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URu$_2$Si$_2$ is surely one of the most mysterious of the heavy-fermioncompounds. Despite more than twenty years of experimental and theoreticalworks, the order parameter of the transition at $T_0 = 17.5$ K is stillunknown. The state below $T_0$ remains called "hidden-order phase" and thestakes are still to identify the energy scales driving the system to thisphase. We present new magnetoresistivity and magnetization measurementsperformed on very-high-quality single crystals in pulsed magnetic fields up to60 T. We show that the transition to the hidden-order state in URu$_2$Si$_2$ isinitially driven by a high-temperature crossover at around 40-50 K, which is afingerprint of inter-site electronic correlations. In a magnetic field$\mathbf{H}$ applied along the easy-axis $\bf{c}$, the vanishing of thishigh-temperature scale precedes the polarization of the magnetic moments, aswell as it drives the destabilization of the hidden-order phase. Stronglyimpurity-dependent magnetoresistivity confirms that the Fermi surface isreconstructed below $T_0$ and is strongly modified in a high magnetic fieldapplied along $\mathbf{c}$, i.e. at a sufficiently-high magnetic polarization.The possibility of a sharp crossover in the hidden-order state controlled by afield-induced change of the Fermi surface is pointed out.

Interplay of magnetism, Fermi surface reconstructions, and hidden-order in the heavy-fermion material URu$_2$Si$_2$