multiferroic with magnetoelectric coupling. We observed the coexistence of coupled ferrimagnetic and ferroelectric ordering in Fe3Se4nanorods well above room temperature, which is a hard magnet with large magnetocrystalline anisotropy. For the first time, we observed spontaneous, reversible ferroelectric polarization in Fe3Se4 nanorods below the magnetic Curie temperature. The coupling is manifested by an anomaly in the dielectric constant and Raman shift at Tc. We do not completely understand the origin of the ferroelect…
We elucidate the close relationship between spontaneous time-reversal symmetry breaking and the physics of excitonic instabilities in strongly correlated multiband systems. The underlying mechanism responsible for the spontaneous breaking of time-reversal symmetry in a many-body system is closely related to the Cooper-like pairing instability of interband particle-hole pairs involving higher order symmetries. Studies of such pairing instabilites have, however, mainly focused on the mean-field aspects of the virtual exciton condensate, which ignores the presence of the underlying collective Fer…
We study the spontaneous non-magnetic time-reversal symmetry breaking in a two-dimensional Fermi liquid without breaking either the translation symmetry or the U(1) charge symmetry. Assuming that the low-energy physics is described by fermionic quasiparticle excitations, we identified an "emergent" local $U(1)^N$ symmetry in momentum space for an $N$-band model. For a large class of models, including all one-band and two-band models, we found that the time-reversal and chiral symmetry breaking can be described by the $U(1)^N$ gauge theory associated with this emergent local $U(1)^N$ symmetry. …
We present a study of the anisotropy of the dielectric, magnetic and magnetoelastic properties of the multiferroic clinopyroxene NaFeGe$_2$O$_6$. Pyroelectric currents, dielectric constants and magnetic susceptibilities as well as the thermal expansion and the magnetostriction were examined on large synthetic single crystals of NaFeGe$_2$O$_6$. The spontaneous electric polarization detected below $T_{\rm C}\simeq 11.6$ K in an antiferromagnetically ordered state ($T_{\rm N}\simeq 13$ K) is mainly lying within the $ac$ plane with a small component along $b$, indicating a triclinic symmetry of t…
Multiferroics (MFs) are materials with two or more ferroic orders, like spontaneous ferroelectric and ferromagnetic polarizations. Such materials can exhibit a magnetoelectric effect whereby magnetic and ferroelectric polarizations couple linearly, reminiscent of, but not identical to the electromagnetic $\boldsymbol{E}\cdot \boldsymbol{B}$ axion coupling. Here we point out a possible mechanism in which an external dark matter axion field couples linearly to ferroic orders in these materials without external applied fields. We find the magnetic response to be linear in the axion-electron coupl…
We study the boundary Majorana modes for the single component p-wave weak topological superconductors or superfluids, which form zero energy flat bands protected by time-reversal symmetry in the orbital channel. However, due to the divergence of density of states, the band flatness of the edge Majorana modes is unstable under spontaneously generated spatial variations of Cooper pairing phases. Staggered current loops appear near the boundary and thus time-reversal symmetry is spontaneously broken in the orbital channel. This effect can appear in both condensed matter and ultra-cold atom system…
Multiferroic CuFe1-xAlxO2 (x=0.02) exhibits a ferroelectric ordering accompanied by a proper helical magnetic ordering below T=7K under zero magnetic field. By polarized neutron diffraction and pyroelectric measurements, we have revealed a one-to-one correspondence between the spin helicity and the direction of the spontaneous electric polarization. This result indicates that the spin helicity of the proper helical magnetic ordering is essential for the ferroelectricity in CuFe1-xAlxO2. The induction of the electric polarization by the proper helical magnetic ordering is, however, cannot be ex…
We discuss a model scenario for multiferroic systems of type II (collinear spins) where the electric dipolar order competes with a frustrated magnetic order in determining the elastic distortions of the lattice ion positions. High magnetic frustration due to second neighbors exchange and small spin easy-axis anisotropy lead to the appearance of the so called quantum magnetic plateau states. Increasing the magnetic field above the plateau border produces composite excitations, where fractionalized spin tertions arise together with spontaneous dipolar flips (in the form of domain walls) and enha…
We argue that that in their recent experiment in which they claim to have found evidence for a time-reversal symmetry broken state, Kaminski et al. overlooked small temperature dependent changes in the superstructure of Bi2212. These subtle changes may manifest themselves by changing the final state configurations of the photoemission process and thus invalidate their ultimate conclusions.
