Electron paramagnetic resonance of Dy${^3+}$-doped CaWO$_4$: spin Hamiltonian, crystal-field analysis, and linear electric field effect

Abstract: We report an electron paramagnetic resonance (EPR) study of Dy${<sup>3+}$ in CaWO$<em>4$ single crystals spanning dopant concentrations from 80~ppb to 247~ppm. The $g$ factors of the ground Kramers doublet at the $S_4$ point-group site, $g</em>\parallel = 7.22 \pm 0.01$ and $g_\perp = 5.45 \pm 0.01$, and the hyperfine constants of \ce{^{161}Dy} and $<sup>{163}$Dy are determined with an order-of-magnitude improvement in precision over the only previous report. A crystal-field analysis constrained jointly by published optical levels and by the measured $g$ tensor identifies the ground doublet as the lower branch of an anticrossing between the near-degenerate $|{\pm}11/2&gt;$ and $|{\mp}13/2&gt;$ states, and explains why optical data alone left the $g$ values unconstrained. \add{The same parameter set, tested on the excited multiplets of the $<sup>6H$ term, reproduces the ${}<sup>6H_{13/2}$ crystal-field levels better than the optical parameters themselves.} The angular dependence of the linewidth in the $ab$ plane reveals broadening by random internal electric fields through the linear electric field effect. Calibrating these fields with the residual Er$<sup>{3+}$ present in the same crystals yields the first electric-field coupling parameters of Dy$<sup>3+$, $$(B_{31}^{2+B_{36}^{2)^{1/2}}} = (34\pm5)\times10<sup>{-6}$$~cm/V, three times the Er$<sup>{3+}$ value and the largest reported for a rare-earth ion in this host.The residual linewidth and the concentration-dependent lineshape asymmetry follow the quadratic field scaling expected for a second-order Stark shift, which escapes the inversion-site cancellation constraining the linear effect. Both couplings trace back to the $\sim 20$~cm$<sup>{-1}$ gap to the first opposite-symmetry doublet, a consequence of the dense crystal-field structure of the $J=15/2$ manifold.