  NASA's NICER telescope has recently provided evidence for non-dipolar
magnetic field structures in rotation-powered millisecond pulsars. These stars
are assumed to have gone through a prolonged accretion spin-up phase, begging
the question of what accretion flows onto stars with complex magnetic fields
would look like. We present results from a suite of GRMHD simulations of
accreting neutron stars for dipole, quadrupole, and quadrudipolar stellar field
geometries. This is a first step towards simulating realistic hotspot shapes in
a general relativistic framework to understand hotspot variability in accreting
millisecond pulsars. We find that the location and size of the accretion
columns resulting in hotspots changes significantly depending on initial
stellar field strength and geometry. We also find that the strongest
contributions to the stellar torque are from disk-connected fieldlines and the
pulsar wind, leading to spin-down in almost all of the parameter regime
explored here. We further analyze angular momentum transport in the accretion
disk due to large scale magnetic stresses, turbulent stresses, wind- and
compressible effects which we identify with convective motions. The disk
collimates the initial open stellar flux forming jets. For dipoles, the
disk-magnetosphere interaction can either enhance or reduce jet power compared
to the isolated case. However for quadrupoles, the disk always leads to an
enhanced net open flux making the jet power comparable to the dipolar case. We
discuss our results in the context of observed neutron star jets and provide a
viable mechanism to explain radio power both in the low- and high-magnetic
field case.
