Tensor network analysis of the maple-leaf antiferromagnet spangolite

TL;DR

This paper uses tensor network methods to analyze the complex magnetic behavior of the maple-leaf antiferromagnet spangolite, revealing a non-trivial dimerized ground state and predicting magnetic phenomena under external fields.

Contribution

It introduces a spatially anisotropic Heisenberg model for spangolite and validates it with advanced tensor network calculations, providing insights into its ground state and thermodynamics.

Findings

Identification of a non-trivially correlated dimer ground state

Prediction of magnetization plateaus at high magnetic fields

Explanation of reduced magnetic moment at high temperatures

Abstract

Spangolite (Cu$_6$Al(SO$_4$)(OH)$_{12}$Cl$\cdot$3H$_2$O) is a hydroxy-hydrated copper sulfate mineral with a one-seventh depleted triangular lattice of Cu$^{2+}$ ions in each layer. Experimental measurements revealed a non-magnetic ground state at $T \sim 8\, \text{K}$ with magnetic properties dominated by dimerization. We propose a spatially anisotropic Heisenberg model for the Cu$^{2+}$ spin-$1/2$ degrees of freedom on this geometrically frustrated and effectively two-dimensional maple-leaf lattice, featuring five symmetry inequivalent couplings with ferromagnetic bonds on hexagons and antiferromagnetic triangular bonds. The validity of the proposed Hamiltonian is demonstrated by state-of-the-art tensor network calculations, which can assess both the nature of the ground state as well as low-temperature thermodynamics, including the effects of a magnetic field. We provide theoretical support for a picture of a non-trivially correlated dimer ground state, which accounts for the appreciable reduction of the magnetic moment at high temperatures observed in experiment, thereby resolving a long-standing puzzle. We predict the static spin structure factor as well as the emergence of magnetisation plateaus at high values of an external magnetic field, explore the nature of the quantum states in them, and study their melting with increasing temperature.