Table 1 Symmetry properties of electromagnetic linear response functions

From: Theory of optical axion electrodynamics and application to the Kerr effect in topological antiferromagnets

Tensor

P

T

PT

Phenomena

Kerr

Faraday

χij

+ 

+

+

Refraction and absorption

No

No

\({\chi }_{ij}^{{\prime} }\)

+ 

−

−

Hall effect

Yes

Yes

\({G}_{ij},{a}_{ijk}^{{\prime} }\)

− 

−

+

Optical magneto-electric effect

Yes

No

\({G}_{ij}^{{\prime} },{a}_{ijk}\)

− 

+

−

Natural optical activity

No

Yes

  1. Response functions are defined in Eq. (1). The sign in the second column shows that parity of the response functions under spatial inversion P, time reversal T, and spacetime inversion PT. Kerr and Faraday in the last column indicate the optical rotation of the light polarization plane in reflection and transmission, respectively (i.e., the Kerr and Faraday effects). Kerr and Faraday effects are allowed when T and PT symmetry are broken, respectively33,53,54.