Longitudinal and transverse static spin fluctuations in layered ferro- and antiferromagnets

TL;DR

This paper investigates the momentum-dependent static spin susceptibilities in layered magnetic systems below their transition temperatures, revealing significant corrections to existing theories and providing a comprehensive approach to understanding spin fluctuations.

Contribution

It introduces advanced expansion methods to accurately describe static spin fluctuations and corrects previous theoretical results for layered ferro- and antiferromagnets.

Findings

Strong corrections to spin-wave and renormalization-group results at low temperatures.

Successful extrapolation of expansion results to the transition temperature T_M.

Fulfillment of the sum rule for spin fluctuation weights outside the critical regime.

Abstract

We analyse the momentum dependence of static non-uniform susceptibilities of layered local-moment systems below Curie (Neel) temperature within the 1/S-expansion, the renormalization-group approach, and first order of 1/N-expansion. We argue that the previously known results of the spin-wave theory and renormalization-group approach for the transverse spin susceptibility acquire strong corrections already at sufficiently low temperatures, which appear due to the interaction of the incomping magnon having momentum q with magnons with momenta k<q. Such corrections can not be treated in the standard renormalization-group approach, but can be described by both, 1/S and 1/N expansions. The results of these expansions can be successfully extrapolated to the magnetic transition temperature T=T_M yielding the correct weight of static spin fluctuations, determined by the O(3) symmetry. For the longitudinal susceptibility, the summation of leading terms of 1/S expansion within the parquet approach allows to fulfill the sumrule for the weights of transverse and longitudinal fluctuations in a broad temperature region below T_M outside the critical regime. We also discuss the effect of longitudinal spin fluctuations on the (sublattice) magnetization of layered systems.