Nonlinear magnetoacoustic interactions in weak ferromagnets

The pinning and interaction of a single domain wall with normal magnetoelastic waves excited during its motion in a single-crystal yttrium orthoferrite plate, were discovered and investigated by a method based on the magneto-optical Faraday effect. The dependences of the bending wave amplitude and the spectra of shear waves, which can be excited by a moving domain wall, were calculated. The results obtained are interpreted with allowance for the interactions of excited oscillations in both the magnetic and elastic subsystems of the orthoferrite.     

Dynamics of antiferromagnetic vortices in yttrium orthoferrite domain walls

The total velocity of solitary flexural waves nonlinearly increases with an increase in the velocity of domain walls and becomes saturated at a level of 20 km s^?1; the smaller the wave amplitude, the more rapidly saturation occurs. Counter collisions of solitary flexural waves lead to the formation of a single wave with a difference amplitude moving in the same direction as the wave with a larger amplitude. The experimental results confirm that solitary flexural waves accompany antiferromagnetic vortices at domain walls in yttrium orthoferrite.     

Solitary flexural waves on a supersonic domain wall in yttrium orthoferrite

Solitary flexural waves on a supersonic domain wall in yttrium orthoferrite are observed and investigated. These waves have a sharp leading edge and a protracted trailing edge, reminiscent of the waves accompanying moving vertical Bloch lines in iron garnet films. The total velocity of the solitary flexural waves in yttrium orthoferrites for all observed amplitudes equals the maximum velocity of the domain walls. Two solitary waves with identical amplitudes colliding head-on are annihilated. The waves possess topological charges, and they move and form dynamic profiles under the influence of gyroscopic forces. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 10, 760–765 (25 May 1997)     

Generation of pairs of antiferromagnetic vortices and their dynamics at a domain wall in yttrium orthoferrite

The stable generation of pairs of antiferromagnetic vortices at a domain wall moving at a velocity of 12 km/s is investigated at the instant it passes through a defect in a thin plate of yttrium orthoferrite. The velocities of a vortex and an antivortex moving in opposite directions along the domain wall and being accompanied by solitary flexural waves are ±16 km/s. The total velocity of antiferromagnetic vortices is close to the maximum velocity of the domain wall, 20 km/s. Such a high velocity can only be due to the action of a quite large gyroscopic force. An external dc magnetic field (±400 Oe) applied along the b axis of the orthoferrite affects this velocity insignificantly. The effective magnetic field that violates the Lorentz invariance of the dynamics considerably exceeds this value.     

Solitary deflection waves on the supersonic domain wall in yttrium orthoferrite

The moving antiferromagnetic vortices are accompanied by solitary deflection waves. These waves allow to investigate generation and nonlinear dynamics of the antiferromagnetic vortices on the moving domain wall with the help of the two- and three-fold digital high speed photography. On the quasi-relativistic domain wall the vortex dynamics is quasi-relativistic with the limiting velocity c=20 km/s, which is equal to the spin-wave velocity. The solitary deflection waves dynamics can be explained assuming existence of the gyroscopic force. A theory for the gyroscopic force in the orthoferrite domain wall is elaborating by A.K. Zvezdin et al. currently. We present a comparison of the theoretical and experimental results on the dynamics of the solitary deflection waves, which accompany the antiferromagnetic vortices in the domain wall of orthoferrites.     

Generation, dynamics, and collisions of bending waves at domain boundaries in yttrium orthoferrite

Solitary bending waves have been observed on domain boundaries of Néel type in wafers of yttrium orthoferrite, having a very sharp leading edge and an extended trailing edge and offset as a whole from the domain boundary and moving with high speeds close to the limiting velocity. Head-on collisions of two such waves of the same amplitude lead to their complete annihilation. Analogous collisions of two such waves, but of different amplitudes, lead to the appearance of a wave with the difference amplitude moving in the same direction as the wave of larger amplitude. The solitary bending waves investigated in this study appear to move under the action of gyroscopic forces acting on magnetic vortices on domain boundaries in yttrium orthoferrite, analogous to vertical Bloch lines with departure of the magnetization vector from the ac plane. From equality of the gyroscopic force with the friction force acting on the leading edge of the solitary bending wave we have estimated the amplitudes of these waves and the magnitudes of the topological charges of the magnetic vortices. Zh. éksp. Teor. Fiz. 115, 2160–2169 (June 1999)     

Effect of a hard-magnetic surface layer in domain structures in the region of spontaneous spin-reorientation phase transition in erbium orthoferrite plates

The rearrangement of domain structures in erbium orthoferrite plates with a hard-magnetic surface layer has been visually investigated and explained on the basis of proposed physical models. It is shown that, when the temperature of such plates approaches the temperature range of spin reorientation, the surface energy density of the domain walls separating the internal and surface domains decreases, resulting in a transition to domain structures that are close to equilibrium.     

Reflection of antiferromagnetic vortices on a supersonic domain wall in yttrium orthoferrite

Reflection of solitary flexural waves propagating in a supersonic domain wall of yttrium orthoferrite from the domain wall part moving with the transverse-sound velocity is observed experimentally. This observation confirms that such a reflection of a solitary flexural wave leads to a change in the sign of the topological charge of the antiferromagnetic vortex accompanied by this wave, which proves a direct relationship between these two objects.     

