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

Abstract

It is shown that at low temperatures, quantum oscillations of nanoscale structural inhomogeneities (the vertical Bloch line and the Bloch point) occur in the domain walls of cylindrical magnetic domains formed in a uniaxial magnetic film with strong magnetic anisotropy. The conditions for the excitation of these oscillations are determined.

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

“…Taking into account that the VBL velocity can be represented as v L  =  ω L A n , where is a “quasiclassical” amplitude of VBL oscillations [15], the expression for F r can be rewritten as …”

“…This problem was studied by us in [15, 24] for small oscillations of Bloch point and vertical Bloch line stabilized by magnetic field in a domain wall of magnetic bubble, where the quantum nature of the change of DW gyrotropic bending was established. Obviously, this effect should also appear in the oscillations of interacting vertical Bloch lines in a DW of stripe domain.…”

“…Let us compare the average energy of vertical Bloch line in uniform magnetic field H x directed along the axis of its oscillations with the “interstate” energy gap ΔW L  =  ℏω L (where ℏ is the Planck constant) (see [15, 22]). Using (7) and (14), after some transformations, we find that n  > > 1 (i.e., quantum transitions from the ground level to quasiclassical zone are considered), and so if the external fields satisfy inequation …”

“…It should be noted that small oscillations of vertical Bloch line in a domain wall of magnetic bubble were studied in [15]. However, the stiffness factor of these oscillations was not associated with the interaction between vertical Bloch lines and was provided by magnetic field applied normally to VBL.…”

“…In this system, there are exchange and magnetostatic interactions between the vertical Bloch lines; as shown below, the resultant force causes minor oscillations of VBL. At the same time, the VBL and Bloch points (intersections of two VBLs) exhibit macroscopic quantum properties at low temperatures (T < 1 K) [10–15]. It is natural to assume that this feature of structural inhomogeneities in DW will be reflected both in the quantum dynamics of two interacting VBLs and in the properties of new data storage devices on their basis.…”