  Magic-angle twisted bilayer graphene (tBLG) has been studied extensively
owing to its wealth of symmetry-broken phases, correlated Chern insulators,
orbital magnetism, and superconductivity. In particular, the anomalous Hall
effect (AHE) has been observed at odd integer filling factors ($\nu=1$ and $3$)
in a small number of tBLG devices, indicating the emergence of a zero-field
orbital magnetic state with spontaneously broken time-reversal symmetry.
However, the AHE is typically not anticipated at half filling ($\nu=2$) owing
to competing intervalley coherent states, as well as spin-polarized and valley
Hall states that are favored by an intervalley Hund's coupling. Here, we
present measurements of two tBLG devices with twist angles slightly away from
the magic angle (0.96$^{\circ}$ and 1.20$^{\circ}$), in which we report the
surprising observation of the AHE at $\nu=+2$ and $-2$, respectively. These
findings imply that a valley-polarized phase can become the ground state at
half filling in tBLG rotated slightly away from the magic angle. Our results
reveal the emergence of an unexpected ground state in the
intermediately-coupled regime ($U/W \sim 1$, where $U$ is the strength of
Coulomb repulsion and $W$ is the bandwidth), in between the strongly-correlated
insulator and weakly-correlated metal, highlighting the need to develop a more
complete understanding of tBLG away from the strongly-coupled limit.