We present spin transport studies on a low-field, room-temperature magnetoelectric multiferroic polycrystalline $\text{Sr}_{3}\text{Co}_{2}\text{Fe}_{24}\text{O}_{41}$ (SCFO)|Pt heterostructure wherein a highly tunable transverse conical magnetic phase is responsible for static and dynamic magnetoelectric coupling. We measured angular dependence of spin Hall magnetoresistance (SMR) at constant magnetic fields ($H$) in the range of 50 to 100 kOe. Application of field below the critical value (2.5 kOe), yielded negative SMR and the $H$-evolution of normalized SMR exhibited a negative gradient. F…
The breakdown of magnons, the quasiparticles of magnetic systems, has rarely been seen. By using an inelastic neutron scattering technique we report the observation of spontaneous magnon decay in multiferroic LuMnO$_3$, a simple two-dimensional Heisenberg triangular lattice antiferromagnet, with large spin, S = 2. The origin of this rare phenomenon lies in the non-vanishing cubic interaction between magnons in the spin Hamiltonian arising from the noncollinear 120$^o$ spin structure. We observed all three key features of the nonlinear effects as theoretically predicted: a roton-like minimum, a…
Resonant and non-resonant X-ray scattering studies on HoFe3(BO3)O4 reveal competing magnetic ordering of Ho and Fe moments. Temperature and X-ray polarization dependent measurements employed at the Ho L3 edge directly reveal a spiral spin order of the induced Ho moments in the ab-plane propagating along the c-axis, a screw-type magnetic structure. At about 22.5 K the Fe spins are observed to rotate within the basal plane inducing spontaneous electric polarization, P. Components of P in the basal plane and along the c-axis can be scaled with the separated magnetic X-ray scattering intensities o…
We study the behavior of spinless fermions in superconducting state, in which the phases of the superconducting order parameter depend on the direction of the link. We find that the energy of the superconductor depends on the phase differences of the superconducting order parameter. The solutions for the phases corresponding to the energy minimuma, lead to a topological superconducting state with the nontrivial Chern numbers. We focus our quantitative analysis on the properties of topological states of superconductors with different crystalline symmetry and show that the phase transition in th…
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…
We report a comprehensive inelastic neutron scattering study of the hybrid molecule-based multiferroic compound (ND4)2FeCl5D2O in the zero-field incommensurate cycloidal phase and the high-field quasi-collinear phase. The spontaneous electric polarization changes its direction concurrently with the field-induced magnetic transition, from mostly aligned with the crystallographic a-axis to the c-axis. To account for such change of polarization direction, the underlying multiferroic mechanism was proposed to switch from the spin-current model induced via the inverse Dzyalloshinskii-Moriya interac…
We put forward the concept of a bulk Rashba effect emerging in a multiferroic material, such as an antiferromagnetic system with a polar crystal structure. According to symmetry considerations, while time-reversal and space-inversion symmetries are both broken, there exist specific spin flipping operations that relate opposite spin sites in the magnetic crystal structure. As a consequence, at certain high-symmetry points in the momentum space, the magnetic point group allows the spin angular momentum to be locked to the linear momentum, a typical feature of the Rashba effect. In such a case, s…
We investigate the new quantum phases on the extended Kane-Mele-Hubbard model of honeycomb lattice in the Hofstadter regime. In this regime, orbital motion of the electrons can induce various topological phases with spontaneously broken symmetries when the spin orbit coupling and electron correlations coexist. Here, we consider the interaction effects in the Kane-Mele model and discuss possible phases in the presence of magnetic field at integer fillings of electrons. In particular, focusing on 2π/3 magnetic flux per plaquette, the realization of numerous quantum phases are discussed within th…
A microscopic model for the room-temperature multiferroic BiFeO$_3$ that includes two Dzyaloshinskii-Moriya interactions and single-ion anisotropy along the ferroelectric polarization predicts both the zero-field spectroscopic modes as well as their splitting and evolution in a magnetic field. Due to simultaneously broken time-reversal and spatial-inversion symmetries, the absorption of light changes as the magnetic field or the direction of light propagation is reversed. We discuss three physical mechanisms that may contribute to this absorption asymmetry known as non-reciprocal directional d…
Recent experiments have pointed to a chiral p-wave-like superconductivity in epitaxial Bi/Ni bilayers that are spontaneously time-reversal symmetry breaking (TRSB), making it a promising platform for exploring physics useful for topologically protected quantum computing. Quite intriguingly, evidence has emerged that in non-epitaxial Bi/Ni bilayers, superconductivity arises due to the formation of NiBi3, which has been reported to host coexisting ferromagnetic and superconducting orders at the surface. We perform high resolution surface magneto-optic Kerr effect (SMOKE) measurements using a Sag…
