Crystal-field magnetostriction of the spin ice under ultrahigh magnetic fields

We present a comprehensive study of the magnetoelastic properties of the Ising pyrochlore oxide Ho$_{2}$Ti$_{2}$O$_{7}$, known as spin ice, by means of high-field magnetostriction measurements and numerical calculations. When a magnetic field is applied along the crystallographic <111> axis, the longitudinal magnetostriction exhibits a broad maximum in the low-field regime around 30 T, followed by a dramatic lattice contraction due to crystal-field (CF) level crossing at $B_{\rm cf} \sim 65$ T. The transverse magnetostriction exhibits a contrasting behavior, highlighting the anisotropic nature of the CF striction. We identify distinct timescales of spin dynamics and CF-phonon dynamics by applying a magnetic field with different field-sweep rates. Our mean-field calculations, based on a point-charge model, successfully reproduce the overall magnetostriction behavior, revealing the competition between the exchange striction and CF striction. A signature of the CF level crossing is also observed through adiabatic magnetocaloric-effect measurements, consistent with our magnetostriction data.