  In the 1950's, Pomeranchuk predicted that, counterintuitively, liquid 3He may
solidify upon heating, due to a high excess spin entropy in the solid phase.
Here, using both local and global electronic entropy and compressibility
measurements, we show that an analogous effect occurs in magic angle twisted
bilayer graphene. Near a filling of one electron per moir'e unit cell, we
observe a dramatic increase in the electronic entropy to about 1kB per unit
cell. This large excess entropy is quenched by an in-plane magnetic field,
pointing to its magnetic origin. A sharp drop in the compressibility as a
function of the electron density, associated with a reset of the Fermi level
back to the vicinity of the Dirac point, marks a clear boundary between two
phases. We map this jump as a function of electron density, temperature, and
magnetic field. This reveals a phase diagram that is consistent with a
Pomeranchuk-like temperature- and field-driven transition from a low-entropy
electronic liquid to a high-entropy correlated state with nearly-free magnetic
moments. The correlated state features an unusual combination of seemingly
contradictory properties, some associated with itinerant electrons, such as the
absence of a thermodynamic gap, metallicity, and a Dirac-like compressibility,
and others associated with localized moments, such as a large entropy and its
disappearance with magnetic field. Moreover, the energy scales characterizing
these two sets of properties are very different: whereas the compressibility
jump onsets at T~30K, the bandwidth of magnetic excitations is ~3K or smaller.
The hybrid nature of the new correlated state and the large separation of
energy scales have key implications for the physics of correlated states in
twisted bilayer graphene.
