Exchange torque in noncollinear spin density functional theory with a semilocal exchange functional

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.