The system of spinless fermions on a hexagonal lattice is studied . We have considered tight-binding model with the hopping integrals between the nearest-neighbor and next-nearest-neighbor lattice sites, that depend on the direction of the link. The links are divided on three types depending on the direction, the hopping integrals are defined by different phases along the links. The energy of the system depends on the phase differences, the solutions for the phases, that correspond to the minimums of the energy, lead to a topological insulator state with the nontrivial Chern numbers. We have a…
We have directly imaged reversible electrical switching of the cycloidal rotation direction (magnetic polarity) in a (111)-BiFeO3 epitaxial-film device at room temperature by non-resonant x-ray magnetic scattering. Consistent with previous reports, fully relaxed (111)-BiFeO3 epitaxial films consisting of a single ferroelectric domain were found to comprise a sub-micron-scale mosaic of magneto-elastic domains, all sharing a common direction of the magnetic polarity, which was found to switch reversibly upon reversal of the ferroelectric polarization without any measurable change of the magneto-…
Mutual interplay between the electronic degrees of freedom in solids, such as charge, spin, orbital, sublattice, and bond degrees of freedom, is a source of cross-correlated phenomena with unconventional electronic ordered states. Such degrees of freedom can be described by four types of multipoles (electric, magnetic, magnetic toroidal, and electric toroidal) in a unified way, which enable us to tightly connect the microscopic degrees of freedom with macroscopic physical responses in a transparent manner. We complete a classification of the multipoles in all 122 magnetic point groups based on…
The low-temperature magnetic phase diagram of the multiferroic system FeTe$_2$O$_5$Br down to 300 mK and up to 9 T is presented. Short-range magnetic correlations within the crystal layers start to develop already at $\sim$50 K, i.e., far above $T_{N1} \sim$ 11.0 K, where the system undergoes a magnetic phase transition into the high-temperature incommensurate (HT-ICM) phase. Only 0.5 K lower, at $T_{N2}$, the system undergoes a second phase transition into the low-temperature incommensurate amplitude-modulated (LT-ICM) phase accompanied by a spontaneous electric polarization. When the magneti…
The symmetry conditions for the development of a macroscopic electrical polarization as a secondary order parameter to a magnetic ordering transition, and the constraints on the direction of the polarization vector, are determined by a non-conventional application of the theory of irreducible co-representations. In our approach, which is suitable for both magnetic and structural modulations, anti-unitary operators are employed to describe symmetry operations that exchange the propagation vector $\textbf{k}$ with $\textbf{-k}$, rather than operations combined with time-reversal as in classical …
We report an unusual canted magnetism due to 3d and 4f electrons, occupying two different crystallographic sites, with its consequence to electric dipole order. This is based on neutron powder diffraction measurements on Tb2BaNiO5 (orthorhombic, Immm centrosymmetric space group), exhibiting Neel order below (TN) 63 K, to understand multiferroic behavior below 25 K. The magnetic structure is made up of Ni and Tb magnetic moments, which are found to be mutually canted in the entire temperature range below TN, though collinearity is seen within each sublattice, as known in the past. First-princip…
We have investigated dielectric properties in a series of crystals of $R$MnO$_{3}$ ($R$ is a rare earth ion) under magnetic fields and quasihydrostatic pressure. We have found that ferroelectric phase appeared in GdMnO$_3$ crystal below 13K. We have confirmed that a small spontaneous polarization exists along a axis ($P_a$) in the orthorhombic $Pbnm$ setting and that $P_a$ can be reversed by the dc electric field. The dielectric anomaly due to the ferroelectric transition accompanied thermal hysteresis and lattice striction. The ferroelectric transition temperature decreased with quasihydrosta…
When matter undergoes a phase transition from one state to another, usually a change in symmetry is observed, as some of the symmetries exhibited are said to be spontaneously broken. The superconducting phase transition in the underdoped high-Tc superconductors is rather unusual, in that it is not a mean-field transition as other superconducting transitions are. Instead, it is observed that a pseudo-gap in the electronic excitation spectrum appears at temperatures T* higher than Tc, while phase coherence, and superconductivity, are established at Tc (Refs. 1, 2). One would then wish to underst…
States of matter that break time-reversal symmetry are invariably associated with magnetism or circulating currents. Recently, one of us proposed a phase, the directional scalar spin chiral order (DSSCO), as an exception: it breaks time-reversal symmetry via chiral ordering of spins along a particular direction, but is spin-rotation symmetric. In this work, we prove the existence of this state via state-of-the-art density matrix renormalization group (DMRG) analysis on a spin-1 chain with nearest-neighbor bilinear-biquadratic interactions and additional third-neighbor ferromagnetic Heisenberg …
In a recent comment [1], Armitage and Hu have suggested that our experiment observing dichroism in angle resolved photoemission (ARPES) [2] could not be conclusively interpreted as arising from time reversal symmetry breaking, arguing that our observations are likely due to structural effects. The concerns expressed by Armitage and Hu that our results could be due to a change in the mirror plane are as important as they are obvious. In fact the first part of their comment merely restates the results of Simon and Varma [3] about the relationship and contrast of effects due to time reversal symm…
