From local degrees of freedom to correlated states in anisotropic 3d transition metal compounds
Creators: name: Lane, Harry
Publisher: name: The University of Edinburgh
Year: 2022
Subjects: n/a

description: Anisotropy plays a crucial role in a wide variety of magnetic systems. In low-dimensional materials it can stabilise magnetic structures, overcoming the tendency for thermal fluctuations to disorder the magnetic correlations. It can also give rise to exotic dynamics such as nonlinear excitations and amplitude fluctuations that are not present in purely isotropic magnets. The origin of magnetic anisotropy lies in the physics of the individual magnetic ion and the crystallographic environment in which it nds itself. The nature of the magnetocrystalline anisotropy is therefore highly dependent on both the crystal structure and the species of magnetic ion. This dependence on the particulars of the system gives rise to starkly different phenomena in different compounds. In this Thesis, the physics of a number of anisotropic 3d transition metal compounds will be investigated, with a particular focus on the interplay between the single-ion physics and correlated phenomena. The Thesis begins with a discussion of the nature of magnetic interactions in the solid state, focusing on the quantum mechanical nature of the spin and orbital degrees of freedom that give rise to magnetism. Chapter 2 then provides an overview of neutron scattering { the principle experimental technique employed in this Thesis. This chapter concentrates on the instrumentation and neutron scattering theory required to interpret the results detailed in the later chapters and includes sections on both time-of-flight and triple-axis spectroscopy. Following the two introductory chapters, Chapter 3 explores the low energy dynamics of quasi-one-dimensional, large-S quantum antiferromagnets with easyaxis anisotropy. Such a situation is present in some 3d transition metal compounds based on ions such as Fe³⁺ or Mn²⁺. A description of these systems is developed using a semiclassical nonlinear δ model. The saddle point approximation leads to a sine-Gordon equation which supports soliton solutions. These correspond to the movement of spatially extended domain walls. Long-range magnetic order in spin chain compounds is typically a consequence of a weak inter-chain coupling. Below the ordering temperature, the coupling to nearby chains leads to an energy cost associated with the separation of two domain walls. From the kink-antikink two-soliton solution, an effective confi nement potential is computed. At distances that are large compared to the size of the solitons the potential is linear, as expected for point-like domain walls. At small distances the gradual annihilation of the solitons weakens the effective attraction and renders the potential quadratic. By numerically solving the effective onedimensional Schrödinger equation with this nonlinear con finement potential, the soliton bound state spectrum is computed. The theory is then applied to CaFe₂O₄, an anisotropic magnet based upon an antiferromagnetic zig-zag network of 3d⁵ Fe³⁺ ions with S = 5/2 and L = 0. Neutron scattering measurements are able to resolve seven discrete energy levels for spectra recorded slightly below the Néel temperature TN ≈ 200 K. These modes are well described by the nonlinear confi nement model in the regime of large spatially extended solitons. Chapter 4 concerns a jeff = 1/2 magnet α-CoV₂O₆, where spin-orbit coupling is much larger than the inter-ion coupling and hence the jeff = 1/2 manifold is well separated from spin-orbital levels. Here, the anisotropy originates from a small crystallographic distortion which can be treated as a small perturbation motivating an effective S = 1/2 Hamiltonian with an Ising/uniaxial symmetry. Low temperature magnetisation data show the existence of magnetisation plateaux, yet these are not accompanied by Bragg peaks in neutron diffraction data and hence are not indicative of transitions to new phases of long-range magnetic order. By application of the Lieb-Schultz-Mattis theorem, the existence of these magnetisation plateaux is reconciled with the absence of corresponding Bragg peaks in α-CoV₂O₆. This analysis relates the underlying symmetries of the ground state to the magnetisation. The presence of uniaxial anisotropy is shown to stabilise metastable short-range magnetic order at different fi eld strengths and temperatures, constructed from antiphase boundaries. Remaining on the theme of metastable antiphase boundary order, Chapter 5 returns to the S = 5=2 antiferromagnet CaFe₂O₄ which exhibits two magnetic orders that show regions of coexistence at some temperatures. By applying neutron scattering and a Green's function formalism, the spin wave excitations in this material are characterised, elucidating the relevant terms in the spin Hamiltonian. In doing so, it is suggested that the low temperature A phase order (↑↑🡣🡣) finds its origins in the freezing of antiphase boundaries created by thermal fluctuations in a parent B phase order (↑↑🡣🡣). The low temperature magnetic order observed in CaFe₂O₄ is thus the result of a competition between the exchange coupling along c, which favors the B phase, and the single-ion anisotropy, which stabilises thermally-generated antiphase boundaries, leading to static metastable A phase order at low temperatures. In Chapter 6, an iron-rich sample of the two-dimensional van der Waals itinerant ferromagnet Fe₃GeTe₂ is investigated using neutron scattering. The excitations are shown to be predominantly two-dimensional in nature and broadened, as expected for an itinerant magnet. The anisotropy strength is shown to be greater in magnitude than has been reported in a recent study of iron- deficient samples, hinting at a crucial role of the iron concentration in the single-ion properties of Fe3GeTe2. A model of domain walls is developed and the extracted exchange parameters from the neutron scattering results are used to calculate the expected domain wall width, based on bulk exchange parameters. This is then compared with scanning tunnelling microscopy (STM) data which are reflective of the surface physics. Strong agreement is found with the STM data suggesting that the surface properties are similar to that of the bulk. Chapter 7 concerns another two-dimensional van der Waals ferromagnet, VI₃. Unlike the 3d⁵ transition metal compound discussed in the preceding chapter, VI₃ is formed from a honeycomb of 3d² V³⁺ ions which carry an orbital degree of freedom. Here the Green's function formalism is extended to treat systems with an orbital degree of freedom, treating the spin-orbit coupling and crystal distortions explicitly. Neutron scattering is used to understand the nature of the low energy spin dynamics in VI₃, demonstrating the existence of two qualitatively different low energy modes. The neutron data are then modelled using the Green's function formalism, allowing a connection to be made between the spectrum and the crystallographic structure and indicating the presence of two differently distorted domains. It is shown that the anisotropy arising due to the cooperative effect of spin-orbit coupling and crystal distortions allows for the stable two-dimensional magnetism at finite temperature. Finally, in Chapter 8 the Green's function formalism is extended to treat noncollinear structures. This formalism is then applied to the noncollinear chargeordered antiferromagnet RbFe²⁺Fe³⁺F₆ - a system of mixed valance formed by two coupled networks of Fe²⁺ (3d⁶) and Fe³⁺ (3d⁵) chains. The spin-orbit coupling and effect of crystal distortions on the Fe²⁺ion are considered explicitly and the neutron scattering response is calculated using the noncollinear Green's function formalism. In addition to spin-orbit excitons, it is shown that the low symmetry of the Fe²⁺ coordination may give rise to low energy amplitude fluctuations that are not captured by linear spin wave theory. It is suggested that noncollinear magnets with low local symmetry may provide candidate systems for stable low energy amplitude modes in condensed matter systems.