Symmetry theory of the flexomagnetoelectric effect in the magnetic domain walls

A local flexomagnetoelectric (A.P. Pyatakov, A.K. Zvezdin, 2009) effect in the magnetic domain walls (DWs) of the cubic hexoctahedral crystal has been investigated on the basis of a symmetry analysis. The strong connection between magnetic symmetry of the DW and the type of the distribution of the electric polarization was shown. Results were systemized in the scope of the DW chirality. It was shown, that new type of the local flexomagnetoelectric coupling corresponds to the presence of the coupled electric charge in the DW. It was found that all time-noninvariant chiral DWs have identical type of spatial distribution of the magnetization and polarization. There are coincidence between the symmetry predictions and results obtaining from the known term of the flexomagnetoelectric coupling for transverse polarization components.     

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.     

Effect of magnetoelectrical interactions on the multiferroic domain walls

The antiferromagnetic domain structure of a multiferroic has been investigated in the presence of a ferroelectric domain structure. It has been demonstrated that an inhomogeneous magnetoelectric (flexomagnetoelectric) interaction leads to pinning of antiferromagnetic domain walls at the walls of the ferroelectric domains and to a change in the structure of antiferromagnetic domain walls.     

Ferroelectricity in spiral magnets

It was recently observed that the ferroelectrics showing the strongest sensitivity to an applied magnetic field are spiral magnets. We present a phenomenological theory of inhomogeneous ferroelectric magnets, which describes their thermodynamics and magnetic field behavior, e.g., dielectric susceptibility anomalies at magnetic transitions and sudden flops of electric polarization in an applied magnetic field. We show that electric polarization can also be induced at domain walls and that magnetic vortices carry electric charge.     

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.     

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.     

Effect of 90° domain walls on the low-field permittivity of PbZr(0.2)Ti(0.8)O3 thin films

We report on the contribution of 90° ferroelastic domain walls in strain-engineered PbZr(0.2)Ti(0.8)O(3) thin films to the room-temperature permittivity. Using a combination of phenomenological Ginzburg-Landau-Devonshire polydomain thin-film models and epitaxial thin-film growth and characterization, the extrinsic or domain wall contribution to the low-field, reversible dielectric response is evaluated as a function of increasing domain wall density. Using epitaxial thin-film strain we have engineered a set of samples that possess a known quantity of 90° domain walls that act as a model system with which to probe the contribution from these ferroelastic domain walls. We observe a strong enhancement of the permittivity with increasing domain wall density that matches the predictions of the phenomenological models. Additionally, we report experimentally measured bounds to domain wall stiffness in such PbZr(0.2)Ti(0.8)O(3) thin films as a function of domain wall density and frequency.     

Reorientation,multidomain states and domain walls in diluted magnetic semiconductors

The competition between surface/interface and intrinsic anisotropies yields a number of specific reorientation effects and strongly influences magnetization processes in diluted magnetic semiconductors as (Ga,Mn)As and (In,Mn)As. We develop a phenomenological theory to describe reorientation transitions and the accompanying multidomain states applicable to layers of these magnetic semiconductors. It is shown that the magnetic phase diagrams of such systems include a region of four-phase domain structure with four adjoining areas of two-phase domains as well as several regions with coexisting metastable states. We demonstrate that the parameters of isolated domain walls in (Ga,Mn)As nanolayers are extremely sensitive to applied magnetic field and can vary in a broad range. This can be used in microdevices of magnetic semiconductors with pinned domain walls. For (Ga,Mn)As epilayers with perpendicular anisotropy the geometrical parameters of domains have been calculated.     

Dynamics of <Emphasis Type="Italic">ab</Emphasis>-type domain walls in magnets with quadratic magnetoelectric interaction

The dynamics of the ab-type 180-degree domain walls was studied in weak ferromagnets with quadratic magnetoelectric interaction in alternating magnetic and electric fields. The features of the oscillatory and drift motion of the domain walls are discussed. The drift velocity of the ab-type domain walls as a function of the frequency and phase shift of the external fields is obtained. The possibility of the drift of the domain walls in a purely electric field is established.     

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.     

Dynamics of domain walls in weak ferromagnets with quadratic magnetoelectric interaction

The dynamics of domain walls of the ab type in weak ferromagnets with a quadratic magnetoelectric interaction has been studied in ac magnetic and electric fields. The specific features of the vibrational and drift motions of the domain walls as functions of parameters of the external fields and characteristics of the material have been discussed. The possibility of drift occuring the domain walls in a purely electric field has been predicted.     

