The electromagnetic susceptibilities of an electron gas in crystals with broken space parity are considered. Because of the spin-orbit coupling, which is inherent in such compounds, their electromagnetic responses, in addition to the conductivity and the magnetic susceptibility also include some cross terms of magnetoelectric nature. It is found that almost all of these electromagnetic susceptibilities, as functions of frequency $\omega$ and wave vector $\mathbf{q}$, should contain nonreciprocal terms that are odd in the wave vector $\mathbf{q}$. Crystals of two types are considered: (i) polar symmetry crystals, in which the coupling between the electron momentum $\mathbf{p}$ and spin $\mathit{\sigma }$ has the form $H_{\mathrm{so}}=\alpha (\mathbf{p}\times \mathbf{c})·\mathit{\sigma }$ (where $\mathbf{c}$ is the polar axis), and (ii) crystals of a cubic space-odd symmetry, in which the Hamiltonian of the spin-orbit coupling in the simplest case has the form $H_{\mathrm{so}}^{\prime }={\alpha }^{\prime }\mathbf{p}·\mathit{\sigma }$. It is shown that effects of $H_{\mathrm{so}}$ and $H_{\mathrm{so}}^{\prime }$ on electromagnetic responses are noticeably different in spite of their rather similar form. All results are derived for the case of impure crystals in the limit of low frequencies $\omega \tau \ll 1$ and long wavelengths $q{v}_F\tau \ll 1$ (where $\tau$ is the mean collision time) when the main kinetic process responsible for the nonreciprocal terms in the susceptibilities is the spin nonconserving impurity scattering, that is, the same process that controls the spin relaxation in such crystals. The effect of the spin-orbit coupling on magnetic neutron scattering is briefly discussed.

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• Spin-orbit coupling
• Transport phenomena
• 3-dimensional systems
• Intermetallic compounds
• Ordered compounds
• Discrete symmetries in condensed matter
• P-symmetry
• Symmetries in condensed matter