Linear Magnetoelectric Effect Research Articles

Linear magnetoelectric effect in g\xf6thite, \u03b1-FeOOH

By means of symmetry analysis, density functional theory calculations, and Monte Carlo simulations we show that goethite, α-FeOOH, is a linear magnetoelectric below its Néel temperature TN = 400 K. The experimentally observed magnetic field induced spin-flop phase transition results in either change of direction of electric polarization or its suppression. Estimated value of magnetoelectric coefficient is 0.57 μC · m−2 · T−1. The abundance of goethite in nature makes it arguably the most widespread magnetoelectric material.

Nonlinear magnetoelectric effect in paraelectric state of Co4Nb2O9 single crystal

We report the structural, magnetoelectric (ME), magnetic and electric control of magnetic properties in Co4Nb2O9 (CNO) single crystal. A detailed ME measurement reveals a nonlinear ME effect instead of a linear ME effect in CNO single crystal. By fitting the magnetization-electric field (M-E) curve, it can be found that the linear ({alpha }_{e}) and quadratic (γ) coefficients equal to ~8.27 ps/m and ~−6.46 ps/MV for upper branch, as well as ~8.38 ps/m and ~6.75 ps/MV for the lower branch. More importantly, a pronounced response was observed under a small cooling magnetic field, which cannot even cause the spin flop. This suggests a magnetoelectric effect can occur at paraelectric state for CNO single crystal. Furthermore, we also found that the magnetization of every axis responds to electric field applied along a-axis, but fails to do so when the electric field is applied c-axis. Such findings supply a direct evidence to the magnetic structure and ME coupling mechanism indirectly reflected by our neutron experiment.

Magnetoelectric Force Microscopy on Antiferromagnetic 180∘ Domains in Cr₂O₃.

Magnetoelectric force microscopy (MeFM) is characterized as methodical tool for the investigation of antiferromagnetic domain states, in particular of the 180 variety. As reference compound for this investigation we use CrO. Access to the antiferromagnetic order is provided by the linear magnetoelectric effect. We resolve the opposite antiferromagnetic 180 domain states of CrO and estimate the sensitivity of the MeFM approach, its inherent advantages in comparison to alternative techniques and its general feasibility for probing antiferromagnetic order.

Mean-field study of correlation-induced antisymmetric spin-orbit coupling in a two-orbital honeycomb model

We investigate a two-orbital Hubbard model on a honeycomb structure, with a special focus on the antisymmetric spin-orbit coupling (ASOC) induced by symmetry breaking in the electronic degrees of freedom. By investigating the ground-state phase diagram by the mean-field approximation in addition to the analysis in the strong correlation limit, we obtain a variety of symmetry-broken phases that induce different types of effective ASOCs by breaking of spatial inversion symmetry. We find several unusual properties emergent from the ASOCs, such as a linear magnetoelectric effect in a spin-orbital ordered phase at 1/4 filling and a spin splitting in the band structure in charge ordered phases at 1/4 and 1/2 fillings. We also show that a staggered potential on the honeycomb structure leads to another type of ASOC, which gives rise to a valley splitting in the band structure at 1/2 filling. We discuss the experimental relevance of our results to candidate materials including transition metal dichalcogenides and trichalcogenides.

Optical Magnetoelectric Resonance in a Polar Magnet (Fe,Zn)_{2}Mo_{3}O_{8} with Axion-Type Coupling.

We report the polarization rotation of terahertz light resonant with the magnetoelectric (ME) spin excitation in the multiferroic (Fe,Zn)_{2}Mo_{3}O_{8}. This resonance reflects the frequency dispersion of the diagonal ME susceptibility (axion term), with which we quantitatively reproduce the thermal and magnetic-field evolution of the observed polarization rotation spectra. The application of the sum rule on the extrapolated dc value of the spectral weight of the ME oscillator provides insight into the dc linear ME effect. The present finding highlights a novel optical functionality of spin excitations in multiferroics that originates from diagonal ME coupling.

