Response and transport properties in complex quantum spin systems

Abstract

Understanding how quantum systems respond to external perturbations lies at the core of condensed matter physics. In spin systems—where localized magnetic moments interact through exchange, spin-orbit coupling, and external fields—these responses are often rich with emergent behavior. Spin degrees of freedom not only govern magnetic ordering and excitations, but also mediate charge and heat transport, and serve as carriers of information in next-generation quantum technologies. This dissertation investigates how complexity—arising from spatial inhomogeneity, many-body interactions, or local spin structure—affects the transport and response properties of quantum spin systems. A central focus of this work is to clarify and reinterpret signatures observed in Hall transport measurements of magnetic materials. In Chapter 1, I explore how spatial inhomogeneities and resistances due to the presence of domain walls can mimic features traditionally associated with topological spin textures, such as skyrmions. Using homogenization theory, we derive rigorous bounds on the anomalous Hall conductivity (AHC) in inhomogeneous conductors under minimal assumptions. While the homogenized AHC must lie within the range of local conductivities, I show that experimental configurations involving inhomogeneous magnetic domains can give rise to apparent anomalies—such as humps in the Hall resistance hysteresis loop—without invoking topological effects. This result offers a non-topological explanation for widely observed transport features and underscores the importance of disentangling geometric, topological, and extrinsic contributions in interpreting experimental data. Chapter 2 addresses a different aspect of spin response: the control of magnetic relaxation dynamics through local environmental design. Motivated by the need to suppress decoherence in spin-based quantum devices, we present a new strategy for engineering long spin relaxation times by embedding a magnetic complex within a chemically compatible, but spin-active, matrix. Specifically, we show that the magnetic relaxation of the [Co(SPh)4]2˘ complex can be slowed by three orders of magnitude when embedded in isostructural lattices of [M(SPh)4]2˘ (M = Ni2+, Fe2+, Mn2+). Magnetometry, EPR, and computational analyses reveal that the host matrices' large positive zero-field splitting and integer spin values generate a dynamically quiet local environment. Unlike traditional strategies that rely on diamagnetic dilution, this approach leverages structured magnetic environments to suppress spin noise—opening new design principles for molecular qubits and coherent spin systems. Finally, Chapter 3 focuses on spin-orbit-driven transport phenomena that underlie much of modern spintronics. In systems with strong spin-orbit coupling (SOC), the spin Hall effect (SHE) and its inverse enable the interconversion of spin and charge currents—offering powerful tools for manipulating non-equilibrium spin states. This chapter examines the microscopic origins of the SHE and ISHE, their dependence on crystal symmetry and SOC strength, and the conditions under which transverse spin currents can be maximized or suppressed. These results contribute to the growing theoretical understanding of spin-charge coupling mechanisms and provide guidelines for optimizing spin current generation in realistic materials and devices. Taken together, the results presented in this dissertation shed light on how local structure, symmetry, and disorder shape the transport and dynamical properties of quantum spin systems. The overarching theme is one of complexity—how microscopically diverse environments and interactions can yield counterintuitive or emergent behavior in macroscopic response. In doing so, this work provides theoretical tools, reinterpretations, and design strategies that are broadly relevant to the study of magnetic materials, spintronic devices, and quantum information platforms.