Magnetic field tuning of crystal field levels and vibronic states in Spin-ice Ho$_2$Ti$_2$O$_7$ observed in far-infrared reflectometry

TL;DR

This study uses far-infrared reflectometry to explore how magnetic fields influence crystal field and vibronic states in the spin-ice material Ho$_2$Ti$_2$O$_7$, revealing magnetoelastic coupling and tunable vibronic interactions.

Contribution

It provides the first detailed IR spectroscopic analysis of magnetic field effects on crystal field and vibronic states in Ho$_2$Ti$_2$O$_7$, including new CEF parameters and insights into phonon-CEF coupling.

Findings

Field-dependent IR features match CEF excitations.

Identification of a zero-field split vibronic state.

Demonstration of tunable phonon-CEF coupling with magnetic field.

Abstract

Low temperature optical spectroscopy in applied magnetic fields provides clear evidence of magnetoelastic coupling in the spin ice material Ho$_2$Ti$_2$O$_7$. In far-IR reflectometry measurements, we observe field dependent features around 30, 61, 72 and 78~meV, energies corresponding to crystal electronic field (CEF) doublets. The calculations of the crystal-field Hamiltonian model confirm that the observed features in IR spectra are consistent with magnetic-dipole-allowed excitations from the ground state to higher $^5$I$_8$ CEF levels. We present the CEF parameters that best describe our field-dependent IR reflectivity measurements. Additionally, we identify a weak field-dependent shoulder near one of the CEF doublets. This indicates that this level is split even in zero-field, which we associate with a vibronic bound state. Modeling of the observed splitting shows that the phonon resides at slightly lower energy compared to the CEF level that it couples to, which is in contrast with previously published inelastic neutron measurements. The magnetic field dependence of the vibronic state shows a gradual decoupling of the phonon with the CEF level as it shifts. This approach should work in pyrochlores and other systems that have magnetic dipole transitions in the IR spectroscopic range, which can elucidate the presence and the ability to tune the nature of vibronic states in a wide variety of materials.