Magnetically induced ferroelectricity in Bi2CuO4

The tetragonal copper oxide ${\mathrm{Bi}}_{2}{\mathrm{CuO}}_{4}$ has an unusual crystal structure with a three-dimensional network of well separated ${\mathrm{CuO}}_{4}$ plaquettes. The spin structure of ${\mathrm{Bi}}_{2}{\mathrm{CuO}}_{4}$ in the magnetically ordered state below ${T}_{\text{N}}\ensuremath{\sim}43$ K remains controversial. Here we present the results of detailed studies of specific heat, magnetic, and dielectric properties of ${\mathrm{Bi}}_{2}{\mathrm{CuO}}_{4}$ single crystals grown by the floating zone technique, combined with the polarized neutron scattering and high-resolution x-ray measurements. Down to 3.5 K our polarized neutron scattering measurements reveal ordered magnetic Cu moments which are aligned within the $ab$ plane. Below the onset of the long range antiferromagnetic ordering we observe an electric polarization induced by an applied magnetic field, which indicates inversion symmetry breaking by the ordered state of Cu spins. For the magnetic field applied perpendicular to the tetragonal axis, the spin-induced ferroelectricity is explained in terms of the linear magnetoelectric effect that occurs in a metastable magnetic state. A relatively small electric polarization induced by the field parallel to the tetragonal axis may indicate a more complex magnetic ordering in ${\mathrm{Bi}}_{2}{\mathrm{CuO}}_{4}$.

Piezomagnetism as a counterpart of the magnetovolume effect in magnetically frustrated Mn-based antiperovskite nitrides

Electric-field control of magnetization promises to substantially enhance the energy efficiency of device applications ranging from data storage to solid-state cooling. However, the intrinsic linear magnetoelectric effect is typically small in bulk materials. In thin films electric-field tuning of spin-orbit interaction phenomena (e.g., magnetocrystalline anisotropy) has been reported to achieve a partial control of the magnetic state. Here we explore the piezomagnetic effect (PME), driven by frustrated exchange interactions, which can induce a net magnetization in an antiferromagnet and reverse its direction via elastic strain generated piezoelectrically. Our $ab~initio$ study of PME in Mn-antiperovskite nitrides identified an extraordinarily large PME in Mn$_3$SnN available at room temperature. We explain the magnitude of PME based on features of the electronic structure and show an inverse-proportionality between the simulated zero-temperature PME and the negative thermal expansion at the magnetic (N\'eel) transition measured by Takenaka et al. in 9 antiferromagnetic Mn$_3$AN systems.

Superexchange theory of electronic polarization driven by relativistic spin-orbit interaction at half filling

By applying Berry-phase theory for the effective half-filled Hubbard model, we derive an analytical expression for the electronic polarization driven by the relativistic spin-orbit (SO) coupling. The model itself is constructed in the Wannier basis, using the input from the first-principles electronic structure calculations in the local-density approximation, and then treated in the spirit of the superexchange theory. The obtained polarization has the following form: ${\bf P}_{ij} = \boldsymbol{\epsilon}_{ji} \boldsymbol{\cal P}_{ij} \cdot [\boldsymbol{e}_i \times \boldsymbol{e}_j]$, where $\boldsymbol{\epsilon}_{ji}$ is the direction of the bond $\langle ij \rangle$, $\boldsymbol{e}_i$ and $\boldsymbol{e}_j$ are the directions of spins in this bond, and $\boldsymbol{\cal P}_{ij}$ is the pseudovector containing all the information about the crystallographic symmetry of the considered system. The expression describes the ferroelectric activity in various magnets with noncollinear but otherwise nonpolar magnetic structures, which would yield no polarization without SO interaction, including the magnetoelectric (ME) effect, caused by the ferromagnetic canting of spins in the external magnetic field, and spin-spiral multiferroics. The abilities of this theory are demonstrated for the the analysis of linear ME effect in Cr$_2$O$_3$ and BiFeO$_3$ and properties multiferroic MnWO$_4$ and $\beta$-MnO$_2$. In all considered examples, the theory perfectly describes the symmetry properties of the induced polarization. However, in some cases, the values of this polarization are underestimated, suggesting that other effects, besides the spin and electronic ones, can also play an important role.

