Unlocking of time reversal, space-time inversion and rotation invariants in magnetic materials

Understand

Time reversal ($T$) and space inversion are symmetries of our universe in the low-energy limit.

• Fundamental theorems relate their corresponding quantum numbers to the spin for elementary particles: $\hat{T}^2=(\hat{P}\hat{T})^2=-1$ for half-odd-integer spins and $\hat{T}^2=(\hat{P}\hat{T})^2=+1$ for integer spins.
• Here we show that for elementary excitations in magnetic materials, this "locking" between quantum numbers is lifted: $\hat{T}^2$ and $(\hat{P}\hat{T})^2$ take all four combinations of $+1$ and $-1$ regardless of the value of the spin, where $T$ now represents the composite symmetry of time reversal and lattice translation.
• Unlocked quantum numbers lead to new forms of minimal coupling between these excitations and external fields, enabling novel physical phenomena such as the "cross-Lamor precession", indirectly observable in a proposed light-absorption experiment.