We develop a microscopic theory of spin-lattice interactions in magnetic insulators, separating rigid-body rotations and the internal angular momentum, or spin, of the phonons, while conserving the total angular momentum. In the low-energy limit, the microscopic couplings are mapped onto experimentally accessible magnetoelastic constants. We show that the transient phonon spin contribution of the excited system can dominate over the magnon spin, leading to nontrivial Einstein-de Haas physics.

We address the theory of magnon-phonon interactions and compute the corresponding quasiparticle and transport lifetimes in magnetic insulators, with a focus on yttrium iron garnet at intermediate temperatures from anisotropy- and exchange-mediated magnon-phonon interactions, the latter being derived from the volume dependence of the Curie temperature. We find in general weak effects of phonon scattering on magnon transport and the Gilbert damping of the macrospin Kittel mode. The magnon transport lifetime differs from the quasiparticle lifetime at shorter wavelengths.

We theoretically investigate pumping of phonons by the dynamics of a magnetic film into a nonmagnetic contact. The enhanced damping due to the loss of energy and angular momentum shows interference patterns as a function of the resonance frequency and magnetic film thickness that cannot be described by viscous ("Gilbert") damping. The phonon pumping depends on the magnetization direction as well as geometrical and material parameters and is observable, e.g., in thin films of yttrium iron garnet on a thick dielectric substrate.

We address the theory of the coupled lattice and magnetization dynamics of freely suspended single-domain nanoparticles. Magnetic anisotropy generates low-frequency satellite peaks in the microwave absorption spectrum and a blueshift of the ferromagnetic resonance (FMR) frequency. The low-frequency resonances are very sharp with maxima exceeding that of the FMR, because their magnetic and mechanical precessions are locked, thereby suppressing the effective Gilbert damping. Magnetic nanoparticles can operate as nearly ideal motors that convert electromagnetic into mechanical energy. The Barnett damping term is essential for obtaining physically meaningful results.

We use the functional renormalization group (FRG) to derive analytical expressions for thermodynamic observables (density, pressure, entropy, and compressibility) as well as for single-particle properties (wave-function renormalization and effective mass) of interacting bosons in two dimensions as a function of temperature T and chemical potential μ. We focus on the quantum disordered and the quantum critical regime close to the dilute Bose gas quantum critical point. Our approach is based on a truncated vertex expansion of the hierarchy of FRG flow equations and the decoupling of the two-body contact interaction in the particle-particle channel using a suitable Hubbard-Stratonovich transformation. Our analytic FRG results extend previous analytical renormalization-group calculations for thermodynamic observables at μ=0 to finite values of μ. To confirm the validity of our FRG approach, we have also performed quantum Monte Carlo simulations to obtain the magnetization, susceptibility, and correlation length of the two-dimensional spin-1/2 quantum XY model with coupling J in a regime where its quantum critical behavior is controlled by the dilute Bose gas quantum critical point. We find that our analytical results describe the Monte Carlo data for μ≤0 rather accurately up to relatively high temperatures T0.1J.