All-Silicon Switchable Magnetoelectric Effect through Interlayer Exchange Coupling.

The magnetoelectric (ME) effect originating from the effective coupling between electric field and magnetism is an exciting frontier in nanoscale science such as magnetic tunneling junction (MTJ), ferroelectric/piezoelectric heterojunctions etc. The realization of switchable ME effect under external electric field in d0 semiconducting materials of single composition is needed especially for all-silicon spintronics applications because of its natural compatibility with current industry. We employ density functional theory (DFT) to reveal that the pristine Si(111)-3×3 R30° (Si3 hereafter) reconstructed surfaces of thin films with a thickness smaller than eleven bilayers support a sizeable linear ME effect with switchable direction of magnetic moment under external electric field. This is achieved through the interlayer exchange coupling effect in the antiferromagnetic regime, where the spin-up and spin-down magnetized density is located on opposite surfaces of Si3 thin films. The obtained coefficient for the linear ME effect can be four times larger than that of ferromagnetic Fe films, which fail to have the reversal switching capabilities. The larger ME effect originates from the spin-dependent screening of the spin-polarized Dirac fermion. The prediction will promote the realization of well-controlled and switchable data storage in all-silicon electronics.

Apparent critical behaviour of sputter-deposited magnetoelectric antiferromagnetic Cr2O3 films near Néel temperature

Chromium(III) oxide is a collinear antiferromagnet with a linear magnetoelectric effect. We are presenting the measurements of the magnetoelectric susceptibility α of a sputter-deposited 500 nm film and a bulk single-crystal substrate of Cr2O3. We investigated the magnetic phase-transition and the critical exponent β of the sublattice magnetization near Néel temperature. For the film, an exponent of 0.49(1) was found below 293 K, and changed to 1.06(4) near the Néel temperature of 298 K. For the bulk substrate, the exponent was constant at 0.324(4). We investigated the reversal probability of antiferromagnetic domains during magnetoelectric field cooling. For the sputtered films, reversal probability was zero above 298 K and stabilized only below 293 K. We attribute this behaviour to formation of grains during film growth, which gives different intergrain and intragrain exchange-coupling energies. The reversal probability dependence on the magnitude of cooling magnetic field could be explained by a phenomenological model. For the bulk substrate, reversal probability was stabilized immediately at the Néel temperature of 307.6 K.

Linear magnetoelectric effect as a signature of long-range collinear antiferromagnetic ordering in the frustrated spinel CoAl2O4

The ground state of the frustrated $A$-site magnetic spinel $\mathrm{CoA}{\mathrm{l}}_{2}{\mathrm{O}}_{4}$ has been a controversial issue whether it is a collinear antiferromagnetic ordering or a spiral spin-liquid state, as the ratio of the two competing interactions ${J}_{2}/{J}_{1}$ lies close to the boundary between these two ground states. Here we address the magnetic ground state in $\mathrm{CoA}{\mathrm{l}}_{2}{\mathrm{O}}_{4}$ with different amounts of $\mathrm{C}{\mathrm{o}}^{2+}/\mathrm{A}{\mathrm{l}}^{3+}$ site disorder from the study of magnetoelectric effect and Monte Carlo simulations. $\mathrm{CoA}{\mathrm{l}}_{2}{\mathrm{O}}_{4}$ with low site disorder exhibits a linear magnetoelectric effect below the magnetic ordering temperature. With increasing disorder, the magnetoelectric effect is suppressed and the sample with $14%$ disorder exhibits a spin glass behavior without the magnetoelectric effect. Monte Carlo simulations support the experimental findings and suggest that the site disorder suppresses long-range antiferromagnetic order and induces a spin glass state. Since the linear magnetoelectric effect requires a long-range magnetic ordering, we suggest that the ground state of $\mathrm{CoA}{\mathrm{l}}_{2}{\mathrm{O}}_{4}$ with low site disorder is a collinear antiferromagnet.

