Magnon-Phonon Interactions in Finite Temperatures

A fundamental problem in many-body physics is the behaviour of collective degrees of freedom (DOF) in finite temperatures. The ubiquitous quasiparticle paradigm – phonons for vibrational DOF and magnons for magnetic DOF - linearizes the theory to arrive at an independent particle description. That this picture fails in finite temperatures is well-known and is usually addressed through a perturbative approach, supplementing the ideal plane waves with magnon-magnon and phonon-phonon scattering. Similarly, spin-lattice coupling can also compromise the validity of the phonon and magnon pictures. Spin-lattice interaction has recently attracted increased experimental and theoretical attention, given its potential significance in many subfields of material science, such as spin-thermoelectrics and spintronics. Still, most treatments remain perturbative, offering only renormalized resonances and finite excitation lifetimes. The inadequacy of such a description is immediately apparent for paramagnetism, or structural phase transitions, where the original ordered ground state of the quasiparticle is gone. This study sets out to establish a new conceptual framework for measuring and evaluating magnon-phonon interactions in crystals, adopting a phenomenological self-energy description which makes no assumptions about the magnitude of the effect. We will model the effect using many-body Green's functions to parameterize the excitation's correlation function and map the interaction into the diffuse X-ray pattern of archetypical systems (Fe, MnO, Co). Next, we will apply the generalized scheme to measure magnetic excitations in metal-organic frameworks inaccessible by traditional probes. Finally, I will explore the existence of paramagnons and magnetic phase transition above the Néel temperature. All three avenues, realized under a shared scheme, offer insight into a new unified phenomenological theory for vibrational-magnetic excitations in finite temperatures.