  Electronic nematicity has been found in a wide range of strongly correlated
electron materials, resulting in the electronic states having a symmetry that
is lower than that of the crystal that hosts them. One of the most astonishing
examples is Sr$_3$Ru$_2$O$_7$, in which a small in-plane component of a
magnetic field induces significant resistivity anisotropy. The direction of
this anisotropy follows the direction of the in-plane field. The microscopic
origin of this field-induced nematicity has been a long-standing puzzle, with
recent experiments suggesting a field-induced spin density wave driving the
anisotropy. Here, we report spectroscopic imaging of a field-controlled
anisotropy of the electronic structure at the surface of Sr$_3$Ru$_2$O$_7$. We
track the electronic structure as a function of the direction of the field,
revealing a continuous change with the angle. This continuous evolution
suggests a mechanism based on spin-orbit coupling resulting in compass-like
control of the electronic bands. The anisotropy of the electronic structure
persists to temperatures about an order of magnitude higher compared to the
bulk, demonstrating novel routes to stabilize such phases over a wider
temperature range.
