Total Moment Sum Rule for Magnets in the Vicinity of Quantum Critical Point

TL;DR

This paper derives a total moment sum rule for quantum magnetic systems near a quantum critical point, accounting for both longitudinal and transverse excitations, aiding the analysis of neutron scattering data.

Contribution

It introduces a sum rule based on extended spin-wave theory that includes longitudinal modes, applicable to specific spin systems with anisotropy or dimerization.

Findings

Sum rule decomposes into elastic, one-magnon, and two-magnon parts.

Applicable to $S=1$ systems with easy-plane anisotropy and spin dimers.

Facilitates interpretation of inelastic neutron scattering measurements.

Abstract

It is known that the longitudinal and transverse excitation modes can exist in the vicinity of a quantum critical point in the ordered phase of quantum magnetic systems. The total moment sum rule for such systems is derived on the basis of the extended spin-wave theory, where both longitudinal and transverse magnetic excitations are taken into account. The sum rule is resolved into elastic, one-magnon, and two-magnon components. The formulation is applicable to spin systems with the longitudinal mode, such as $S=1$ systems with single-ion anisotropy of easy-plane type and spin dimer systems. The result helps us analyze and understand measured data of inelastic neutron scattering.