  We theoretically explore atomic Bose-Einstein condensates (BECs) subject to
position-dependent spin-orbit coupling (SOC). This SOC can be produced by
cyclically laser coupling four internal atomic ground (or metastable) states in
an environment where the detuning from resonance depends on position. The
resulting spin-orbit coupled BEC phase-separates into domains, each of which
contain density modulations - stripes - aligned either along the x or y
direction. In each domain, the stripe orientation is determined by the sign of
the local detuning. When these stripes have mismatched spatial periods along
domain boundaries, non-trivial topological spin textures form at the interface,
including skyrmions-like spin vortices and anti-vortices. In contrast to
vortices present in conventional rotating BECs, these spin-vortices are stable
topological defects that are not present in the corresponding homogenous
stripe-phase spin-orbit coupled BECs.
