We observe a seemingly complex magnetic field dependence of dielectric constant of hexagonal YbMnO3 near the spin ordering temperature. After rescaling, the data taken at different temperatures and magnetic fields collapse on a single curve describing the sharp anomaly in nonlinear magnetoelectric response at the magnetic transition. We show that this anomaly is a result of the competition between two magnetic phases. The scaling and the shape of the anomaly are explained using the phenomenological Landau description of the competing phases in hexagonal manganites.
We use symmetry analysis to show that the G, C and A-type antiferromagnetic Pnma perovskites can exhibit magnetoelectric (ME) responses when a ferroelectric instability is induced with epitaxial strain. Using first-principles calculations we compute the values of the allowed ME response in strained CaMnO3 as a model system. Our results show that large linear and non-linear ME responses are present and can diverge when close to the ferroelectric phase transition. By decomposing the electronic and ionic contributions, we explore the detailed mechanism of the ME response.
The linear magnetoelectric response of Cr2O3 at zero temperature is calculated from first principles by tracking the change in magnetization under a macroscopic electric field. Both the spin and the orbital contributions to the induced magnetization are computed, and in each case the response is decomposed into lattice and electronic parts. We find that the transverse response is dominated by the spin-lattice and spin-electronic contributions, whose calculated values are consistent with static and optical magnetoelectric measurements. In the case of the longitudinal response, orbital contribut…
We present a first-principles scheme for computing the magnetoelectric response of multiferroics. We apply our method to BiFeO3 (BFO) and related compounds in which Fe is substituted by other magnetic species. We show that under certain relevant conditions -- i.e., in absence of incommensurate spin modulation, as in BFO thin films and some BFO-based solid solutions -- these materials display a large linear magnetoelectric response. Our calculations reveal the atomistic origin of the coupling and allow us to identify the most promising strategies to enhance it.
We show that inducing structural softness in regular magnetoelectric (ME) multiferroics -- i.e., tuning the materials to make their structure strongly reactive to applied fields -- makes it possible to obtain very large ME effects. We present illustrative first-principles results for BiFeO3 thin films.
We demonstrate that the electronic contribution to the linear magnetoelectric response, usually omitted in first-principles studies, can be comparable in magnitude to that mediated by lattice distortions, even for materials in which responses are strong. Using a self-consistent Zeeman response to an applied magnetic field for noncollinear electron spins, we show how electric polarization emerges in linear magnetoelectrics through both electronic- and lattice-mediated components -- in analogy with the high- and low-frequency dielectric response to an electric field. The approach we use is conce…
We report a theoretical study of the non-linear magnetoelectric response of GdFeO$_3$ through an analytical approach combined with a Heisenberg model which is fitted against first-principles calculations. Our theory reproduces the non-linear change of polarization under applied magnetic field reported experimentally such that it allows to analyze the origin of the large responses in the different directions. We show that the non-linear character of the response in these materials originates from the fact that the antiferromagnetic order of Gd atoms changes non-linearly with respect to the appl…
We present a first-principles scheme for the computation of the magnetoelectric response of magnetic insulators. The method focuses on the lattice-mediated part of the magnetic response to an electric field, which we argue can be expected to be the dominant contribution in materials displaying a strong magnetoelectric coupling. We apply our method to Cr2O3, a relatively simple and experimentally well studied magnetoelectric compound.
We study the magnetoelectric and electrocaloric response of strain-engineered, multiferroic SrMnO$_3$, using a phenomenological Landau theory with all parameters obtained from \emph{first-principles}-based calculations. This allows to make realistic and materials-specific predictions about the magnitude of the corresponding effects. We find that in the vicinity of a tetracritical point, where magnetic and ferroelectric phase boundaries intersect, an electric field has a huge effect on the antiferromagnetic order, corresponding to a magnetoelectric response several orders of magnitude larger th…
We demonstrate that magnetic vortices in which spins are coupled to polar lattice distortions via superexchange exhibit an unusually large linear magnetoelectric response. We show that the periodic arrays of vortices formed by frustrated spins on Kagomé lattices provide a realization of this concept; our {\it ab initio} calculations for such a model structure yield a magnetoelectric coefficient that is 30 times larger than that of prototypical single phase magnetoelectrics. Finally, we identify the design rules required to obtain such a response in a practical material.
