Macroscopic Quantum Tunneling of a Domain Wall in a Ferromagnetic Metal

TL;DR

This paper investigates the quantum tunneling behavior of magnetic domain walls in ferromagnetic metals, highlighting the significant impact of dissipation on tunneling rates, especially for thin walls, using an instanton approach based on the Hubbard model.

Contribution

It introduces a novel analysis of macroscopic quantum tunneling in ferromagnetic metals considering dissipation effects from itinerant electrons, extending previous insulator models.

Findings

Dissipation significantly reduces tunneling rates for thin domain walls.

Ohmic dissipation persists at zero temperature due to gapless Stoner excitations.

Thick domain walls experience negligible dissipation effects.

Abstract

The macroscopic quantum tunneling of a planar domain wall in a ferromagnetic metal is studied by use of an instanton method. Based on the Hubbard model, the effective action of the magnetization is derived within the assumption of slow dependences on space and time. The resulting action is formally similar to that of a ferromagnetic Heisenberg model but with a term non-local in time that describes the dissipation due to the itinerant electron. The crucial difference from the case of the insulator is the presence of the ohmic dissipation even at zero temperature due to the gapless Stoner excitation. The reduction of the tunneling rate due to the dissipation is calculated. The dissipative effect is found to be very large for a thin domain wall with thickness of a few times the lattice spacing, but is negligible for a thick domain wall. The results are discussed in the light of recent experiments on ferromagnets with strong anisotropy. (Submitted to J. Phys. Soc. Jpn)