TY - JOUR

T1 - Effective field theory of magnons

T2 - Chiral magnets and the Schwinger mechanism

AU - Hongo, Masaru

AU - Fujimori, Toshiaki

AU - Misumi, Tatsuhiro

AU - Nitta, Muneto

AU - Sakai, Norisuke

N1 - Publisher Copyright:
©2021 American Physical Society

PY - 2021/10/1

Y1 - 2021/10/1

N2 - 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) 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, focusing on one-dimensionally noncollinear 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 clarify the reason for this qualitative difference based on the symmetry-breaking pattern. As another application, we 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.

AB - 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) 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, focusing on one-dimensionally noncollinear 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 clarify the reason for this qualitative difference based on the symmetry-breaking pattern. As another application, we 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.

UR - http://www.scopus.com/inward/record.url?scp=85116730411&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85116730411&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.104.134403

DO - 10.1103/PhysRevB.104.134403

M3 - Article

AN - SCOPUS:85116730411

SN - 2469-9950

VL - 104

JO - Physical Review B

JF - Physical Review B

IS - 13

M1 - 134403

ER -