On the free energy of the flexomagnetoelectric interactions

It was shown that free energy density of the local flexomagnetoelectric effect is determined by the four phenomenological constants in case of the cubic (hexoctahedral) crystal. The well-known single-constant Lifshitz invariant term is correct only when fixed electric polarization induces the inhomogeneity of the magnetization. Proposed phenomenological theory was applied to the magnetic domain walls. The domain wall structure has been investigated in details. The four-constant phenomenological theory conforms to the symmetry based predictions (Bar'yakhtar et al., 1984, [12]). The proposed experimental verification of the four-constant flexomagnetoelectric phenomenology is a detection of the shift of the Néel domain walls under the strong homogeneous electric field.     

Symmetry theory of the flexomagnetoelectric effect in the Bloch lines

It was shown that there are 48 magnetic point groups of the Bloch lines including 22 (11 time-invariant and 11 time-noninvariant) enantiomorphic and 26 non-enantiomorphic groups. The Bloch lines with the time-noninvariant enantiomorphism have identical types (parities) of the magnetization and polarization dependences. The list of soliton-like Bloch lines is derived from the symmetry classification. The tip electrode method of the creation of these Bloch lines is suggested for the potential applications in the magnetoelectric memory devices. The method of the experimental determination of the flexomagnetoelectric properties of the Bloch lines carried by the Bloch domain wall has been suggested. New type of the flexomagnetoelectric coupling, which is determined by the spatial derivatives of the electric polarization, can be found in the vicinity of the Curie temperature or compensation point of the ferrimagnets. The multi-state Bloch line magnetoelectric/multiferroic memory is proposed. It can be considered as a concept of the magnetoelectric enhancement of existing Bloch line memory invention.     

Flexomagnetoelectric interaction in cubic,tetragonal and orthorhombic crystals

The phenomenological theory of the flexomagnetoelectric coupling in crystals of the cubic, tetragonal and orthorhombic crystal systems has been suggested. Secondary role of the crystal structure chirality was shown. Oppositely, significant role of the crystallographic point group type (symmetric, alternating, dihedral or cyclic) in the flexomagnetoelectric coupling has been derived. It was shown, that conceptually new features of the flexomagnetoelectric effects are expected in the crystals of the cyclic groups (crystal classes 4/m, 4? and 4). Proposed verification of the theory is investigation of the domain wall bend details (changes of the effect symmetry). Special case of such verification near the compensation point is suggested. First-principles mechanisms of the flexomagnetoelectric interaction were discussed.     

Symmetry theory of the flexomagnetoelectric interaction in the magnetic vortices and skyrmions

Symmetry classification of the magnetic vortices and skyrmions has been suggested. Relation between symmetry based predictions and direct calculation has been shown. It was shown that electric dipole moment of the vortex is located inside the small vortex core. The antivortices and antiskyrmions do not carry the total core electric dipole induced by the flexomagnetoelectric interaction in the hexoctahedral cubic crystal. The volumetric bound electric charge is distributed around the core. Switching of the core electric dipole direction produces the switching of the core magnetization or vortex chirality and vice versa. The vortices and skyrmions with time-invariant enantiomorphism have two degenerative states: clockwise and counterclockwise state.     

Low-frequency resonance of domain walls in the iron garnet Tb3Fe5O12 near the magnetic compensation point

The vibrational motion dynamics of domain walls (DWs) in the iron garnet Tb₃Fe₅O₁₂, a low-frequency magnetic field, and the temperature range 200–295 K (which includes the magnetic compensation point of this ferrimagnet, T _c ≈ 249 K) is studied by a magnetooptical method. The temperature dependence of the DW vibration amplitude in this garnet crystal near T _c has a resonance character. A theoretical model of the magnetic resonance of DWs is proposed to interpret the obtained experimental results; according to this model, the DW mass tends to infinity and the resonance frequency tends to zero when temperature approaches the magnetic compensation point.     

复合外场中磁光材料(BiTm)3(FeGa)5O12薄膜畴壁运动特性的研究

通过对BiTm)₃(FeGa)₅O₁₂膜施工加低频交变磁场,匀速率增加的直流磁场和同时对该膜施加这两种磁场(复合外场),用照相划线读数方法和通过电荷耦合器件(CCD)-计算机作数字化处理获得磁畴壁(DW)的相对百分数。结果表明:(1)复合外场下DW运动规律中存在交互作用项;(2)低频交变磁场幅值(140A/m)远低于等效阻力场(10³A/m)时,DW可以运动,但不同步,频率大于1Hz时明显滞后,(3)利用图像转换有利于提高实验结果的分辨率。     

The defects influence on domain wall propagation in bistable glass-coated microwires

