Magnons and phonons are collective excitations in crystals that often behave as independent quasiparticles when their mutual coupling is weak. When magnetoelastic coupling becomes strong, interactions between spin and lattice degrees of freedom can open gaps at band crossings and give rise to hybridized excitations known as magnon-polarons. Because such hybridized modes appear only when energy matching, symmetry compatibility, and microscopic coupling all align, their presence and momentum dependence provide a particularly sensitive probe of the underlying spin–lattice interactions.

In this talk, I will use the olivine-type silicate Co₂SiO₄ to illustrate how this physics plays out in a real material. I will begin by presenting inelastic neutron-scattering measurements that reveal a rich set of hybridized excitations involving magnons, phonons, and spin–orbit excitons. To understand these observations, I will introduce an effective spin Hamiltonian that captures the main features of the magnetic excitations and discuss density functional theory calculations that reproduce the phonon spectrum. Building on these microscopic descriptions, a symmetry analysis of the magnon and phonon modes reveals which excitations can hybridize and where in momentum space such coupling is allowed. This framework naturally leads to a minimal hybridization model that explains the observed avoided crossings and mode mixing, providing a unified picture of the hybridized excitation spectrum in Co₂SiO₄.

More broadly, this work establishes olivine-type oxides as a clean setting for studying magnetoelastic coupling and illustrates how combining dynamical measurements with symmetry-based modeling can reveal microscopic interactions that are difficult to access otherwise.

The magnetic moment of muon can be characterized by its gyro-magnetic factor $g$, which is numerically close to 2. Fermilab announced a new experimental result for muon $g-2$ on June 3, 2025.
The new result is consistent with the previous BNL measurement, but with about 4 times higher precision. For the Standard Model prediction, the recent theoretical muon $g-2$ white paper was released on May 27, 2025. The new theory result is consistent with the new experimental result, but is about 3 sigma larger than the previous theory white paper result, released on June 8, 2020. Two hadronic contributions, HVP (hadronic vacuum polarization) and HLbL (hadronic light-by-light), are the dominant sources of the theoretical uncertainty. The change in the central value is largely due to the many advances in lattice QCD calculations of these hadronic contributions, particularly the HVP contribution. In this talk, I will describe the theoretical determination of muon $g-2$ with focus on the lattice QCD calculations of the hadronic contributions.

TBA