  Spin qubits hosted in silicon (Si) quantum dots (QD) are attractive due to
their exceptionally long coherence times and compatibility with the silicon
transistor platform. To achieve electrical control of spins for qubit
scalability, recent experiments have utilized gradient magnetic fields from
integrated micro-magnets to produce an extrinsic coupling between spin and
charge, thereby electrically driving electron spin resonance (ESR). However,
spins in silicon QDs experience a complex interplay between spin, charge, and
valley degrees of freedom, influenced by the atomic scale details of the
confining interface. Here, we report experimental observation of a valley
dependent anisotropic spin splitting in a Si QD with an integrated micro-magnet
and an external magnetic field. We show by atomistic calculations that the
spin-orbit interaction (SOI), which is often ignored in bulk silicon, plays a
major role in the measured anisotropy. Moreover, inhomogeneities such as
interface steps strongly affect the spin splittings and their valley
dependence. This atomic-scale understanding of the intrinsic and extrinsic
factors controlling the valley dependent spin properties is a key requirement
for successful manipulation of quantum information in Si QDs.