We studied the domain wall (DW) dynamics of magnetically bistable amorphous glass-coated Fe₇₄B₁₃Si₁₁C₂ microwires. In according to our experimental results magnetic field dependences of DW velocity of studied microwires can be divided into two groups: with uniform or uniformly accelerated DW propagation along the microwire. Strong correlation between the type of the magnetic field dependence of domain wall velocity, v(H), and the distribution of the local nucleation fields has been observed.Moreover, we observed abrupt increasing of DW velocity (jump) on the magnetic field dependences of the domain wall velocity, v(H), for the both types of the v(H) dependences. At the same time usual linear increasing of the domain wall velocity with magnetic field persists below these jumps. It was found that the jump height correlates with the location of nucleation place of the new domain wall. We have measured local nucleation field distribution in all the microwires. From local nucleation field distribution we have obtained the DW nucleation locations and estimated the jump height     

Domain-wall resistance in ferromagnetic (Ga,Mn)As

A series of microstructures designed to pin domain walls (DWs) in (Ga,Mn)As with perpendicular magnetic anisotropy has been employed to determine extrinsic and intrinsic contributions to DW resistance. The former is explained quantitatively as resulting from a polarity change in the Hall electric field at DW. The latter is 1 order of magnitude greater than a term brought about by anisotropic magnetoresistance and is shown to be consistent with disorder-induced mistracking of the carrier spins subject to spatially varying magnetization.     

Directed motion of domain walls in biaxial ferromagnets under the influence of periodic external magnetic fields

Directed motion of domain walls (DWs) in a classical biaxial ferromagnet placed under the influence of periodic unbiased external magnetic fields is investigated. Using the symmetry approach developed in this article the necessary conditions for the directed DW motion are found. This motion turns out to be possible if the magnetic field is applied along the easiest axis. The symmetry approach prohibits the directed DW motion if the magnetic field is applied along any of the hard axes. With the help of the soliton perturbation theory and numerical simulations, the average DW velocity as a function of different system parameters such as damping constant, amplitude, and frequency of the external field, is computed.     

On the effect of inhomogeneous magnetoelectric (flexomagnetoelectric) interaction on the spectrum and properties of magnons in multiferroics

The features of the magnon spectrum in easy-plane multiferroics (such as BiFeO₃), which allow inhomogeneous magnetoelectric (flexomagnetoelectric) interaction P[(L?)L ? LdivL], where L and P are the antiferromagnetic moment and electric polarization, respectively, have been theoretically analyzed. It has been shown that, in contrast to the magnon spectrum of a usual easy-plane antiferromagnet, a multiferroic with this magnetic structure is characterized by, first, the interaction between magnons of both branches propagating along the weak ferromagnetic moment and the appearance of a minimum (or zero) of the frequency of one of the branches, which reflects the instability of the system with respect to the transition to an inhomogeneous state with increasing flexomagnetoelectric interaction and, second, the nonequivalence (nonreciprocity) of the propagation of spin waves along and against the antiferromagnetism vector, which coincides with the toroidal moment in this system.     

Rashba coupling induced spin accumulation in two-dimensional domain wall

Non-equilibrium spin accumulation in two-dimensional domain wall (DW) in the presence of external electric field and Rashba type spin-orbit coupling within the Boltzmann semi-classical model is investigated. Transport and relaxation of spin polarized current in the DW is governed by spin-flip rates which are determined by the Rashba interaction and magnetic impurities. Numerical results show that at low impurity densities and nonadiabatic transport regimes, the Rashba interaction significantly enhances spin polarization of conduction electrons inside the DW.     

Electric polarization of magnetic textures: New horizons of micromagnetism

A common scenario of magnetoelectric coupling in multiferroics is the electric polarization induced by spatially modulated spin structures. It is shown in this paper that the same mechanism works in magnetic dielectrics with inhomogeneous magnetization distribution: the domain walls and magnetic vortexes can be the sources of electric polarization. The electric field driven magnetic domain wall motion is observed in iron garnet films. The electric field induced nucleation of vortex state of magnetic nanodots is theoretically predicted and numerically simulated. From the practical point of view the electric field control of micromagnetic structures suggests a low-power approach for spintronics and magnonics.     

Density functional theory description of the mechanism of ferromagnetism in nitrogen-doped SnO2

Based on first-principles calculations, we have studied the occurrence of spin polarization in the magnetic metal oxide SnO₂ doped with nonmagnetic nitrogen (N) impurities. It was found that the local magnetic moments are localized mainly on the N dopant, causing a total moment of 0.95μB per cell. The long-range magnetic coupling of N-doped SnO₂ may be attributed to a p-p coupling interaction between the N impurity and host valence states.     

Vertex correction of the anisotropic magnetic impurities to the spin polarization of 2D electron gas

In terms of Kubo's formula and Green's function method, for the two-dimensional electron gas (2DEG) with Rashba spin-orbit coupling (SOC), we study the spin polarization due to the effect from magnetic impurities with anisotropic spin dependent delta type coupling to electrons when an external dc electric field in plane is applied. The vertex correction of impurities in ladder approximation is carried out in the limit of EF?1/τ, Δ. We find that the strength of spin polarization can be significantly modified by vertex correction and the spin polarization is relevant to the anisotropy coefficient γ, but the direction of net spin polarization cannot be changed.     

