Determining the range of magnetic interactions from the relations between magnon eigenvalues at high-symmetry k points

TL;DR

This paper introduces a method to determine the relevant range of magnetic exchange interactions in materials by analyzing magnon energies at high-symmetry points, avoiding complex matrix diagonalization.

Contribution

It presents a novel relation between magnon energies and exchange interactions, enabling estimation of interaction ranges from limited experimental data.

Findings

Relates magnon energies at high-symmetry points to exchange interaction range.

Provides a theoretical tool for tabulating the relation between SSME and interaction range.

Applicable to general quadratic Hamiltonians with Fermi or Boson operators.

Abstract

Magnetic exchange interactions (MEIs) define networks of coupled magnetic moments and lead to a surprisingly rich variety of their magnetic properties. Typically MEIs can be estimated by fitting experimental results. But how many MEIs need to be included in the fitting process for a material is not clear a priori, which limits the quality of results obtained by these conventional methods. In this paper, based on linear spin-wave theory but without performing matrix diagonalization, we show that for a general quadratic spin Hamiltonian, there is a simple relation between the Fourier transform of MEIs and the sum of square of magnon energies (SSME). We further show that according to the real-space distance range within which MEIs are considered relevant, one can obtain the corresponding relationships between SSME in momentum space. We also develop a theoretical tool for tabulating the rule about SSME. By directly utilizing these characteristics and the experimental magnon energies at only a few high-symmetry k points in the Brillouin zone, one can obtain strong constraints about the range of exchange path beyond which MEIs can be safely neglected. Our methodology is also general applicable for other Hamiltonian with quadratic Fermi or Boson operators.