Low-temperature specific heat of a Zr${\mathrm{O}}_2$: ${\mathrm{Y}}_2$${\mathrm{O}}_3$ oxygen conductor

The specific heat of a partially stabilized Zr${\mathrm{O}}_2$: ${\mathrm{Y}}_2$ ${\mathrm{O}}_3$ ceramic containing 4.3% oxygen vacancies is reported between 2 and 15 K. An excess specific heat above 6 K attributed to the oxygen vacancies is accurately described by an Einstein term with an oscillator frequency of 62 ${\mathrm{cm}}^{-1\mathrm{}}$. A second excess specific heat below 5 K follows a Schottky term ($\delta =38\mathrm{}$ mK) and is believed due to the electric quadrupole moment of the hafnia impurity. The Debye temperatures obtained from the Einstein and Schottky fits are 475 and 470 K, respectively. No evidence for a tunneling contribution to the specific heat was found.