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 LiY1−xHoxF4, 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 Li and 7 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 AJ = 0.02703 ± 0.00003 cm −1 and B = 0.04 ± 0.01 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 LiY1−xHoxF4.