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 dichroism: the spin current, magnetostriction, and single-ion anisotropy. We conclude that the non-reciprocal directional dichroism in \BF is dominated by the spin-current polarization and is insensitive to the magnetostriction and easy-axis anisotropy. With three independent spin-current parameters, our model accurately describes the non-reciprocal directional dichroism observed for magnetic field along $[1,-1,0]$. Since some modes are almost transparent to light traveling in one direction but opaque for light traveling in the opposite direction, BiFeO$_3$ can be used as a room-temperature optical diode at certain frequencies in the GHz to THz range. Our work demonstrates that an analysis of the non-reciprocal directional dichroism spectra based on an effective spin model supplemented by first-principles calculations can produce a quantitative microscopic theory of the magnetoelectric couplings in multiferroic materials.
The magnetic field induced rearrangement of the cycloidal spin structure in ferroelectric mono-domain single crystals of the room-temperature multiferroic BiFeO$_3$ is studied using small-angle neutron scattering (SANS). The cycloid propagation vectors are observed to rotate when magnetic fields applied perpendicular to the rhombohedral (polar) axis exceed a pinning threshold value of $\sim$5\,T. In light of these experimental results, a phenomenological model is proposed that captures the rearrangement of the cycloidal domains, and we revisit the microscopic origin of the magnetoelectric effe…
The presence of domains in ferroic materials can negatively affect their macroscopic properties and hence their usefulness in device applications. From an experimental perspective, measuring materials comprising multiple domains can complicate the interpretation of material properties and their underlying mechanisms. In general, BiFeO$_3$ films tend to grow with multiple magnetic domains and often contain multiple ferroelectric and ferroelastic domain variants. By growing (111)-oriented BiFeO$_3$ films on an orthorhombic TbScO$_3$ substrate, we are able to overcome this, and, by exploiting the…
Using the results of x-ray and neutron diffraction experiments, we show that the ferroelectric polarization, in ~22 nm particles of BiFeO3, exhibits a jump by ~30% around the magnetic transition point T_N (~635 K) and a suppression by ~7% under 5T magnetic field at room temperature (<<T_N). These results confirm presence of strong multiferroic coupling even in nanoscale BiFeO3 and thus could prove to be quite useful for applications based on nanosized devices of BiFeO3.
Magnetic phase transitions in multiferroic bismuth ferrite (BiFeO3) induced by magnetic field, epitaxial strain, and composition modification are considered. These transitions from a spatially modulated spin spiral state to a homogenous antiferromagnetic one are accompanied by the release of latent magnetization and a linear magnetoelectric effect that makes BiFeO3-based materials efficient room-temperature single phase multiferroics.
Artificial superlattices of (BiFeO3)m(SrTiO3)m (m= 1 to 10 unit cells) consisting of multiferroic BiFeO3 and insulating SrTiO3 layers were fabricated on (100)-oriented SrTiO3 substrates by pulsed laser ablation. The remnant polarization and leakage current behavior were studied varying the periodicity (8-80A) of the superlattice. The leakage current was reduced by few orders of magnitude on increase of periodicity compared to single layer BiFeO3 thin films. Reduced leakage and intrinsic polarization hysteresis was observed and was confirmed by PUND analysis for periodicities in the range 20-60…
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…
We apply ultrafast X-ray diffraction with femtosecond temporal resolution to monitor the lattice dynamics in a thin film of multiferroic BiFeO$_3$ after above-bandgap photoexcitation. The sound-velocity limited evolution of the observed lattice strains indicates a quasi-instantaneous photoinduced stress which decays on a nanosecond time scale. This stress exhibits an inhomogeneous spatial profile evidenced by the broadening of the Bragg peak. These new data require substantial modification of existing models of photogenerated stresses in BiFeO$_3$: the relevant excited charge carriers must rem…
The spin wave spectra of multiferroic BiFeO3 films is calculated using a phenomenological Landau theory that includes magnetostatic effects. The lowest frequency magnon dispersion is shown to be quite sensitive to the angle between spin wave propagation vector and the Neel moment. Since electrical switching of the Neel moment has recently been demonstrated in this material, the sensitivity of the magnon dispersion permits direct electrical switching of spin wave propagation. This effect can be used to construct spin wave logical gates without current pulses, potentially allowing reduced power …
Raman scattering measurements on BiFeO3 single crystals show an important coupling between the magnetic order and lattice vibrations. The temperature evolution of phonons shows that the lowest energy E and A1 phonon modes are coupled to the spin order up to the Neel temperature. Furthermore, low temperature anomalies associated with the spin re-orientation are observed simultaneously in both the E phonon and the magnon. These results suggest that magnetostriction plays an important role in BiFeO3.
