Cryogenic spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> nuclear quadrupole resonance: Electric field gradient via Rabi frequency goniometry and spin relaxati

A straightforward way to determine the electric field gradient $-$ principal axes frame (EFG-PAF) on single crystal samples with spin 3/2 nuclei is demonstrated. Nuclear quadrupole resonance (NQR) spectroscopy is used to determine the Rabi frequency for $^{35}$Cl in a single crystal of potassium chlorate (KClO$_3$) by comparing the NQR signal for powder and single crystal samples. By exploiting the geometrical dependence of the Rabi frequency with respect to the excitation direction, EFG-PAF is readily determined. Furthermore, relaxation times $T_1$ and $T_2^*$ were measured at multiple temperatures ranging from $17~\textrm{K}$ to $200 ~$K, extending the results of previous works to colder temperatures where new relaxation mechanisms become dominant. The experiments were performed in a cryogen-free cryostat, which posed distinct challenges compared to a conventional cryogenic cooling setup. The successful operation of the NQR probe within a cryogen-free cryostat has the potential to make the technique more accessible and widen applications.