Continuous transformation between ferro and antiferro circular structures in $J_1-J_2-J_3$ frustrated Heisenberg model

TL;DR

This paper investigates the $J_1-J_2-J_3$ Heisenberg model on a square lattice, revealing new local order, complex excitations, and phase crossovers using a self-consistent Green's function approach across the entire parameter space.

Contribution

It introduces a novel application of the spherically symmetric self-consistent method to explore the full parameter space of the $J_1-J_2-J_3$ model, uncovering new magnetic phases and excitations.

Findings

Discovery of antiferromagnetic isotropical helices in spin liquids.

Identification of circular concentric dispersionless structures in the structure factor.

Observation of a crossover between antiferromagnetic-like and ferromagnetic-like orders.

Abstract

Frustrated magnetic compounds, in particular low-dimensional, are topical research due to persistent uncover of novel nontrivial quantum states and potential applications. The problem of this field is that many important results are scattered over the localized parameter ranges, while areas in between still contain hidden interesting effects. We consider $J_1-J_2-J_3$ Heisenberg model on the square lattice and use the spherically symmetric self-consistent approach for spin-spin Green's functions in "quasielastic" approximation. We have found a new local order in spin liquids: antiferromagnetic isotropical helices. On the structure factor we see circular concentric dispersionless structures, while on any radial direction the excitation spectrum has "roton" minima. That implies nontrivial magnetic excitations and consequences in magnetic susceptibility and thermodynamics. On the $J_1-J_2-J_3$ exchange parameters globe we discover a crossover between antiferromagnetic-like local order and ferromagnetic-like; we find stripe-like order in the middle. In fact, our "quasielastic" approach allows investigation of the whole $J_1-J_2-J_3$ globe.