Giant effective magnetic moments of chiral phonons from orbit-lattice coupling

Circularly polarized lattice vibrations carry angular momentum and lead to magnetic responses in applied magnetic fields or when resonantly driven with ultrashort laser pulses. Recent measurements have found responses that are orders of magnitude larger than those calculated in prior theoretical studies. Here, we present a microscopic model for the effective magnetic moments of chiral phonons in magnetic materials that can reproduce the experimentally measured magnitudes and that allows us to make quantitative predictions for materials with giant magnetic responses using microscopic parameters. Our model is based on orbit-lattice couplings that hybridize optical phonons with orbital electronic transitions. First, we test our model by applying it to $4f$ rare-earth halide paramagnets, which are known to exhibit a giant phonon Zeeman effect. Next, we predict that this effect can also occur for optical phonons in $3d$ transition-metal oxide magnets. We show that the nature of low-energy excitations involved in phonon hybridization is remarkably different than that of rare-earth systems. The temperature trend of phonon magnetic moment in $d$-orbital magnets also reveals valuable insights about the magnetic ground state and the unique interplay of spin, orbital, and lattice degree of freedom. In both cases, we find that chiral phonons can carry giant effective magnetic moments of the order of a Bohr magneton, orders of magnitude larger than previous predictions.