Precise determination of low energy electronuclear Hamiltonian for LiY${}_{1-x}$Ho${}_x$F${}_4$

Abstract

We use complementary optical spectroscopy methods to directly measure the lowest crystal-field energies of the rare-earth quantum magnet LiY${}_{1-x}$Ho${}_x$F${}_4$, including their hyperfine splittings, with more than 10 times higher resolution than previous work. We are able to observe energy level splittings due to the ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ isotopes, as well as non-equidistantly spaced hyperfine transitions originating from dipolar and quadrupolar hyperfine interactions. We provide refined crystal field parameters and extract the dipolar and quadrupolar hyperfine constants $A_J=0.02703\pm 0.00003$ ${\text{cm}}^{-1}$ and $B=0.04\pm 0.01$ ${\text{cm}}^{-1}$, respectively. Thereupon we determine all crystal-field energy levels and magnetic moments of the ${}^5{I}_8$ ground state manifold, including the (non-linear) hyperfine corrections. The latter match the measurement-based estimates. The scale of the non-linear hyperfine corrections sets an upper bound for the inhomogeneous line widths that would still allow for unique addressing of a selected hyperfine transition. e.g. for quantum information applications. Additionally, we establish the far-infrared, low-temperature refractive index of LiY${}_{1-x}$Ho${}_x$F${}_4$.

9 pages, 6 Figures, 3 Tables