  Kramers degeneracies play an essential role in the spectrum of electronic
materials. Here we argue that beyond spectral properties, Kramers degeneracy
plays a critical role in the nonlinear response of PT symmetric magnets. In
particular, we uncover a class of second-order Kramers nonlinearities that only
arise in the presence of Kramers degeneracy, vanishing in non-degenerate PT
symmetric materials. Kramers nonlinearties depend on a circular dichroism
between PT related Kramers states and enable to trace out the quantum geometry
of the degenerate band structure. We find pronounced Kramers nonlinearitites in
the nonlinear polarization responses of even layer antiferromagnetic
MnBi$_2$Te$_4$ that enable to identify its antiferromagnetic order. This
provides novel means for diagnosing Kramers pairs and addressing the internal
Kramers degree of freedom.
