Incommensurate, helical spin ground states on the Hollandite lattice

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.

arXiv comment11 pages, 8 figures

References in corpus (11)

• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Exact spectra, spin susceptibilities and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice
• Quantum frustration in organic Mott insulators: from spin liquids to unconventional superconductors
• Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets
• Spin and orbital frustration in MnSc_2S_4 and FeSc_2S_4
• Phase diagram for a class of spin-half Heisenberg models interpolating between the square-lattice, the triangular-lattice and the linear chain limits
• First-Principles Studies of the Atomic, Electronic, and Magnetic Structure of a-MnO2 (Cryptomelane)
• Exchange Interactions and High-Energy Spin States in Mn_12-acetate
• Ground States of Spin-1/2 Triangular Antiferromagnets in a Magnetic Field
• Nonplanar ground states of frustrated antiferromagnets on an octahedral lattice

Cited by in corpus (7)

• Detecting topological phases in the square-octagon lattice with statistical methods
• Projective symmetry group classification of Abrikosov fermion mean-field ansätze on the square-octagon lattice
• Competing orders in a frustrated Heisenberg model on the Fisher lattice
• Incommensurate Single-Angle Spiral Orderings of Classical Heisenberg Spins on Zigzag Ladder Lattices
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments
• Quantum theory of spin waves for Helical ground states in Hollandite lattice
• Classical ground states, spin-wave and PCUT analysis of ${\mathrm{H}}_2\mathrm{SQ}$ system