Gyroscopic dynamics of antiferromagnetic vortices in the orthoferrite domain wall

The method of generation of antiferromagnetic vortices on the supersound domain wall in the orthoferrites was proposed. Moving antiferromagnetic vortices were accompanied by the solitary deflection waves. These waves were used for investigation of generation and nonlinear dynamics of the antiferromagnetic vortices on a moving domain wall with the help of two- and three-fold digital high-speed photography and Faraday rotation in the orthoferrites plates cut perpendicular to the optical axis. The full velocity of antiferromagnetic vortex nonlinearly increases and saturates on the spin velocity level c. The vortices with smallest topological charges saturate earlier than with big one. The vortices velocity along the domain wall u increases up to the maximum and goes to the dependence u²+v²=c². Vortex dynamics is quasirelativistic on quasirelativistic domain wall. The theory of gyroscopic force in the domain wall of orthoferrites was elaborated by Zvezdin et al. and was confirmed our earlier experimental results.     

Gyroscopic dynamics of antiferromagnetic vortices in domain boundaries of yttrium orthoferrite

It is established experimentally that the magnetic field directed along the b axis has little effect on the velocities of antiferromagnetic vortices in the domain boundary (DB) of yttrium orthoferrite and fails to explain the presence of an appreciable gyroscopic force acting on these vortices. This force is induced by the dynamic canting of magnetic sublattices proportional to the DB velocity. Due to the canting, the velocities of antiferromagnetic vortices depend initially quadratically on the DB velocity, as was experimentally found in this work. The dynamics of antiferromagnetic vortices in the yttrium orthoferrite DBs is gyroscopic and quasi-relativistic, with the limiting velocity of 20 km/s equal to the velocity of spin waves at the linear portion of their dispersion curve.     

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.     

Gyroscopic quasi-relativistic dynamics of antiferromagnetic vortex in domain boundary of yttrium orthoferrite

It is demonstrated that the quasi-relativistic dynamics of antiferromagnetic vortices in a quasi-relativistic domain boundary of yttrium orthoferrite are caused by the unusually strong gyroscopic force.     

Generation and gyroscopic quasi-relativistic dynamics of antiferromagnetic vortices in domain walls of yttrium orthoferrite

An unusual nonlinear relation between the velocity of an antiferromagnetic (AFM) vortex along a domain wall (DW) on the DW velocity is detected. This relation has a maximum whose position depends on the topological charge of the vortex. As the DW velocity increases from the value corresponding to the maximum to its limiting value, the AFM-vortex velocity decreases and tends to zero. The total AFM-vortex velocity increases nonlinearly with the DW velocity and levels off at 20 km/s, which is equal to the velocity of spin waves in the linear section of their dispersion law. The experimental data are approximated satisfactorily. The dynamics of AFM vortices in DWs of yttrium orthoferrite, just as the dynamics of the DWs, is quasi-relativistic and gyroscopic.     

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)     

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.     

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.     

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)     

Gyroscopic force acting on the magnetic vortex in a weak ferromagnet

The gyroscopic (Magnus) force in weak ferromagnets acting on magnetic vortices when the domain walls move in the external magnetic field has been investigated. The general expressions for the gyroscopic force in weak ferromagnets are obtained. The particular calculation of the gyroscopic force in rhombic weak ferromagnets is performed using the method that allows one to calculate it neglecting the internal structure of a vortex in the domain wall. It is shown that the gyroscopic force for most types of domain walls is nonzero and is determined by the mean sublattice magnetization, the Dzyaloshinsky interaction constant, and the constant of the exchange interaction between the sublattices.     

Domain wall dynamics near the limit velocity in a cubic ferromagnet with induced magnetic anisotropy

A research has been conducted into the dynamics of the 180° domain wall in a cubic ferromagnet with induced magnetic anisotropy, this domain wall moving at a velocity close to the limit one. The Landau–Lifshits equation has been reduced to a modified double Sine–Gordon equation with the highest dispersion. A solution has been found which corresponds to the moving 180° domain wall. This paper has determined the dependencies of the velocity of the domain wall's stationary movement on the quality factor and on the ratio of the induced and the cubic magnetic anisotropy constants in slabs with the developed (0 0 1) and (0 1 1) surfaces.     

Interaction of a moving domain wall with surface magnetoelastic waves in yttrium orthoferrite

The amplitude-frequency characteristics of magnetoelastic surface waves excited by moving domain walls in a lamellar yttrium orthoferrite samples are discovered and measured. The results of analysis of the effect of magnetoelastic surface waves on the dynamics of domain walls in this orthoferrite are considered. The nonlinear interaction between magnetoelastic surface waves accompanying a moving domain wall is analyzed.     

Steady motion of the magnetic vortex under the magnus force in weak ferromagnets

The problem of steady motion of the magnetic vortex in a moving domain wall under the action of the Magnus force in weak ferromagnets was studied. Dynamic bending of the domain wall containing a moving vortex was analyzed. The formulas describing the dependences of the vortex velocity on the velocity of the domain wall in which it moves were derived.     

Magnus force and magnetic vortex dynamics in weak ferromagnets

The problem of steady motion of the magnetic vortex in a moving domain wall under the action of the Magnus force in weak ferromagnets was studied. Dynamic bending of the domain wall containing a moving vortex was analyzed. The formulas describing the dependences of the vortex velocity on the velocity of the domain wall in which it moves were derived.     

Influence of an external electric field on the motion of a ferroelectric domain wall

The study of the influence of an external electric field on the motion from rest of a domain wall in ferroelectric crystals is presented. The solution of the problem representing the translational and rotational motions of the chain is sought in terms of solitary waves. Both electric and mechanical state of the structure in domains can be determined. The evolution of the velocity of the wall altered by the applied field is determined by means of energy arguments accounting for electromechanical couplings. A numerical simulation is given which illustrates the transient motion from rest of a wall separating two ferroelectric domains.     

Ginzburg-Landau theory and solitary waves in shape-memory alloys

A one-dimensional dynamic Ginzburg-Landau theory of the martensitic phase transition in shape-memory alloys is established. The nonlinear equations of motion yield solitary wave solutions of kink and of soliton type. The kink solutions which cannot move without external force represent single domain walls either between austenite and martensite or between two martensite variants. The soliton solutions correspond to a matrix of austenite or of martensite containing a moving sheet of the other phase. The velocity of the solitons depends on their amplitude. In the static case they reduce to the critical nucleus. The energy of each type of solitary waves is calculated.     

Unidirectional anisotropy of the velocity of domain walls in ferrite-garnet films

A mechanism to explain the gigantic unidirectional anisotropy of the velocity of domain walls, which includes the local rotation of the magnetization in front of a moving domain wall, initiated by radiated spin waves is proposed. Institute of General Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 45–48, September, 1997.     

Domain Wall Migration in 3-d in the Presence of Diffusing Impurities

A new three-dimensional simulation procedure was developed for domain wall (grain boundary, APB, magnetic, etc.) migration in the presence of diffusing impurities. The simulation is based upon a kinetic Monte Carlo algorithm and an extended Ising model, incorporating both conserved and non-conserved dynamics. The simulations show a dependence of the domain wall velocity on driving force which is very similar to that seen in 2-d and in qualitative agreement with experiment. That is, the presence of a low mobility regime at small driving force and an abrupt transition to a high mobility regime at larger forces, under some conditions, and a continuous, non-linear dependence of the velocity on the force in others. The main qualitative difference between the 2-d and 3-d simulation results is in how the domain wall roughness depends on driving force. The velocity-driving force relation is not consistent with classic continuum models, but may be described, in the high velocity regime, by a theory based upon a discrete version of these models.