  Time-reversal (T) symmetry breaking is a fundamental physics concept
underpinning a broad science and technology area, including topological
magnets, axion physics, dissipationless Hall currents, or spintronic memories.
A best known conventional model of macroscopic T-symmetry breaking is a
ferromagnetic order of itinerant Bloch electrons with an isotropic spin
interaction in momentum space. Anisotropic electron interactions, on the other
hand, have been a domain of correlated quantum phases, such as the T-invariant
nematics or unconventional superconductors. Here we report discovery of a
broken-T phase of itinerant Bloch electrons with an unconventional anisotropic
spin-momentum interaction, whose staggered nature leads to the formation of two
ferromagnetic-like valleys in the momentum space with opposite spin splittings.
We describe qualitatively the effect by deriving a non-relativistic
single-particle Hamiltonian model. Next, we identify the unconventional
staggered spin-momentum interaction by first-principles electronic structure
calculations in a four-sublattice antiferromagnet Mn5Si3 with a collinear
checkerboard magnetic order. We show that the staggered spin-momentum
interaction is set by nonrelativistic spin-symmetries which were previously
omitted in relativistic physics classifications of spin interactions and
topological quasiparticles. Our measurements of a spontaneous Hall effect in
epilayers of antiferromagnetic Mn5Si3 with vanishing magnetization are
consistent with our theory predictions. Bloch electrons with the unconventional
staggered spin interaction, compatible with abundant low atomic-number
materials, strong spin-coherence, and collinear antiferromagnetic order open
unparalleled possibilities for realizing T-symmetry broken spin and topological
quantum phases.