Three‐Dimensional,Time‐Resolved Profiling of Ferroelectric Domain Wall Dynamics by Spectral‐Domain Optical Coherence Tomography

We apply here spectral‐domain optical coherence tomography (SD‐OCT) for the precise detection and temporal tracking of ferroelectric domain walls (DWs) in magnesium‐doped periodically poled lithium niobate (Mg:PPLN). We reproducibly map static DWs at an axial (depth) resolution down to ～ 0.6 μm, being located up to 0.5 mm well inside the single crystalline Mg:PPLN sample. We show that a full 3‐dimensional (3D) reconstruction of the DW geometry is possible from the collected data, when applying a special algorithm that accounts for the nonlinear optical dispersion of the material. Our OCT investigation provides valuable reference information on the DWs’ polarization charge distribution, which is known to be the key to the electrical conductivity of ferroelectric DWs in such systems. Hence, we carefully analyze the SD‐OCT signal dependence both when varying the direction of incident polarization, and when applying electrical fields along the polar axis. Surprisingly, the large backreflection intensities recorded under extraordinary polarization are not affected by any electrical field, at least for field strengths below the switching threshold, while no significant signals above noise floor are detected under ordinary polarization. Finally, we employed the high‐speed SD‐OCT setup for the real‐time DW tracking upon ferroelectric domain switching under high external fields.     

Toroidal moments as indicator for magneto-electric coupling: the case of BiFeO<Subscript>3</Subscript> versus FeTiO<Subscript>3</Subscript>

In this paper we present an analysis of the magnetic toroidal moment and its relation to the various structural modes in R3c-distorted perovskites with magnetic cations on either the perovskite A or B site. We evaluate the toroidal moment in the limit of localized magnetic moments and show that the full magnetic symmetry can be taken into account by considering small induced magnetic moments on the oxygen sites. Our results give a transparent picture of the possible coupling between magnetization, electric polarization, and toroidal moment, thereby highlighting the different roles played by the various structural distortions in multiferroic BiFeO₃ and in the recently discussed isostructural material FeTiO₃, which has been predicted to exhibit electric field-induced magnetization switching.     

Spin chirality and electric polarization in multiferroic compounds (, Er)

Polarized neutron diffraction experiments have been performed on multiferroic materials RMn₂O₅ (R=Ho, Er) under electric fields in the ferroelectric commensurate (CM) and the low-temperature incommensurate (LT-ICM) phases, where the former has the highest electric polarization and the latter has reduced polarization. It is found that, after cooling in electric fields down to the CM phase, the magnetic chirality is proportional to the electric polarization. Also we confirmed that the magnetic chirality can be switched by the polarity of the electric polarization in both the CM and LT-ICM phases. These facts suggest an intimate coupling between the magnetic chirality and the electric polarization. However, upon the transition from the CM to LT-ICM phase, the reduction of the electric polarization is not accompanied by any reduction of the magnetic chirality, implying that the CM and LT-ICM phases contain different mechanisms of the magnetoelectric coupling.     

Local structure of multiferroic RMn2O5: Important role of the R site

The temperature and magnetic field dependent local structure of RMn₂O₅ systems was examined. While no significant displacements of the Mn ions are observed, it is found that the R-O distribution exhibits changes at low temperature which are possibly related to the changes in the electric polarization. Density functional computations are used to explore the system dynamics and to link the local structural measurements with anomalous changes in the infrared absorption spectra. The anomalous R-O distribution and observed coupling to magnetic fields point to the need to properly treat the 4f electrons on the R sites in these systems.     

Scattering polarization in the presence of magnetic and electric fields

The polarization of radiation by scattering on an atom embedded in combined external quadrupole electric and uniform magnetic fields is studied theoretically. Limiting cases of scattering under Zeeman effect, and Hanle effect in weak magnetic fields are discussed. The theory is general enough to handle scattering in intermediate magnetic fields (Hanle-Zeeman effect) and for arbitrary orientation of magnetic field. The quadrupolar electric field produces asymmetric line shifts, and causes interesting level-crossing phenomena either in the absence of an ambient magnetic field, or in its presence. It is shown that the quadrupolar electric field produces an additional depolarization in the Q/I profiles and rotation of the plane of polarization in the U/I profile over and above that arising from magnetic field itself. This characteristic may have a diagnostic potential to detect steady-state and time-varying electric fields that surround radiating atoms in solar atmospheric layers.     

Spin-polarized transport in one-dimensional waveguide structures with spatially-periodic electronic and magnetic fields

We investigate theoretically the spin-polarized transport in one-dimensional waveguide structure with spatially-periodic electronic and magnetic fields. The interplay of the spin-orbit interaction and in-plane magnetic field significantly modifies the spin-dependent transmission and the spin polarization. The in-plane magnetic fields increase the strength of the Rashba spin-orbit coupling effect for the electric fields along y axis and decrease this effect for reversing the electric fields, even counteract the Rashba spin-orbit coupling effect. It is very interesting to find that we may deduce the strength of the Rashba effect through this phenomenon.