Slow crystalline electric field fluctuations in the Kondo lattice SmB${}_6$

Abstract

This work reports on the temperature dependence of the electron spin resonance (ESR) of Gd${}^{3+}$-doped SmB${}_6$ single crystals at X- and Q-band microwave frequencies in different crystallographic directions. We found an anomalous inhomogeneous broadening of the Gd${}^{3+}$ ESR linewidth ($\hat{I}”H$) within 5.3 K $\le T\le$ 12.0 K which is attributed to slow crystalline electric field (CEF) fluctuations, slower than the timescale of the ESR microwave frequencies used ($\sim$10 GHz). This linewidth inhomogeneity may be associated to the coupling of the Gd${}^{3+}$ $S$-states to the breathing mode of the SmB${}_6$ cage, and can be simulated by a random distribution of the 4${}^{th}$ CEF parameter, $b_4$, that strikingly takes negative and positive values. The temperature at which this inhomogeneity sets in, is related to the onset of a continuous insulator-to-metal phase transition. In addition, based on the interconfigurational fluctuation relaxation model, the observed exponential $T$-dependence of $\hat{I}”H$ above $T\simeq$ 10 K gives rise to an excitation energy notably close to the hybridization gap of SmB${}_6$ ($\hat{I}”\simeq$ 60 K). This charge fluctuation scenario provides important ingredients to the physical properties of SmB${}_6$. We finally discuss the interplay between charge and valence fluctuations under the view of slow CEF fluctuations in SmB${}_6$ by coupling the Gd${}^{3+}$ ions to the breathing phonon mode via a dynamic Jahn-Teller-like mechanism.