Enhancement of magnetoelectric operating temperature in compressed Cr2O3 under hydrostatic pressure

The effect of hydrostatic pressure on structure and magnetism was investigated by a combined theoretical and experimental study for Cr2O3 showing the linear magnetoelectric effect below the Néel temperature TN ≈ 307 K. Based on first-principles calculations and Monte-Carlo simulations, we predicted that TN linearly increases with increasing applied pressure P with the slope of (1/TN)(dTN/dP) = +1.9 × 10−2 GPa−1. This theoretical prediction was qualitatively verified by our experimental observation about the pressure dependence of TN, which was detected by measurements of dielectric constant through the magnetoelectric coupling [(1/TN)(dTN/dP) = +1.6 × 10−2 GPa−1]. These results provide an effective way to enhance magnetoelectric operating temperature in the rare room-temperature magnetoelectric, Cr2O3.

Electromagnon resonance in a collinear spin state of the polar antiferromagnet Fe2Mo3O8

Magnetic excitations are investigated for a hexagonal polar magnet Fe2Mo3O8 by terahertz spectroscopy. We observed magnon modes including an electric-field active magnon, electromagnon, in the collinear antiferromagnetic phase with spins parallel to the c axis. We unravel the nature of these excitations by investigating the correlation between the evolution of the mode profile and the magnetic transition from antiferromagnetic to ferrimagnetic order induced by magnetic field or Zn-doping. We propose that the observed electromagnon mode involves the collective precession of the spins with oscillating in-plane electric polarization through the mechanism of the linear magnetoelectric effect.

Linear and nonlinear magnetoelectric effects in lead zirconate titanate–nickel ferrite bulk composites

Linear and nonlinear magnetoelectric (ME) effects in lead zirconate titanate (PZT)–nickel ferrite bulk composites have been experimentally studied. The maximum values of a ME response signal for the linear and nonlinear ME effects amounted to 260 mV/A and 34 kV/m, respectively. A relationship between the linear and nonlinear ME effects is established based on analysis of experimental data.

Теория линейного и нелинейного магнитоэлектрического эффекта в слоистых магнитострикционно- пьезоэлектрических композитах.

The theory of linear and nonlinear magnetoelectric effect in layered magnetostrictive-piezoelectric multiferroics is presented based on the joint solution of the equations of motion and constitutive relations for the magnetostrictive and piezoelectric subsystems, considering the boundary conditions on the interface. It is shown that, in weak bias magnetic fields, the value of nonlinear effect is comparable with linear, and along with the main resonance, there is an additional resonance. Value of the resonance amplitude is not dependent on bias magnetic field and is excited at the frequency of magnetic field twice less the main resonance frequency. Trilayer nickel–polymer–PZT–polymer nickel disc-shaped structure is designed for the experiment. Frequency and field dependence of magnetoelectric effect is presented for this structure.

Magnetic Structures of Orthorhombic Li2M(SO4)2 (M = Co, Fe) and LixFe(SO4)2 (x = 1, 1.5) Phases.

We report herein on the magnetic properties and structures of orthorhombic Li2M(SO4)2 (M = Co, Fe) and their oxidized phases LixFe(SO4)2 (x = 1, 1.5), which were previously studied as potential cathode materials for Li-ion batteries. The particular structure of these orthorhombic compounds (space group Pbca) consists of a three-dimensional network of isolated MO6 octahedra enabling solely super-super-exchange interactions between transition metals. We studied the magnetic properties of these phases via temperature-dependent susceptibility measurements and applied neutron powder diffraction experiments to solve their magnetic structures. All compounds present an antiferromagnetic long-range ordering of the magnetic spins below their Néel temperature. Their magnetic structures are collinear and follow a spin sequence (+ + - - - - + +), with the time reversal associated with the inversion center, a characteristic necessary for a linear magneto-electric effect. We found that the orientation of the magnetic moments varies with the nature of M. While Li2Co(SO4)2 and Li1Fe(SO4)2 adopt the magnetic space group Pb'c'a', the magnetic space group for Li2Fe(SO4)2 and Li1.5Fe(SO4)2 is P1121'/a, which might hint for a possible monoclinic distortion of their nuclear structure. Moreover we compared the orthorhombic phases to their monoclinic counterparts as well as to the isostructural orthorhombic Li2Ni(SO4)2 compound. Finally, we show that this possible magneto-electric feature is driven by the topology of the magnetic interactions.

