Field evolution of low-energy excitations in the hyperhoneycomb magnet $\beta$-Li${}_2$IrO${}_3$

${}^7$Li nuclear magnetic resonance (NMR) and terahertz (THz) spectroscopies are used to probe magnetic excitations and their field dependence in the hyperhoneycomb Kitaev magnet $\beta$-Li${}_2$IrO${}_3$. Spin-lattice relaxation rate ($1\mathrm{/}{T}_1$) measured down to 100,mK indicates gapless nature of the excitations at low fields (below $H_c\simeq 2.8$,T), in contrast to the gapped magnon excitations found in the honeycomb Kitaev magnet $\alpha$-RuCl${}_3$ at zero applied magnetic field. At higher temperatures in $\beta$-Li${}_2$IrO${}_3$, $1\mathrm{/}{T}_1$ passes through a broad maximum without any clear anomaly at the N'eel temperature $T_N\simeq 38$,K, suggesting the abundance of low-energy excitations that are indeed observed as two peaks in the THz spectra, both correspond to zone-center magnon excitations. At higher fields (above $H_c$), an excitation gap opens, and a re-distribution of the THz spectral weight is observed without any indication of an excitation continuum, in contrast to $\alpha$-RuCl${}_3$ where an excitation continuum was reported.