Using inelastic neutron scattering technique, we measured the spin wave dispersion over the entire Brillouin zone of room temperature multiferroic BiFeO3 single crystals with magnetic excitations extending to as high as 72.5 meV. The full spin waves can be explained by a simple Heisenberg Hamiltonian with a nearest neighbor exchange interaction (J=4.38 meV), a next nearest neighbor exchange interaction (J'=0.15 meV), and a Dzyaloshinskii-Moriya-like term (D=0.107 meV). This simple Hamiltonian determined, for the first time, for BiFeO3 provides a fundamental ingredient for understanding of the …
Multiferroic BiFeO3 epitaxial films with thickness ranging from 40 nm to 960 nm were grown by pulsed laser deposition on SrTiO3 (001) substrates with SrRuO3 bottom electrodes. X-ray characterization shows that the structure evolves from angularly-distorted tetragonal with c/a ~ 1.04 to more bulk-like distorted rhombohedral (c/a ~ 1.01) as the strain relaxes with increasing thickness. Despite this significant structural evolution, the ferroelectric polarization along the body diagonal of the distorted pseudo-cubic unit cells, as calculated from measurements along the normal direction, barely ch…
We have identified three of the four magnetoelectric modes of multiferroic BiFeO$_3$ measured using THz spectroscopy. Excellent agreement with the observed peaks is obtained by including the effects of easy-axis anisotropy along the direction of the electric polarization. By distorting the cycloidal spin state, anisotropy splits the $Ψ_{\pm 1}$ mode into peaks at 20 and 21.5 cm$^{-1}$ and activates the lower $Φ_{\pm 2}$ mode at 27 cm$^{-1}$ (T=200 K). An electromagnon is identified with the upper $Ψ_{\pm 1}$ mode at 21.5 cm$^{-1}$. Our results also explain recent Raman and inelastic neutron-sc…
Using THz spectroscopy, we show that the spin-wave spectrum of multiferroic BiFeO$_3$ in its high-field canted antiferromagnetic state is well described by a spin model that violates rhombohedral symmetry. We demonstrate that the monoclinic distortion of the canted antiferromagnetic state is induced by the single-ion magnetoelastic coupling between the lattice and the two nearly anti-parallel spins. The revised spin model for BiFeO$_3$ contains two new single-ion anisotropy terms that violate rhombohedral symmetry and depend on the direction of the magnetic field.
Low-energy magnon excitations in multiferroic BiFeO$_3$ were measured in detail as a function of temperature around several Brillouin zone centers by inelastic neutron scattering experiments on single crystals. Unique features around 1 meV are directly associated with the interplay of the Dzyaloshinskii-Moriya interaction and a small single-ion anisotropy. The temperature dependence of these and the exchange interactions were determined by fitting the measured magnon dispersion with spin-wave calculations. The spectra best fits an easy-axis type magnetic anisotropy and the deduced exchange and…
We present results of an {\it ab initio} density functional theory study of three bismuth-based multiferroics, BiFeO$_{3}$, Bi$_{2}$FeCrO$_{6}$, and BiCrO$_{3}$. We disuss differences in the crystal and electronic structure of the three systems, and we show that the application of the LDA+$U$ method is essential to obtain realistic structural parameters for Bi$_{2}$FeCrO$_{6}$. We calculate the magnetic nearest neighbor coupling constants for all three systems and show how Anderson's theory of superexchange can be applied to explain the signs and relative magnitudes of these coupling constants…
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…
The spin-driven polarizations of type-I multiferroics are veiled by the preexisting ferroelectric (FE) polarization. Using first-principles calculations combined with a spin model, we uncover two hidden but huge spin-driven polarizations in the room-temperature multiferroic BiFeO3. One is associated with the global inversion symmetry broken by a FE distortion and the other is associated with the local inversion symmetry broken by an antiferrodistortive octahedra rotation. Comparison with recent neutron scatterings reveals that first polarization reaches 3.0 $μ$C/cm$^2$, which is larger than in…
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…
We present a microscopic theory that shows the importance of spin-orbit coupling in perovskite compounds with heavy ions. In BiFeO3 (BFO) the spin-orbit coupling at the bismuth ion sites results in a special kind of magnetic anisotropy that is linear in the applied E-field. This interaction can convert the cycloid ground state into a homogeneous antiferromagnet, with a weak ferromagnetic moment whose orientation can be controlled by the E-field direction. Remarkably, the E-field control of magnetism occurs without poling the ferroelectric moment, providing a pathway for reduced energy dissipat…
Non-reciprocal directional dichroism, also called the optical-diode effect, is an appealing functional property inherent to the large class of non-centrosymmetric magnets. However, the in-situ electric control of this phenomenon is challenging as it requires a set of conditions to be fulfilled: Special symmetries of the magnetic ground state, spin-excitations with comparable magnetic- and electric-dipole activity and switchable electric polarization. We demonstrate the isothermal electric switch between domains of Ba$_2$CoGe$_2$O$_7$ possessing opposite magnetoelectric susceptibilities. Combin…
We have studied the magnetic field dependence of far-infrared active magnetic modes in a single ferroelectric domain \BFO/ crystal at low temperature. The modes soften close to the critical field of 18.8\,T along the [001] (pseudocubic) axis, where the cycloidal structure changes to the homogeneous canted antiferromagnetic state and a new strong mode with linear field dependence appears that persists at least up to 31\,T. A microscopic model that includes two \DM/ interactions and easy-axis anisotropy describes closely both the zero-field spectroscopic modes as well as their splitting and evol…
We propose that concurrently magnetic and ferroelectric, i.e. multiferroic, compounds endowed with electrically-active magnetic excitations (electromagnons) provide a key to produce large directional dichroism for long wavelengths of light. By exploiting the control of ferroelectric polarization and magnetization in a multiferroic oxide Ba$_2$CoGe$_2$O$_7$, we demonstrate the realization of such a directional light-switch function at terahertz frequecies in resonance with the electromagnon absorption. Our results imply that this hidden potential is present in a broad variety of multiferroics.
