A general formalism for the determination of the effective mass of the nanoscale structural inhomogeneities of the domain wall in uniaxial ferromagnets

Abstract

On the basis of the method of gyrotropic Thiele forces, we build a formalism that allows the determination of the effective mass of the nanoscales structural elements of the domain wall (DW): vertical Bloch line and Bloch point in uniaxial ferromagnets. As shown, the effective mass of these magnetic inhomogeneities depends on the value of the gyrotropic domain wall bend that is created by their movement.Electronic supplementary materialThe online version of this article (doi:10.1186/s11671-015-0861-z) contains supplementary material, which is available to authorized users.

Quantum Oscillations of Interacting Nanoscale Structural Inhomogeneities in a Domain Wall of Magnetic Stripe Domain

“…Therefore, integrating (5) with the integrand near this point, we obtain an expression that matches well with the formula for the effective mass of VBL in [16, 19]: …”

“…We will determine the effective mass of the vertical Bloch line m L , using the general formalism proposed in [16]. To do this, we need to find the gyrotropic bending of DW due to the motion of VBL at velocity v L .…”

“…The effective mass of VBL can be found from the following equation (see [16]):where F g  = 2 πM S v L / γ is the gyrotropic force acting on the DW from the moving VBL.…”

Quantum Oscillations of the Nanoscale Structural Inhomogeneities of the Domain Wall in Magnetic Bubble

“…The above mentioned characteristics of q n,BL and q n,BP are consistent with the conclusions of Ref. [ 14 ] about the nature of DW gyrotropic bend caused by the dynamics of BL and BP. Besides, using formulae ( 13 ) and ( 14 ), one can find that at h → ∞ q n,BL , q n,BP → 0, i.e., the effect of quantum oscillations of nanoscale structural inhomogeneities in DW occurs only in thin films.…”

“…Evidently, the average value of work done by this external to DW force should be related to the BL kinetic energy [ 14 ]. Given this requirement, integration of ( 12 ) and some transformations of ( 1 )–( 4 ) allow establishing the quantum behavior of DW gyrotropic bending: …”