The capability to control the properties of quantum materials by external parameters is a crucial milestone of condensed matter physics. In this perspective, the flow of direct current is an appealing control parameter, allowing to trigger exotic electronic and magnetic states while being compatible with modern integrated electronics.

The strongly correlated Mott insulator Ca₂RuO₄ offers a unique playground for exploring non-equilibrium steady states triggered by direct current, where phenomena such as modulation of the Mott gap or inter-phase Peltier effects have been recently reported. When conducting measurements with current, however, the effects of the unavoidable Joule heating need to be carefully addressed. On the one hand, direct current heating can be used to trigger the metal–insulator transition of Ca₂RuO₄ and control regions of phase coexistence. On the other hand, localised heating of materials used for building sample holders can lead to effects of extrinsic nature, such as unexpectedly strong diamagnetic-like signals. It is hence necessary to formulate a robust measurement protocol to perform measurements with applied electrical current, with the aim of limiting the Joule heating and accurately assess the sample temperature.

In this talk, I will present recent advances in studying the properties of Ca₂RuO₄ bulk single crystals under the flow of electric current, focusing on its electronic and magnetic properties. I will discuss the challenges involved in dealing with large currents, describe a simple model that allows to account for the main contributions of Joule heating, in view of unravelling current-induced phenomena intrinsic to this strongly correlated material.