Magnetometry and Thermodynamic Studies of Anisotropic Honeycomb and Hyperhoneycomb Magnets

Abstract

This thesis presents results from high-sensitivity piezocantilever single-crystal torque magnetometry, magnetisation, and calorimetry measurements on the magnetically ordered phases of four related quantum magnetic materials, linked by their tricoordinated honeycomb and hyperhoneycomb magnetic sublattices and strong spin-orbit coupling.

The first two materials investigated, honeycomb $\alpha {\text{-Na}}_2{\text{PrO}}_3$, and its hyperhoneycomb polymorph $\beta {\text{-Na}}_2{\text{PrO}}_3$, are candidates to display unconventional magnetic behaviour from bond-dependent Kitaev interactions. That these physics may occur in the $4f$ rare-earths has remained experimentally largely unexplored. In both cases, this is the first time high-quality single crystals of the material have been magnetically characterised.

In $\alpha {\text{-Na}}_2{\text{PrO}}_3$I find a sharp transition to long range order below $T_N=4.6\mathrm{K}$, and strongly contrasting angular dependence of torque in three crystal planes, and show that this can be naturally explained by a canted antiferromagnetic structure. I also propose a minimal anisotropic exchange model, compatible with crystal symmetry, explaining the observed magnetic structure. Finally, I report torque magnetometry up to $35\mathrm{T}$, showing clear evidence of a spin-flop transition for certain orientations of the magnetic field, consistent with the minimal model and observe non-monotonic field dependence of crossover between spin-flop and paramagnetic phases.

In $\beta {\text{-Na}}_2{\text{PrO}}_3$, I find a sharp transition to magnetic order below $T_N=5.2\mathrm{K}$ and show torque magnetometry consistent with the four sublattice non-collinear magnetic structure found in neutron diffraction experiments. I explore the proposed bond-anisotropic minimal magnetic model with mean field calculations and show that it predicts a metamagnetic spin-flop transition for certain field orientations. Additionally, I report torque magnetometry up to $67\mathrm{T}$, finding the predicted field-driven phase transition at $26\mathrm{T}$ as well as a high-field transition to the polarised state.

The final two materials investigated in this thesis are the honeycomb transition metal titanates ${\text{CoTiO}}_3$and ${\text{FeTiO}}_3$. These materials are isostructural with honeycomb layers of magnetic ions, ordering as an easy-plane and easy-axis antiferromagnet respectively. Previously published neutron scattering experiments found evidence for in-plane anisotropy in ${\text{CoTiO}}_3$, driven by a quantum zero-point fluctuation mechanism. In this thesis I use torque magnetometry to directly probe the in-plane anisotropy of both ${\text{CoTiO}}_3$and ${\text{FeTiO}}_3$and in both cases find clear evidence of six-fold clock anisotropy which cannot be attributed to single-ion anisotropy.

This website is web version of my doctoral thesis, which is also available in it’s original format from the Bodleian library. There are some slight structural differences between this and the original manuscript to better present the content for the web. Additionally, some figures from references which were included may be omitted for copyright reasons, as permission was granted for use in a thesis rather than this website. The html generation was done by LaTeXMLand I have to commend the maintainers there for their very fine job.

This thesis reports research into magnetic structures of periodic crystals where the magnetic ions exist on tricoordinated honeycomb or hyper-honeycomb lattices. The primary experimental technique used to study these materials is piezocantilever torque magnetometry, many of the experiments reported were performed in the Clarendon Laboratories at the University of Oxford. However, in order to access stronger magnetic fields, additional experiments were performed alongside instrument scientists at the European Magnetic Field Lab facilities: HFML Nijmegen in The Netherlands and HZDR Dresden in Germany. Alongside these torque magnetometry results, I report data from other techniques such as X-ray diffraction for crystal structure, AC calorimetry to study heat capacity anomalies in phase transitions, and both single-crystal and powder magnetisation. I support these experimental results with mean-field calculations of the response of the magnetic systems to applied magnetic field.

Chapter 1: Introduction to Quantum Magnetism

In the first chapter I introduce the basics of quantum magnetism, to provide an overview of the motivation for this research. This starts with an explanation of the origin of the magnetic moment in isolated magnetic ions, followed by an explanation of how these magnetic ions interact and stabilise magnetic order at low temperatures. Finally, the so-called $J,K,\mathrm{\Gamma }$ model on a honeycomb or hyper-honeycomb lattice is explored to motivate the materials investigated in this thesis.

Chapter 2: Experimental Methods

This chapter explains each of the experimental methods used in this project.

Chapter 3: General Optimisation Algorithm to Find Classical Magnetic Ground States

Chapter 3 introduces and explains the Riemannian optimisation algorithm used for the mean-field calculations reported later in the thesis.

Chapter 4: Canted antiferromagnetic magnetic order in honeycomb $\alpha {\text{-Na}}_2{\text{PrO}}_3$revealed by single crystal torque measurements

In the first results chapter, the Kitaev-candidate honeycomb magnet $\alpha {\text{-Na}}_2{\text{PrO}}_3$is reported, starting from structure using X-ray diffraction of single-crystals. This is followed by the single-crystal physics of the ${\text{Pr}}^{4+}$ions and a discussion of the previously published data on powder samples. I then report torque magnetometry in three orthogonal rotation planes, and up to $35\mathrm{T}$, revealing a canted antiferromagnetic structure for the first time. This is accompanied by calculations to support a minimal model to stabilise this magnetic structure.

Chapter 5: Magnetic order and high-field magnetic phase transitions in hyperhoneycomb $\beta {\text{-Na}}_2{\text{PrO}}_3$

The next material reported is the hyper-honeycomb polymorph of the same material, $\beta {\text{-Na}}_2{\text{PrO}}_3$. This chapter reports torque magnetometry and AC calorimetry revealing magnetic ordering below $5.2\mathrm{K}$. This is followed by a discussion of the magnetic structure revealed by currently unpublished neutron diffraction studies, and an exploration of Hamiltonians which could stabilise the reported magnetic structure. Finally, I report torque magnetometry up to $65\mathrm{T}$, revealing high magnetic field phase transitions.

Chapter 6: Six-fold clock-anisotropy in honeycomb titanates ${\text{CoTiO}}_3$and ${\text{FeTiO}}_3$

The final results chapter reports torque magnetometry in isostructural honeycomb antiferromagnets ${\text{CoTiO}}_3$and ${\text{FeTiO}}_3$. These follow recently published results which predict a 6-fold clock anisotropy in easy-plane ${\text{CoTiO}}_3$from analysis of inelastic neutron scattering (INS) data. With high resolution torque magnetometry I find clear direct evidence for such clock anisotropy, and am able to estimate the energy scale of the effect to within the same order of magnitude as the estimate from INS data. This is followed by the same treatment for easy-axis ${\text{FeTiO}}_3$, which finds the same effect with a much larger energy scale. In both cases, single-ion anisotropy can be rejected as the origin, and I discuss possible origins of the effect.

Chapter 7: Concluding Remarks

Finally, I summarise the results and position my view of the key conclusions from this project.