We present a thorough density functional theory study of the magneto-electric (ME) effect in Cr$_{2}$O$_{3}$. The spin-lattice ME tensor $α$ was determined in the low-field and spin flop (SF) phases, using the method of dynamical magnetic charges, and found to be the sum of three distinct components. Two of them, a large relativistic "cycloidal" term and a small longitudinal term, are independent on the spin orientation. The third, only active in the SF phases is also of relativistic origin and arises from magnetic-field-induced chirality, leading to a non-toroidal ME response.
We report the discovery of linear magnetoelectric effect in the well-known green phase compound, Sm2BaCuO5, which crystallizes in the centrosymmetric orthorhombic (Pnma) structure. Magnetization and specific heat measurements reveal the long-range antiferromagnetic ordering of Cu2+ and Sm3+-ions moments at TN1 = 23 K and TN2 = 5 K, respectively. Applied magnetic field induces dielectric anomaly at TN1 whose magnitude increases with field, which results in significant (1.7%) magnetocapacitance effect. On the other hand, the dielectric anomaly observed in zero-applied magnetic field at TN2 shows…
In a linear magnetoelectric the lattice is coupled to electric and magnetic fields: both affect the longitudinal-transverse splitting of zone-center optical phonons on equal footing. A response matrix relates the macroscopic fields (D,B) to (E,H) at infrared frequencies. It is shown that the response matrices at frequencies 0 and \infty fulfill a generalized Lyddane-Sachs-Teller relationship. The rhs member of such relationship is expressed in terms of weighted averages over the longitudinal and transverse excitations of the medium, and assumes a simple form for an harmonic crystal.
Multiferroic particulate composites have been fabricated by taking the morphotropic phase boundary composition of ferroelectric phase Bi(Ni1/2Ti1/2)O3-PbTiO3 and magnetic phase (Ni,Zn)Fe2O4. The ferroelectric phase has coexisting monoclinic and tetragonal perovskite structures with space group Pm and P4mm, respectively whereas the magnetic phase has spinel cubic structure with space group Fd3m. Rietveld structural analysis for the each components of composite reveals that the tetragonality (c/a) of the ferroelectric phase continuously increases with increasing the concentration of magnetic pha…
The exchange-driven contribution to the magnetoelectric susceptibility $\hatα$ is formulated using a microscopic model Hamiltonian coupling the spin degrees of freedom to lattice displacements and electric field, which may be constructed from first-principles data. Electronic and ionic contributions are sorted out, and the latter is resolved into a sum of contributions from different normal modes. If intrasublattice spin correlations can be neglected, the longitudinal component $α_\parallel$ becomes proportional to the product of magnetic susceptibility and sublattice magnetization in accordan…
We report here the realization of ferroelectricity, ferromagnetism and magnetocapacitance effect in SrFe12O19 ceramics at room temperature. The ceramics demonstrate a saturated polarization hysteresis loop, two I-V peaks and large anomaly of dielectric constant near Curie temperature. These evidences confirmed the ferroelectricity of SrFe12O19 ceramics after annealing in O2 atmosphere. The remnant polarization of the SrFe12O19 ceramic is 103 μC/cm2. The material also exhibits strong ferromagnetic characterization, the coercive field and remnant magnetic moment are 6192Oe and 35.8emu/g, respect…
Large magnetoelectric response in thin films is highly desired for high-throughput and high-density microelectronic applications. However, the d0 rule in single-phase compounds usually results in a weak interaction between ferroelectric and magnetic orders; the magnetoelectric coupling via elastic resonance in composites restricts their thin-film integration in broadband. Here, we effectuate a concurrence of ferroelectric-like and antiferromagnetic phase transitions in Sr2IrO4/SrTiO3 superlattices by artificial design periodically non-equivalent interfaces, where a maximum magnetoelectric coef…
We discuss the second-order magnetoelectric effect, in which a quadratic or bilinear electric field induces a linear magnetization, in terms of the ferroic ordering of magnetic octupoles. We present the decomposition of a general rank-3 tensor into its irreducible spherical tensors, then reduce the decomposition to the specific case of the magnetic octupole tensor, $\mathcal{M}_{ijk} = \int μ_i (\mathbf{r}) r_j r_k d^3 \mathbf{r}$. We use first-principles density functional theory to compute the size of the local magnetic multipoles on the chromium ions in the prototypical magnetoelectric Cr$_…
