Coupled magnetoelastic waves in ferromagnetic shape-memory alloys

Damping of Magnetoelastic Waves

“…The magnetoelastic component of the dissipative function is constructed on the basis of similar principles and considerations. From expressions (6) and (7), it follows that must consist of the time derivatives of the strain tensor and the components of the effective magnetic field. It is known that the dissipative function must be invariant with respect to the transformations of the crystal symmetry group.…”

“…However, this interaction reveals itself substantially in the case of magnetoacoustic resonance, when the spin-wave frequency approaches the sound frequency, and the quasispin and quasisound branches in the wave spectrum begin to repulse each other [3,4]. The results of relevant studies also demonstrate that the magnetoelastic interaction increases, if magnetically ordered systems approach the point of spin-reorientation phase transition [4] or structural phase transition in the lattice [6,7].…”

Interaction of Elastic and Spin Waves in a Uniaxial Ferromagnet

“…Here, is the magnetic energy of the crystal. In the case of uniaxial ferromagnet, it looks like [11]…”

“…) can be described by considering a magnetoacoustic resonance at the corresponding frequency ℎ = [11,12]. In this case, the dispersion laws of coupled magnetoelastic oscillations are transformed into the following dispersion equation, which has a common form for all ground states and wave vector directions:…”

“…This dispersion law consists of two branches: quasimagnon and quasiphonon ones [11,12]. From expression (25), we can easily see that, when the system approaches the magnetoacoustic resonance, → ℎ , it is the quantities and that govern the "repulsion" between the quasimagnon and quasiphonon branches.…”