Bismuth ferrite (BiFeO$_3$) is one of the very few known single-phase multiferroic materials. While the bulk compound is rhombohedral (R), the discovery of an epitaxial strain-induced structural transition into a so-called 'super tetragonal-phase' (T-phase) in this material incited a flurry of research activity focused on gaining an understanding of this phase transition and its possible functionalities. This metastable phase of BiFeO$_3$ is also multiferroic, with giant ferroelectric polarization and coexisting antiferromagnetic order, but above all it is the strain relaxation-induced phase m…
Single phase BiFeO3 nanoparticles have been successfully synthesized for the first time by a novel citrate combustion method without using any solvent. Well mixed metal nitrates along with citric acid which is used as fuel combust to give BiFeO3 nanoparticles after annealing. These particles are single phase in nature and crystallize in the rhombohedral distorted perovskite structure (space group-R3c) which has been confirmed by the Rietveld refinement of the room temperature powder x-ray diffraction data. Nearly spherical particles of average particle size 47 nm have been seen from transmissi…
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…
The idea of embedding and transmitting information within the fluctuations of the magnetic moments of spins (spin waves) has been recently proposed and experimentally tested. The coherence of spin waves, which describes how well defined these excitations are, is of course vital to this process, and themost significant factor that affects the spin-wave coherence is temperature. Here we present neutron inelastic scattering measurements of the full threedimensional spin-wave dispersion in BiFeO3, which is one of the most promising functional multiferroic material, for temperatures from 5K to 700K…
Multiferroic materials have attracted much interest due to the unusual coexistence of ferroelectric and (anti-)ferromagnetic ground states in a single compound. They offer an exciting platform for new physics and potentially novel devices. BiFeO$_3$ is one of the most celebrated of multiferroic materials with highly desirable properties. It is the only known room-temperature multiferroic with $T_\mathrm{C}\approx 1100~ \mathrm{K}$ and $T_\mathrm{N}\approx 650~\mathrm{K}$, and exhibits one of the largest spontaneous electric polarisation, $P\approx 80~μ\mathrm{C/cm}^2$. At the same time, it has…
Despite its great technological importance, the magnetoelectric (ME) couplings in \BF are barely understood. By using a first-principles approach, we uncover the {\it dynamic} ME couplings of the long-range spin-cycloid in BiFeO$_3$. Based on a microscopic Hamiltonian, our first-principles approach disentangles the hidden ME couplings due to spin-current and exchange-striction. Beyond the spin-current polarization governed by the inverse Dzyaloshinskii-Moriya interaction \cite{iDM}, various spin-current polarizations derived from both ferroelectric and antiferrodistortive distortions cooperati…
The dependencies on strain and oxygen vacancies of the ferroelectric polarization and the weak ferromagnetic magnetization in the multiferroic material bismuth ferrite, BiFeO_3, are investigated using first principles density functional theory calculations. The electric polarization is found to be rather independent of strain, in striking contrast to most conventional perovskite ferroelectrics. It is also not significantly affected by oxygen vacancies, or by the combined presence of strain and oxygen vacancies. The magnetization is also unaffected by strain, however the incorporation of oxygen…
Spectroscopic modes provide the most sensitive probe of the very weak interactions responsible for the properties of the long-wavelength cycloid in the multiferroic phase of \BF below $\TN \approx 640$ K. Three of the four modes measured by THz and Raman spectroscopies were recently identified using a simple microscopic model. While a Dzyaloshinskii-Moriya (DM) interaction $D$ along $[-1,2,-1]$ induces the cycloid with wavevector $(2π/a)(0.5+δ, 0.5, 0.5-δ)$ ($δ\approx 0.0045$), easy-axis anisotropy $K$ along the $[1,1,1]$ direction of the electric polarization ${\bf P}$ induces higher harmonic…
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…
We report the results of direct measurement of remanent hysteresis loops on nanochains of BiFeO$_3$ at room temperature under zero and $\sim$20 kOe magnetic field. We noticed a suppression of remanent polarization by nearly $\sim$40\% under the magnetic field. The powder neutron diffraction data reveal significant ion displacements under a magnetic field which seems to be the origin of the suppression of polarization. The isolated nanoparticles, comprising the chains, exhibit evolution of ferroelectric domains under dc electric field and complete 180$^o$ switching in switching-spectroscopy pie…
