NMR Spectroscopy and the Crystal-Field Interaction in Holmium Trifluoride

TL;DR

This study combines advanced NMR techniques and computer modeling to analyze the crystal-field interactions in HoF3, revealing distinct spectra from inequivalent sites and interpreting hyperfine splittings with a detailed Hamiltonian.

Contribution

It introduces a new computer-controlled CW spectrometer for low-relaxation conditions, and provides the first detailed NMR analysis of hyperfine splittings in HoF3 with a comprehensive Hamiltonian model.

Findings

Distinct spectra from two inequivalent Ho sites were observed.

Hyperfine splittings were interpreted using a 15-parameter crystal-field Hamiltonian.

A computer program was developed to automate Hamiltonian diagonalization.

Abstract

The work to be described falls into three parts: (1) The computer-controlled CW spectrometer was designed to supplement the Manchester pulsed microwave spectrometer in situations where rapid nuclear relaxation makes spin-echo spectroscopy difficult. Its operating range is 4-8 GHz. Resonator designs and modulation strategies will be discussed in the light of practical experience. (2) Both CW and pulsed NMR have been used to study the field dependence of the hyperfine splittings of $^{165}$Ho in HoF$_3$ and, as a dilute substituent, in YF$_3$. The low site symmetry results in a singlet crystal-field ground state for the Ho$^{3+}$ ion, giving Van Vleck paramagnetism and enhanced nuclear magnetism at low temperatures. The measurements were made at temperatures in the range 1.5 to 4.2 K and in fields of up to 8 T. This work has revealed, for the first time, distinct spectra from the two subtly inequivalent rare-earth sites in the orthorhombic unit cell. Because of the non-colinear spin structure of HoF$_3$, the NMR and magnetometry measurements give independent and complimentary information about the ionic moments. (3) The measured hyperfine splittings have been interpreted in terms of a 15-parameter crystal-field Hamiltonian appropriate to the $C_{1h}$ site symmetry. This work has entailed a substantial effort to clarify the notational confusion that exists in the literature. A computer program has been developed to automate conversion between notational conventions prior to diagonalization of the 136-dimensional electronic-nuclear Hamiltonian comprising the Zeeman, crystal-field and hyperfine interactions. [abridged]