We report microwave spectroscopy of ${{}^{167}\mathrm{Er}}^{3+}$ doped in ${\mathrm{CaWO}}_4$, which reveals the hyperfine splitting of the erbium electronic ground state ($Z_1, J_{\mathrm{eff}}=15/2$) induced by the $I=7/2$ nuclear spin. From spectra measured below $\sim 50\mathrm{mK}$ in magnetic fields up to 200 mT, we extract spin-Hamiltonian parameters including the electron $\mathbf{g}$, hyperfine $\mathbf{A}$, and nuclear electric quadrupolar $\mathbf{Q}$ tensors. Crucially, our analysis demonstrates unambiguously that the previously unobserved nuclear electric quadrupolar moment is essential to reproduce the experimental data. With these refined parameters, we identify zero first-order Zeeman (ZEFOZ) transitions at zero magnetic field. Extending the analysis to finite fields, we uncover that ZEFOZ points lie either along the $c$ axis or within the $a\text{−}b$ plane. These results establish ${\mathrm{CaWO}}_4$ as a promising host for long lifetime quantum memories.

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• Spin waves
• Zeeman effect
• Rare-earth doped crystals
• Rare-earth ions
• Microwave techniques