Control of physical property in terms of external fields is essential for contemporary technologies. The conductance can be controlled by a gate electric field in a field effect transistor, which is a main component of the integrated circuit. Optical phenomena induced by an electric field such as electroluminescence and electrochromism are useful for display and other technologies. Control of microwave propagation seems also imperative for future wireless communication technology. Microwave properties in solids are dominated mostly by magnetic excitations, which cannot be easily controlled by …
We extend the recently-developed theory of bulk orbital magnetization to finite electric fields, and use it to calculate the orbital magnetoelectric response of periodic insulators. Working in the independent-particle framework, we find that the finite-field orbital magnetization can be written as a sum of three gauge-invariant contributions, one of which has no counterpart at zero field. The extra contribution is collinear with and explicitly dependent on the electric field. The expression for the orbital magnetization is suitable for first-principles implementations, allowing to calculate th…
We revisit the description of the magnetic field around antiferromagnetic magnetoelectrics in the context of recent developments regarding magnetoelectric monopoles. Using Maxwell's equations, we calculate the magnetic and electric fields associated with a free charge in a bulk uniaxial magnetoelectric, as well as in a finite sphere of magnetoelectric material. We show that a charge in the prototypical magnetoelectric Cr$_2$O$_3$, which is uniaxial with a diagonal magnetoelectric response, induces an internal magnetic field with both monopolar and quadrupolar components, but that only the quad…
We study theoretically the coupled multiferroic dynamics of one-dimensional ferroelectric/ferromagnet chains driven by harmonic magnetic and electric fields as a function of the chain length. A linear magnetoelectric coupling is dominated by the spin-polarized screening charge at the interface. We performed Monte-Carlo simulations and calculations based on the coupled Landau-Lifshitz-Gilbert and Landau-Khalatnikov equations showing that the net magnetization and the total polarization of thin heterostructures, i.e. with up to ten ferroelectric and ferromagnetic sites counted from the interface…
We have investigated the magnetoelectric and magnetodielectric response in FeVO$_4$, which exhibits a change in magnetic structure coincident with ferroelectric ordering at $T_{N2}$$\approx$15 K. Using symmetry considerations, we construct a model for the possible magnetoelectric coupling in this system, and present a discussion of the allowed spin structures in FeVO$_4$. Based on this model, in which the spontaneous polarization is caused by a trilinear spin-phonon interaction, we experimentally explore the magnetoelectric coupling in FeVO$_4$ thin films through measurements of the electric f…
Chromia is a magnetoelectric insulator whose bulk magnetoelectric susceptibility contains a non-zero pseudoscalar component, like that present in magnetized topological insulators. We reveal the dynamic axion field of chromia by measuring the temperature dependence of its non-linear magnetoelectric response using a lock-in technique with an AC electric field stimulus. The electric field dependence, magnetic field dependence, and temperature behavior of the second harmonic lock-in signal are all in agreement with theoretical expectations. Our results demonstrate that chromia magnetoelectric res…
Magnetoelectric (ME) materials are of fundamental interest and have been investigated for their broad potential for technological applications. The search for, and eventually the theoretical design of, materials with large ME couplings present challenging issues. First-principles methods have only recently been developed to calculate the full ME response tensor $α$ including both electronic and ionic (i.e., lattice-mediated) contributions. The latter is proportional to both the Born dynamical electric charge $Z^{\rm e}$ and its analogue, the dynamical magnetic charge $Z^{\rm m}$. Here we prese…
Terahertz magnetic resonance driven by the light electric field, now referred to as electromagnon, has stimulated interest due to its strong candidate for future spin-electronics. One unique characteristic of electromagnons is the terahertz magnetochromism, a color change by external magnetic field, as recently demonstrated in the hexaferrite. By taking perovskite manganites and hexaferrite as model cases, the current understating of the electromagnon activity is discussed in terms of the symmetric exchange mechanism.
