Large out-of-equilibrium magnetocaloric effect in rare-earth zirconate pyrochlores

We explore the magnetic properties of Nd$_2$Zr$_2$O$_7$ and Pr$_2$Zr$_2$O$_7$ single crystals subjected to pulsed magnetic fields up to 60 T using magnetization and magnetocaloric-effect (MCE) measurements, with initial temperatures ranging from 2 to 31K. The MCE data exhibit pronounced and unconventional hysteresis loops, in which the sample temperature increases during both the up-sweep and down-sweep of the field. In Nd$_2$Zr$_2$O$_7$, the MCE further displays a striking plateau as a function of time, followed by a rapid temperature rise that begins at the maximum applied field, across pulses with differing peak-field strengths. Our magnetization measurements reveal an inferred temperature of the magnetic subsystem that differs significantly from the directly measured sample temperature and exhibits opposite hysteresis: the temperature is higher on the up-sweep than the down-sweep, unlike the direct measurements. These observations indicate a breakdown of thermal equilibrium between magnetic and lattice degrees of freedom on the timescale of the pulse ($\sim 10^{-1}$s). We interpret the results using a phenomenological model involving two thermally coupled subsystems - the magnetic ions and phonons, and a thermal reservoir, which accounts well for the behavior of Pr$_2$Zr$_2$O$_7$. However, it fails to reproduce the plateau seen in Nd$_2$Zr$_2$O$_7$. Agreement with Nd$_2$Zr$_2$O$_7$ data is improved substantially if we allow the thermal coupling between the magnetic and the lattice subsystems to depend on the product $\frac{HdH}{dt}$. Our results reveal anomalously slow heat transfer between magnetic and lattice subsystems and point toward a novel mechanism for dynamically controlling the heat flow in Nd$_2$Zr$_2$O$_7$ via the rate of magnetic field variation.