Influence of the linear magneto-electric effect on the lateral shift of light reflected from a magneto-electric film

We present a theoretical investigation of the lateral shift of an infrared light beam reflected from a magnetic film deposited on a non-magnetic dielectric substrate, taking into account the linear magneto-electric interaction in the magnetic film. We use the stationary phase method to evaluate the lateral shift. It is shown that the magneto-electric coupling leads to a six-fold enhancement of the lateral shift amplitude of a p-(s-) polarized incident beam reflected into a s-(p-) polarized beam. A reversal of the magnetization in the film leads to a nonreciprocal sign change of the lateral shift.

Magnetoelectric effect in simple collinear antiferromagnetic spinels

We report the discovery of the linear magnetoelectric effect in a family of spinel oxides, $\mathrm{C}{\mathrm{o}}_{3}{\mathrm{O}}_{4}$ and $\mathrm{Mn}{B}_{2}{\mathrm{O}}_{4}$ $(B=\mathrm{Al},\text{Ga})$ with simple collinear antiferromagnetic spin structure. An external magnetic field induces a dielectric anomaly at ${T}_{\mathrm{N}}$, accompanied by the generation of electric polarization that varies linearly with magnetic field. Magnetization and magnetoelectric measurements on a single crystal of $\mathrm{MnG}{\mathrm{a}}_{2}{\mathrm{O}}_{4}$ together with a phenomenological theory suggest that the easy axis direction is [111] with the corresponding magnetic symmetry $\phantom{\rule{4pt}{0ex}}R{\overline{3}}^{\ensuremath{'}}{m}^{\ensuremath{'}}$. The proposed theoretical model of single-ion contribution of magnetic ions located in a noncentrosymmetric crystal environment stands for a generic mechanism for observing magnetoelectric effects in these and other similar materials.

Magnetoelectric properties of 500-nmCr2O3films

The linear magnetoelectric effect was measured in 500 nm Cr2O3 films grown by rf sputtering on Al2O3 substrates between top and bottom thin film Pt electrodes. Magnetoelectric susceptibility was measured directly by applying an AC electric field and measuring the induced AC magnetic moment using superconducting quantum interference device magnetometry. A linear dependence of the induced AC magnetic moment on the AC electric field amplitude was found. The temperature dependence of the magnetoelectric susceptibility agreed qualitatively and quantitatively with prior measurements of bulk single crystals, but the characteristic temperatures of the film were lower than those of single crystals. It was also possible to reverse the sign of the magnetoelectric susceptibility by reversing the sign of the magnetic field applied during cooling through the N\'eel temperature. A competition between total magnetoelectric and Zeeman energies is proposed to explain the difference between film and bulk Cr2O3 regarding the cooling field dependence of the magnetoelectric effect.

Origin of the giant linear magnetoelectric effect in perovskitelike multiferroicBiFeO3

In this article the mechanism of the linear magnetoelectric (ME) effect in the rhombohedral multiferroic BiFeO$_3$ is considered. The study is based on the symmetry approach of the GinzburgLandau type, in which polarization, antiferrodistortion, and antiferromagnetic momentum vectors are viewed as ordering parameters. We demonstrate that the linear ME effect in BFO is caused by reorientation of the antiferrodistortion vector in either electric or magnetic field. The numerical estimations, which show quantitative agreement with the results of the recent measurements in film samples, have been performed. A possibility of significant enhancement of the magnetoelectric effect by applying an external static electric field has been investigated. The considered approach is promising for explaining the high values of the ME effect in composite films and heterostructures with BFO.