A series of manganites Tb1-xHoxMnO3 (0<=x<=0.6) with orthorhombic structure are synthesized and detailed investigations on their multiferroicity are performed. Successive magnetic transitions upon temperature variation are evidenced for all samples, and both the Mn3+ spiral spin ordering and rare-earth spin ordering are suppressed with increasing x. Significant enhancement of both the polarization and magnetoelectric response within 0.2<x<0.4 is observed, which may be ascribed to the competition possibly existing between spiral and E-type spin orders. Theoretical calculation is given based on …
Nonlinear Magnetoelectric Effect under Magnetic Octupole Order: Its Application to a $d$-Wave Altermagnet and a Pyrochlore Lattice with All-In/All-Out Magnetic Order
Thin FeRh film was extensively studied recently, and an emergent substrate- and capping-dependent interfacial ferromagnetism (FM) was widely observed in experiments. However, the voltage modulation of this interfacial ferromagnetism is barely studied, which would have profound applications in antiferromagnetic (AFM) FeRh-based magnetoelectric-random access memory (MeRAM). Using ab initio techniques, we comparatively study the interfacial ferromagnetic properties and magnetoelectric responses of ultrathin FeRh films capped by heavy transition metal Ta. We find that Ta capping reverses the phase…
We derive compact analytical expressions for the coupled spin-charge susceptibility of a clean helical metal at the surface of a three dimensional topological insulator (TI). These expressions lead to unconventional non-collinear RKKY interactions between two impurity magnetic moments placed on the surface of a TI, and predict the generation of electric currents by time-dependent magnetic moments. We determine the influence of gate and bias voltages on the interlayer exchange coupling between two single-domain ferromagnetic monolayers deposited on top of a TI.
We report coupling between magnetic and electric orders for antiferromagnetic polycrystalline FeVO4 in which magnetism-induced polarization has been recently found in noncollinear antiferromagnetic state below the second antiferromagnetic phase transition at TN2=15.7K. In this low symmetry phase space group P-1, the magnetic field dependence of electric polarization evidences a clear magnetoelectric coupling in the noncollinear spin-configured antiferromagnetic phase. The discontinuity of magnetodielectric effect observed at the vicinity of the polar to nonpolar transition evidences competitio…
Our measured dielectric constant and mechanical response of multiferroic BiFeO3 indicate four phase transitions below room temperature. Features correlate with those reported at 50K (from a peak in the zero-field-cooled magnetic susceptibility) and 230K (from splitting between field-cooled and zero-field-cooled magnetic data[1], and 200K (from magnon light scattering cross sections[2]). The primary order parameter is not the polarization in any of the low-T transitions. Instead, the transition near 230 K shows strong elastic coupling, while that at 50K is fundamentally magnetic, but magnetostr…
Magnetoelectric responses are a fundamental characteristic of materials that break time-reversal and inversion symmetries (notably multiferroics) and, remarkably, of "topological insulators" in which those symmetries are unbroken. Previous work has shown how to compute spin and lattice contributions to the magnetoelectric tensor. Here we solve the problem of orbital contributions by computing the frozen-lattice electronic polarization induced by a magnetic field. One part of this response (the "Chern-Simons term") can appear even in time-reversal-symmetric materials and has been previously sho…
