Effective field theory of magnon: Dynamics in chiral magnets and Schwinger mechanism

Abstract

We develop the effective field theoretical descriptions of spin systems in the presence of symmetry-breaking effects: the magnetic field, single-ion anisotropy, and Dzyaloshinskii-Moriya interaction. Starting from the lattice description of spin systems, we show that the symmetry-breaking terms corresponding to the above effects can be incorporated into the effective field theory as a combination of a background (or spurious) $\SO(3)$ gauge field and a scalar field in the symmetric tensor representation, which are eventually fixed at their physical values. We use the effective field theory to investigate mode spectra of inhomogeneous ground states, with focusing on one-dimensionally inhomogeneous states, such as helical and spiral states. Although the helical and spiral ground states share a common feature of supporting the gapless Nambu-Goldstone modes associated with the translational symmetry breaking, they have qualitatively different dispersion relations: isotropic in the helical phase while anisotropic in the spiral phase. We also discuss the magnon production induced by an inhomogeneous magnetic field, and find a formula akin to the Schwinger formula. Our formula for the magnon production gives a finite rate for antiferromagnets, and a vanishing rate for ferromagnets, whereas that for ferrimagnets interpolates between the two cases.

45 pages, 8 figures

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Cited by in corpus (6)

• Advances in QED with intense background fields
• Spin relaxation rate for heavy quarks in weakly coupled QCD plasma
• Magnon dynamics in a Skyrmion-textured domain wall of antiferromagnets
• Exact Ground States and Domain Walls in One Dimensional Chiral Magnets
• Effective field theory of fluctuating wall in open systems: from a kink in Josephson junction to general domain wall
• Schwinger mechanism of magnon-antimagnon pair production on magnetic field inhomogeneities and the bosonic Klein effect