  We present a semilocal exchange-correlation energy functional for
noncollinear spin density functional theory based on short-range expansions of
the spin-resolved exchange hole and the two-body density matrix. Our functional
is explicitly derived for noncollinear magnetism, U(1) and SU(2) gauge
invariant, and gives rise to nonvanishing exchange-correlation torques. Testing
the functional for frustrated antiferromagnetic chromium clusters, the exchange
part is shown to perform favorably compared to the far more expensive Slater
and optimized effective potentials, and a delicate interplay between exchange
and correlation torques is uncovered.
