General Magnetic Transition Dipole Moments for Electron Paramagnetic Resonance

We present general expressions for the magnetic transition rates in electron paramagnetic resonance (EPR) experiments of anisotropic spin systems in the solid state. The expressions apply to general spin centers and arbitrary excitation geometry (Voigt, Faraday, and intermediate). They work for linear and circular polarized as well as unpolarized excitation, and for crystals and powders. The expressions are based on the concept of the (complex) magnetic transition dipole moment vector. Using the new theory, we determine the parities of ground and excited spin states of high-spin ($S=5/2$) ${\mathrm{Fe}}^{\mathrm{III}}$ in hemin from the polarization dependence of experimental EPR line intensities.

Figure 1

Sketches of magneto-optical excitation geometries described in the text. Electric (${\mathit{E}}_1$) and magnetic (${\mathit{B}}_1$) field components of the mw/THz radiation are depicted by red and green oscillating lines, respectively. $\mathit{k}$ (yellow arrow) denotes the propagation direction of the radiation. The static magnetic field ${\mathit{B}}_0$ is indicated by the gray arrow. Magnet coils are shown as gray tori. (a) EPR excitation of a sample (blue box) inside a mw resonator (pale yellow box with black contours). The standing wave in the resonator ensures maximum ${\mathit{B}}_1$ and minimum ${\mathit{E}}_1$ at the sample position. In the present case, ${\mathit{B}}_1$ is aligned perpendicular to ${\mathit{B}}_0$. (b) and (c) depict traveling wave excitation in Voigt geometry (b), where $\mathit{k}\perp {\mathit{B}}_0$, and Faraday geometry (c), where $\mathit{k}\parallel {\mathit{B}}_0$.

Figure 2

Relative EPR absorption of high-spin ${\mathrm{Fe}}^{\mathrm{III}}$ ($S=5/2$) in hemin at 458 GHz (black circles) and 845 GHz (red triangles) plotted vs the polarization angle $\alpha$, which was in the used excitation geometry the angle between ${\mathit{n}}_0$ and ${\mathit{n}}_1$. Simulated relative EPR absorptions are plotted as black solid (458 GHz) and red dashed (845 GHz) lines, respectively. The inset depicts the calculated spin energies normalized to the ground state level as a function of the magnetic field applied perpendicular to the hard axis of hemin. The black and red arrows mark the transitions observed at 458 GHz and 845 GHz, respectively.