Isospin Pomeranchuk effect in twisted bilayer graphene

In condensed-matter systems, higher temperatures typically disfavour ordered phases, leading to an upper critical temperature for magnetism, superconductivity and other phenomena. An exception is the Pomeranchuk effect in ³He, in which the liquid ground state freezes upon increasing the temperature¹, owing to the large entropy of the paramagnetic solid phase. Here we show that a similar mechanism describes the finite-temperature dynamics of spin and valley isospins in magic-angle twisted bilayer graphene². Notably, a resistivity peak appears at high temperatures near a superlattice filling factor of -1, despite no signs of a commensurate correlated phase appearing in the low-temperature limit. Tilted-field magnetotransport and thermodynamic measurements of the in-plane magnetic moment show that the resistivity peak is connected to a finite-field magnetic phase transition³ at which the system develops finite isospin polarization. These data are suggestive of a Pomeranchuk-type mechanism, in which the entropy of disordered isospin moments in the ferromagnetic phase stabilizes the phase relative to an isospin-unpolarized Fermi liquid phase at higher temperatures. We find the entropy, in units of Boltzmann's constant, to be of the order of unity per unit cell area, with a measurable fraction that is suppressed by an in-plane magnetic field consistent with a contribution from disordered spins. In contrast to ³He, however, no discontinuities are observed in the thermodynamic quantities across this transition. Our findings imply a small isospin stiffness^4,5, with implications for the nature of finite-temperature electron transport^6-8, as well as for the mechanisms underlying isospin ordering and superconductivity^9,10 in twisted bilayer graphene and related systems.