Incommensurate, helical spin ground states on the Hollandite lattice

TL;DR

This paper models classical Heisenberg spins on the Hollandite lattice, revealing four incommensurate helical ground states driven by geometrical frustration, with implications for experimental identification via neutron diffraction.

Contribution

It introduces a detailed model showing how anisotropic interactions lead to multiple helical ground states on the Hollandite lattice, connecting them to collinear antiferromagnetic states.

Findings

Four distinct incommensurate helical ground states identified

Helical states arise from geometrical frustration in the lattice

Magnetic form factors provided for experimental detection

Abstract

We present a model of classical Heisenberg spins on a Hollandite lattice, which has been developed to describe the magnetic properties of $\alpha$-MnO$_2$ and similar compounds. The model has nearest neighbor interacting spins, however the strength and the sign of spin-spin interactions is anisotropic and depends on the nature of the bonds. Our analysis shows that the Hollandite lattice supports four different incommensurate and helical magnetic ground states depending on the relative strengths and signs of spin-spin interactions. We show that the incommensurate helical ground states appear due to the geometrical frustration present in the model. We demonstrate that each of the four helical incommensurate magnetic phases are continuously connected to four different collinear antiferromagnetic ground states as the strength of spin-spin interaction along some bonds is increased. The present results give support to the presence of helical states that have been previously suggested experimentally for Hollandite compounds. We provide an in-depth analysis of the magnetic form factors for each helical phase and describe how it could be used to identify each of these phases in neutron diffraction experiments.