Excitation of bending vibration by a moving domain wall in a plate of yttrium orthoferrite

Elastic vibrations have been experimentally found induced by a moving domain wall in a sample of yttrium orthoferrite 10⁻⁴ m thick. Calculations have been carried out to suggest their relevance to flexural Lamb waves.     

Magnetostrictive domain walls in antiferromagnetic NiO

We report high-resolution observations of antiferromagnetic (AF) domain walls at the surface of NiO and determine the typical width of AF walls in this material to be of the order of 150 nm. We observe a number of different types of domain walls, including double walls caused by long-range interaction between walls. We describe the observed wall profiles by a model containing the exchange interaction and magnetostriction as basic ingredients. The good agreement of this model with experiment shows that the formation of walls between antiferromagnetic domains in NiO and their properties are dominated by magnetoelastic interactions.     

Electroacoustic waves confined by a moving domain wall superlattice of a ferroelectric crystal

The dispersion properties of electroacoustic wave modes confined by a superlattice of uniformly moving 180° domain walls in a tetragonal ferroelectric crystal are considered. It is shown that the manifold of partial electroacoustic interfacial waves in the lattice is restricted to the first allowed band, the configuration of which in the plane of spectral variables can significantly vary under the action of the moving domain walls.     

Specific Features in the Spectrum of Nonlinear Magnetoelastic Waves Propagating in a (111) Plate with Combined Anisotropy

Nonlinear magnetoelastic waves with stationary profiles propagating in a cubic ferromagnetic with [111] uniaxial induced anisotropy are investigated theoretically. It is demonstrated that a new type of nonlinear waves engendered by the resonant motion of the 60-degree domain wall propagates along the [111] axis without magnetization escape from the plane of spin rotation. Some other cases of nonlinear magnetoelastic wave propagation in the examined magnetic are also studied.     

Excitation spectrum and thermodynamics of domain walls in the biaxial ferromagnet

The problem on spectrum of linear excitations in the presence of a moving domain wall in 1D Heisenberg ferromagnet with orthorhombic anisotropy is exactly solved. The explicit expressions for spin waves scattering on the domain wall are obtained. The phase shift of a spin wave, as the result of collision of spin wave with a moving wall, is exactly determined. The change in magnon density of states is calculated from this scattering data, and the contribution of domain walls to the classical low-temperature thermodynamics is found.     

Dynamics of domain walls under the action of pulse and gradient magnetic fields in rare-earth orthoferrites

Experimental and theoretical investigations of solitary domain wall dynamics in an yttrium orthoferrite plate under the action of a pulse magnetic field were carried out. The investigations are performed under conditions in which the change in the gradient magnetic field is comparable to the magnitude of the pulse magnetic field shifting the domain walls when the latter are displaced from their equilibrium position.     

Dynamics of a Néel domain wall with a fine structure in rare-earth orthoferrites

The dynamics of an isolated domain wall (DW) with a fine structure moving at a supersonic velocity in a rare-earth orthoferrite is studied. A set of nonlinear equations of motion of the center of a DW structure line is derived. A steady-state solution to these equations adequately describes the experimental data for yttrium orthoferrite. The effect of an external magnetic field on the steady-state velocity of a DW with structural lines is investigated.     

Reflection of electroacoustic waves from a system of moving domain walls in a ferroelectric

The interaction of electroacoustic waves with a periodic domain structure formed in a tetragonal ferroelectric by a finite number of uniformly moving 180° domain walls is considered in the quasi-static approximation. It is established that the inclusion of the domain-wall motion leads to a significant modification of the reflectance spectra of electroacoustic waves according to the number, intensity, and location of the Bragg reflectance peaks.     

Interaction of a shear wave with a moving domain wall in a ferromagnetic crystal with allowance for the external magnetic field

The boundary-value problem of the magnetoelastic wave interaction with a moving domain wall in a ferromagnetic crystal is solved in the nonexchange magnetostatic approximation with allowance for the external magnetic field. It is shown that the difference introduced by magnetic field between the ferromagnetic resonance frequencies of the domains does not cause any noticeably departure of the refraction characteristics of reflected and transmitted waves from those observed at zero frequency mismatch. By contrast, the magnitudes of the transmission and reflection coefficients strongly depend on the external magnetic field and on the mobility of the domain wall. The dependence of the magnitude of the reflection coefficient on the external magnetic field at a fixed angle of shear wave incidence is found to possess two ferromagnetic resonance peaks. The positions and heights of the peaks may vary depending on the mobility of the domain wall.     

Spectral properties of electroacoustic waves in a ferroelectric with a moving periodic domain structure

The propagation of shear waves in a tetragonal ferroelectric with a moving superlattice of 180° domain walls (DW) is considered in a quasistatic approximation. It is found that the spectrum of shear waves consists of alternating allowed and forbidden bands in both cases of static and moving superlattices. It is shown that, due to the Doppler shift in the wave eigenfrequencies, the motion of the DW superlattice causes the degenerate roots of the dispersion equation to split and the splitting increases with the vibration mode number. The acoustic nonreciprocity induced by the moving DW superlattice in the ferroelectric is discussed.