Tunneling and zero-point vibrations of 180°-domain walls in ferromagnetic materials

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Abstract
The experimentally established dependence of the velocity v of 180°-domain walls in four ferromagnetic Ni-base alloys on the applied magnetic field H and on temperature T is analyzed. T ranges from 1.3 to 5 K. The relation v(H,T) is governed by the interaction of the domain walls with obstacles. The temperature dependence of the walls’ release from these obstacles is derived from Gibbs’ formula. Below 2 K, quantum-mechanical effects noticeably enhance the release of domain walls from obstacles. This is analyzed in two alternative models: (i) tunneling of the domain wall is allowed for; (ii) the wall is treated as a harmonic oscillator, whose eigenstates are calculated quantum-mechanically. Zero-point vibrations are included in this model. These models lead to two alternative functions v(H,T). Both of them represent the experimental data nearly equally well, though the agreement for model (i) (tunneling) is slightly better. Fitting the two functions to the data yields two sets of adjustable parameters. An analysis of their magnitude favors model (i), indicating that in the investigated nickel-base alloys tunneling may be more important than zero-point vibrations for the mobility of 180°-domain walls.

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