The origin of hysteresis in resistive switching in magnetite is Joule heating

In many transition metal oxides the electrical resistance is observed to undergo dramatic changes induced by large biases. In magnetite, Fe$_3$O$_4$, below the Verwey temperature, an electric field driven transition to a state of lower resistance was recently found, with hysteretic current-voltage response. We report the results of pulsed electrical conduction measurements in epitaxial magnetite thin films. We show that while the high- to low-resistance transition is driven by electric field, the hysteresis observed in $I-V$ curves results from Joule heating in the low resistance state. The shape of the hysteresis loop depends on pulse parameters, and reduces to a hysteresis-free "jump" of the current provided thermal relaxation is rapid compared to the time between voltage pulses. A simple relaxation time thermal model is proposed that captures the essentials of the hysteresis mechanism.