Topological magnetoelectric effect (TME) is a hallmark response of the topological field theory, which provides a paradigm shift in the study of emergent topological phenomena. However, its direct observation is yet to be realized due to the demanding magnetic configuration required to gap all the surface states. Here, we theoretically propose that the axion insulators with a simple ferromagnetic configuration, such as MnBi2Te4/(Bi2Te3)n family, provide an ideal playground to realize TME. In a designed triangular prism geometry, all the surface states are magnetically gapped. Under a vertical …
While tremendous success has been achieved to date in creating both single phase and composite magnetoelectric materials, the quintessential electric-field control of magnetism remains elusive. In this work, we demonstrate a linear magnetoelectric effect which arises from a novel carrier-mediated mechanism, and is a universal feature of the interface between a dielectric and a spin-polarized metal. Using first-principles density functional calculations, we illustrate this effect at the SrRuO$_3$/SrTiO$_3$ interface and describe its origin. To formally quantify the magnetic response of such an …
Employing a new experimental technique to measure magnetoelectric response functions, we have measured the magnetoelectric effect in composite films of nano granular metallic iron in anatase titanium dioxide at temperatures below 50 K. A magnetoelectric resistance is defined as the ratio of a transverse voltage to bias current as a function of the magnetic field. In contrast to the anomalous Hall resistance measured above 50 K, the magnetoelectic resistance below 50 K is significantly larger and exhibits an even symmetry with respect to magnetic field reversal $H\to -H$. The measurement techni…
In-plane temperature dependent dielectric behavior of BiFeO3 (BFO) as-grown thin films show diffuse but prominent phase transitions near 450 (+/-10) K and 550 K with dielectric loss temperature dependences that suggest skin layer effects. The 450 K anomalies are near the "transition" first reported by Polomska et al. [Phys. Stat. Sol. 23, 567 (1974)]. The 550 K anomalies coincide with the surface phase transition recently reported [Xavi et al. PRL 106, 236101 (2011)]. In addition, anomalies are found at low temperatures: After several experimental cycles the dielectric loss shows a clear relax…
We demonstrate computationally the existence of magnetoelectric multipoles, arising from the second order term in the multipole expansion of a magnetization density in a magnetic field, in noncentrosymmetric magnetic metals. While magnetoelectric multipoles have long been discussed in the context of the magnetoelectric effect in noncentrosymmetric magnetic insulators, they have not previosuly been identified in metallic systems, in which the mobile carriers screen any electrical polarization. Using first-principles density functional calculations we explore three specific systems: First, a con…
Magneto-capacitance effect was investigated using the impedance spectroscopy on single crystals of LuFe2O4. The intrinsic impedance response could be separated from the interfacial response and showed a clear hysteresis loop below TFerri ~ 240 K under the magnetic field. The neutron diffraction experiment under the magnetic field proves the origin of dielectric property related to the motion of nano-sized ferromagnetic domain boundary. These results imply that the modification of the microscopic domain structure is responsible for the magnetoelectric effect in LuFe2O4.