Polarization relaxation in a ferroelectric crystal having different states of the domain structure and surface

Slow polarization relaxation of a ferroelectric in a weak electric field is investigated in triglycine sulfate crystals with different states of the domain structure and surface. An automated setup is described that allows one to register relaxation with record accuracy. It is shown that under conditions of little change in the “degree of metastability” of the structure, the variation of the polarization ΔP with time t follows the law ΔP=C/(1+t/ta)ⁿ in all cases, where the parameters C, a, and n depend on the state of the structure and the surface. We present a phenomenological analysis of the experimental data based on the assumption that the nuclei are independent and contribute additively to the total polarization of the crystal, and construct spectra of the energy barriers of the domain walls. Aspects of the transformation of the spectra with variation of the nature of the domain structure, depth of surface relief, and magnitude of the external electric field are elucidated. Fiz. Tverd. Tela (St. Petersburg) 39, 2046–2052 (November 1997)     

Effect of piezomagnetism on coupling of electric and magnetic domain walls in hexagonal manganites

The profiles of antiferromagnetic domain walls in hexagonal manganites RMnO₃ are obtained numerically depending on anisotropy and internal strain due to the lattice distortion at the ferroelectric domain walls. It is found that the piezomagnetism can lower the free energy of the system thus it favors the coupling between electric and magnetic domain walls. Due to the piezomagnetic effect, the clamped antiferromagnetic domain walls with spin orientation angle ψ changing from 0 to π have different profiles comparing with those of ψ changing from 0 to -π, and the former is energetically more favorable than the latter when the internal strain is tensile at the FEL domain walls while it is the contrary for compressive strain. Moreover, the strongest coupling between the FEL domain walls and the favorable AFM domain walls can be achieved at an optimized internal strain.     

The decay of low-frequency elastic oscillations in a Ba2NaNb5O15 crystal

The internal friction and shear modulus of a barium sodium niobate crystal were studied using the torsion pendulum technique at a frequency of ～25 Hz in the temperature range from 80 to 800 K. An internal friction relaxation peak of the domain nature was observed at 228 K. A relaxation process responsible for this internal friction peak is explained through compensation of the electric charge (induced by a piezoelectric effect at the 180° domain walls) by charged point defects diffusing toward the domain walls.     

Electric field induced nuclear spin resonance mediated by oscillating electron spin domains in GaAs-based semiconductors

We demonstrate an alternative nuclear spin resonance using a radio frequency (rf) electric field [nuclear electric resonance (NER)] instead of a magnetic field. The NER is based on the electronic control of electron spins forming a domain structure. The rf electric field applied to a gate excites spatial oscillations of the domain walls and thus temporal oscillations of the hyperfine field to nuclear spins. The rf power and burst duration dependence of the NER spectrum provides insight into the interplay between nuclear spins and the oscillating domain walls.     

Magnetoelectric control of domain walls in a ferrite garnet film

A displacement of magnetic domain walls under the effect of an electric field is observed in epitaxial ferrite garnet films (on substrates with the (210) orientation). The displacement of the domain walls changes to the opposite when the electric field changes sign, and it is independent of the direction of magnetization in the domains. The mechanism proposed for explaining the observed phenomenon is based on the inhomogeneous magnetoelectric effect.     

Structure and dynamic properties of the twisted magnetic domain wall in an electric field

The structure of the domain wall in a magnetically uniaxial ferromagnetic film placed in an external electric field has been studied. It has been shown that the domain wall has a complex twisted structure whose characteristics (thickness, profile, and limit velocity of steady motion) depend on the film thickness, quality factor, and external electric field. The effect of the electric field on the domain wall is caused by inhomogeneous magnetoelectric coupling taking place in domain walls with a twisted structure.     

Analysis of the ferroelastic domains and phase transition in the K2SO4 crystal

Abstract

The domain structures of the β-K₂SO₄ crystal were analyzed by group theory. We obtained the permissible kinds of domain association and domain walls from the results of the group theory. It is suggested from the analysis that the (110) and (130) planes are W_mb walls. The value of the spontaneous strain of K₂SO₄ wast = 6.32 × 10^?3 at room temperature and also its temperature dependence was observed.     

Vacuum sampling in the landscape during inflation

We consider the phenomenological consequences of sampling multiple vacua during inflation motivated by an enormous landscape. A generic consequence of this sampling is the formation of domain walls, characterized by the scale mu of the barriers that partition the accessed vacua. We find that the success of big bang nucleosynthesis (BBN) implies mu > or = 10 TeV, as long as the sampled vacua have a nondegeneracy larger than O(MeV4). Otherwise, the walls will dominate and eventually form black holes that must reheat the universe sufficiently for BBN to take place; in this case, we obtain mu > or = 10(-5)MP. These black holes are not allowed to survive and contribute to cosmic dark matter density.