The dielectric and magnetic polarizations of quantum paraelectrics and paramagnetic materials have in many cases been found to initially increase with increasing thermal disorder and hence exhibit peaks as a function of temperature. A quantitative description of these examples of order-by-disorder phenomenona has remained elusive in nearly ferromagnetic metals and in dielectrics on the border of displacive ferroelectric transitions. Here we present an experimental study of the evolution of the dielectric susceptibility peak as a function of pressure in the nearly ferroelectric material, strontium titanate, which reveals that the peak position collapses towards absolute zero as the ferroelectric quantum critical point is approached. We show that this behaviour can be described in detail without the use of adjustable parameters in terms of the Larkin-Khmelnitskii-Shneerson-Rechester (LKSR) theory, first introduced nearly 50 years ago, of the hybridization of polar and acoustic modes in quantum paraelectrics, in contrast to alternative models that have been proposed. Our study allows us to construct for the first time a detailed temperature-pressure phase diagram of a material on the border of a ferroelectric quantum critical point comprising ferroelectric, quantum critical paraelectric and hybridized polar-acoustic regimes. Furthermore, at the lowest temperatures, below the susceptibility maximum, we observe a new regime characterized by a linear temperature dependence of the inverse susceptibility that differs sharply from the quartic temperature dependence predicted by the LKSR theory. We find that this non-LKSR low temperature regime cannot be accounted for in terms of any detailed model reported in the literature, and its interpretation poses a new empirical and conceptual challenge.
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