Using ultrafast optical spectroscopy, we show that polaronic behavior associated with interfacial antiferromagnetic order is likely the origin of tunable magnetotransport upon switching the ferroelectric polarity in a La$_{0.7}$Ca$_{0.3}$MnO$_{3}$/BiFeO$_{3}$ (LCMO/BFO) heterostructure. This is revealed through the difference in dynamic spectral weight transfer between LCMO and LCMO/BFO at low temperatures, which indicates that transport in LCMO/BFO is polaronic in nature. This polaronic feature in LCMO/BFO decreases in relatively high magnetic fields due to the increased spin alignment, while…
Magnetic dc susceptibility between 1.5 and 800 K, ac susceptibility and magnetization, thermodynamic properties, temperature dependence of radio and audio-wave dielectric constants and conductivity, contact-free dielectric constants at mm-wavelengths, as well as ferroelectric polarization are reported for single crystalline BiFeO3. A well developed anomaly in the magnetic susceptibility signals the onset of antiferromagnetic order close to 635 K. Beside this anomaly no further indications of phase or glass transitions are indicated in the magnetic dc and ac susceptibilities down to the lowest …
We present a first-principles study of multiferroic BiFeO3 at high pressures. Our work reveals the main structural (change in Bi's coordination and loss of ferroelectricity), electronic (spin crossover and metallization), and magnetic (loss of order) effects favored by compression and how they are connected. Our results are consistent with the striking manifold transition observed experimentally by Gavriliuk et al. [Phys. Rev. B 77, 155112 (2008)] and provide an explanation for it.
How the magnetoelectric coupling actually occurs on a microscopic level in multiferroic BiFeO3 is not well known. By using the high-resolution single crystal neutron diffraction techniques, we have determined the electric polarization of each individual elements of BiFeO3, and concluded that the magnetostrictive coupling suppresses the electric polarization at the Fe site below TN. This negative magnetoelectric coupling appears to outweigh the spin current contributions arising from the cycloid spin structure, which should produce a positive magnetoelectric coupling.
Sizeable b and c components of the 4f moments and pronounced circular dichroism are observed in the ferroelectric phase of DyMnO_3 by soft X-ray diffraction at the Dy-M_5 resonance. This points to cycloidal order of the 4f moments and indicates that inversion-symmetry breaking in this material is not characteristic of the Mn spins alone. The circular dichroism allows to image chiral domains that are imprinted on the surface of a DyMnO$_3$ single crystal, exploiting the local charging by the X-ray beam via the photoelectric effect. These findings suggest a novel approach to control and image do…
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…
The spin-driven component of electric polarization in a single crystal of multiferroic BiFeO$_{3}$ was experimentally investigated in pulsed high magnetic fields up to 41 T. Sequential measurements of electric polarization for various magnetic field directions provide clear evidence of electric polarization normal to the hexagonal $c$ axis (${\bf P}_{\rm t}$) in not only the cycloidal phase, but also the field-induced canted antiferromagnetic phase. The direction of ${\bf P}_{\rm t}$ is directly coupled with the ferromagnetic moment in the canted antiferromagnetic phase, and thus controlled by…
In this article we review and discuss a mechanism for coupling between electric polarization and magnetization that can ultimately lead to electric-field switchable magnetization. The basic idea is that a ferroelectric distortion in an antiferromagnetic material can "switch on" the Dzyaloshinskii-Moriya interaction which leads to a canting of the antiferromagnetic sublattice magnetizations, and thus to a net magnetization. This magnetization M is coupled to the polarization P via a trilinear free energy contribution of the form P(M x L), where L is the antiferromagnetic order parameter. In par…
Logical devices based on spin waves offer the potential to avoid dissipation mechanisms that limit devices based on either the charge or spin of mobile electrons. Multiferroic magnetoelectrics, which are materials that combine ferroelectric and magnetic order, allow direct switching of magnetic order and thence of spin-wave properties using an applied electric field. The intrinsic coupling between polarization and magnetic moments, generated by strong electronic correlations in these multiferroic materials, is argued to provide new approaches to spin-wave injection and spin-wave switching usin…
