Crystal-Field--Driven Magnetoelectric Coupling in the Non-Kramers Hexaaluminate PrMgAl11O19

We report broadband dielectric spectra of the non-Kramers hexaaluminate PrMgAl\textsubscript{11}O\textsubscript{19}, revealing a pronounced interplay between permittivity and magnetization at cryogenic temperatures. The zero-field dielectric response follows a Barrett-type quantum-paraelectric form, while a broad dielectric anomaly near \SI{5}{K} shows a complex field dependence that mirrors the multi-hump behavior of the magnetic specific heat, evidencing robust magnetoelectric coupling. The inverse permittivity ${\epsilon }^{\mathrm{\prime }-1}(T,H)$ scales linearly with $M^2$, consistent with a biquadratic $P^2{M}^2$ term in a Landau framework. Fits yield temperature-dependent coupling constant $\lambda (T)$ that decreases with heating from ($1.07\pm 0.01)\times {10}^{-4}{\mu }_{\mathrm{B}}^{-2}$ (at 5,K) to $(4.77\pm 0.02)\times {10}^{-5}{\mu }_{\mathrm{B}}^{-2}$ (at 10,K), reflecting the thermal population of low-lying energy levels of Pr${}^{3+}$. Consistently, the uniaxial thermal expansion develops an additional low-temperature hump below $\sim \text{SI}30K$ that is progressively suppressed by magnetic field, recovering an approximately saturated response by \SI{9}{T}. These results identify PrMgAl\textsubscript{11}O\textsubscript{19} as a paradigmatic non-Kramers hexaaluminate where quantum paraelectricity and magnetoelectric interactions are intrinsically entangled, establishing hexaaluminates as a tunable platform for magnetoelectric physics in frustrated quantum materials.