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Crystals and glasses differ by the amplitude and the temperature dependenceof their thermal conductivity. However, there are crystals known to displayglass-like thermal conductivity. Here, we show that EuTiO$_3$, a quantumparaelectric known to order antiferromagnetically at 5.5 K, is one such system.The temperature dependence of resistivity and Seebeck coefficient yield aninsulating band gap of $\sim 0.22$ eV. Thermal conductivity is drasticallyreduced. Its amplitude and temperature dependence are akin to what is seen inamorphous silica. Comparison with non-magnetic perovskite solids, SrTiO$_3$,KTaO$_3$, and EuCoO$_3$, shows that what impedes heat transport are $4f$ spinsat Eu$^{2+}$ sites, which couple to phonons well above the orderingtemperature. Thus, in this case, superexchange and valence fluctuations, notmagnetic frustration, are the drivers of the glass-like thermal conductivity.

Glass-like thermal conductivity and narrow insulating gap of EuTiO$_3$