We use symmetry analysis and first principles calculations to show that the linear magnetoelectric effect can originate from the response of orbital magnetic moments to the polar distortions induced by an applied electric field. Using LiFePO4 as a model compound we show that spin-orbit coupling partially lifts the quenching of the 3d orbitals and causes small orbital magnetic moments ($μ_{(L)}\approx 0.3 μ_B$) parallel to the spins of the Fe$^{2+}$ ions. An applied electric field $\mathbf{E}$ modifies the size of these orbital magnetic moments inducing a net magnetization linear in $\mathbf{E}…
Magnetoelectric effect is a fundamental physics phenomenon that synergizes electric and magnetic degrees of freedom to generate distinct material responses like electrically tuned magnetism, which serves as a key foundation of the emerging field of spintronics. Here, we show by first-principles studies that ferroelectric (FE) polarization of an In2Se3 monolayer can modulate the magnetism of an adjacent transition-metal (TM) decorated graphene layer via an FE induced electronic transition. The TM nonbonding d-orbital shifts downward and hybridizes with carbon p states near the Fermi level, supp…
Three-dimensional topological insulator films in contact with magnetic layers exhibit intriguing magneto-optical and magnetoelectric phenomena, but little is known beyond the linear response regime. We demonstrate that the presence of two electric fields parallel to the surface of the film induces a perpendicular AC polarization, whereas a static polarization can be induced by applying a single circularly polarized electromagnetic wave. These phenomena are determined by the second-order susceptibility, which also controls the manner in which the anomalous Hall current is modulated by a perpend…
Two kinds of specimens, with the major phase of Sr3Co2Fe24O41 (Sr3Co2Z) and SrCo2Fe16O27 (SrCo2W) hexaferrites respectively, were fabricated through solid-state reaction. The phase composition, magnetic and dielectric properties, magnetodielectric (MD) effect, magnetoelectric (ME) effect and pyroelectric properties were studied. Results show that magnetic and dielectric anomalies are induced by the magnetocrystalline anisotropy (MCA) transition. They can be considered as characteristic properties (e.g., Sr3Co2Z at 370 K) but are not a sufficient condition for the MD and ME coupling. The T-bloc…
In this work, we analysed GdMnO3 magnetoelectric thin films prepared by a general sol-gel method. The film formation temperature is analysed by termogravimetric analysis, while the lattice parameters of the Pbnm orthorhombic films are determined from the analysis of the x-ray spectra. The x-ray results also reveal that GdMnO3 films are under compression along the b axis. The lattice dynamic analysis carried out by Raman spectroscopy confirms the formation of films with a Pbnm orthorhombic structure. Moreover, the analysis of the Raman spectra suggests that besides film-substrate interaction, t…
By combining single crystal x-ray and neutron diffraction, and the magnetodielectric measurements on single crystal Fe4Nb2O9, we present the magnetic structure and the symmetry-allowed magnetoelectric coupling in Fe4Nb2O9. It undergoes an antiferromagnetic transition at TN=93 K, followed by a displacive transition at TS=70 K. The temperature-dependent dielectric constant of Fe4Nb2O9 is strongly anisotropic with the first anomaly at 93 K due to the exchange striction as a result of the long range spin order, and the second one at 70 K emanating from the structural phase transition primarily dri…
Single-crystal growth and magnetic, magnetoelectric, and optical properties of ferroaxial-type SrMn$_2$Ni$_6$Te$_3$O$_{18}$
Osaka Metropolitan University（大阪公立大学）；The University of Tokyo（东京大学）；Kyoto University（京都大学）；High Energy Accelerator Research Organization（高能加速器研究机构）；The University of Osaka（大阪大学）
Magnetic-field effect on the magnetic and electric properties in a chiral polar ordered corundum Ni$_2$InSbO$_6$ has been investigated. Single-crystal soft x-ray and neutron diffraction measurements confirm long-wavelength magnetic modulation. The modulation direction tends to align along the magnetic field applied perpendicular to the polar axis, suggesting that the nearly proper-screw type helicoid should be formed below 77\,K. The application of a high magnetic field causes a metamagnetic transition. In a magnetic field applied perpendicular to the polar axis, a helix-to-canted antiferromag…
A quantized version of the magnetoelectric effect, known as the topological magnetoelectric effect, can exist in a time-reversal invariant topological insulator with all its surface states gapped out by magnetism. This topological phase, called the axion insulator phase, has been theoretically proposed but is still lack of conclusive experimental evidence due to the small signal of topological magnetoelectric effect. In this work, we propose that the dynamical in-plane magnetization in an axion insulator can generate a "pseudo-electric field", which acts on the surface state of topological ins…
