Forbidden Transitions (Δm=±1) in the Paramagnetic Resonance Absorption ofMn2+in Calcite

The forbidden transitions of the type $\Delta m=\pm 1$ for ${\mathrm{Mn}}^{2+}$ in single crystals of calcite have been investigated at $X$-band frequencies. The results can be fitted with the spin Hamiltonian $\mathcal{H}=g{\mu }_B\overrightarrow{\mathrm{H}}·\overrightarrow{\mathrm{S}}+B_2^0{O}_2^0+B_2^0{O}_2^0+B_4^0{O}_4^0+B_4^3{O}_4^3+C_4^3{O}_4^3+A\left(S_x{I}_z\right)+B(S_x{I}_x+S_y{I}_y)-g_N{\mu }_N\left(\overrightarrow{\mathrm{H}}·\overrightarrow{\mathrm{I}}\right)+Q^{\prime }[I_z^2-\frac{1}{3}I(I+1\mathrm{}\left)\right]+Q^{\prime \prime }(I_x^2-I_y^2)]$. At room temperature, the best computer fit for the parameter is $g_{\parallel }=2.\mathrm{}0019\pm 0.0006, g_{\perp }=2.\mathrm{}0018\pm 0.0006,$ $B_2^0=24.\mathrm{}99\pm 0.10, B_4^0=0.\mathrm{}0397\pm 0.0002,$ $A=87.\mathrm{}01\pm 0.04, B=87.\mathrm{}26\pm 0.04,$