Time-reversal asymmetry without local moments via directional scalar spin chirality

Invariably, time-reversal symmetry (TRS) violation in a state of matter is identified with static magnetism in it. Here, a directional scalar spin chiral order (DSSCO) phase is introduced that disobeys this basic principle: it breaks TRS but has no density of static moments. It can be obtained by melting the spin moments in a magnetically ordered phase but retaining residual broken TRS. Orbital moments are then precluded by the spatial symmetries of the spin rotation symmetric state. It can exist in one, two and three dimensions under different conditions of temperature and disorder. Recently, polar Kerr effect experiments in the mysterious pseudogap phase of the underdoped cuprates hinted at a strange form of broken TRS below a temperature $T_{K}$, that exhibits a hysteretic "memory effect" above $T_{K}$ and begs reconciliation with nuclear magnetic resonance (which sees no moments), X-ray diffraction (which finds charge ordering tendencies) and the Nernst effect (which detects nematicity). Remarkably, the DSSCO provides a phenomenological route for reconciling all these observations, and it is conceivable that it onsets at the pseudogap temperature $\sim T^{*}$. A testable prediction of the existence of the DSSCO in the cuprates is a Kerr signal above $T_{K}$ triggered and trainable by a current driven along one of the in-plane axes, but not by a current along the other.