Impact of Absorption due to Zero-Field Splitting on Loss in Dielectrics: A Case Study in Sapphire

The coherence times of superconducting qubits are limited by loss mechanisms, whose microscopic origins have remained elusive. We propose a mechanism caused by transitions between zero-field-split states of paramagnetic impurities or defects. We derive the absorption cross section for a magnetic dipole transition and apply it to calculate the loss tangent. For Cr, Fe, and V impurities in sapphire, we find loss tangents at 4.5 GHz in the range of 10${}^{-9}$-10${}^{-8}$, comparable to the loss measured in experiments. This value suggests that magnetic loss may be a limiting factor in the coherence times of superconducting qubits.