Theory of Magnetically Induced Electric Field Gradients in CubicFe2+

The detection of a nonvanishing quadrupole interaction in ferrous compounds in which the ${\mathrm{Fe}}^{2+}$ ion occupies a site of cubic symmetry has been achieved in several cases, using Mössbauer spectroscopy. In some cases, the onset of this interaction has been found to be simultaneous with the appearance of magnetic ordering. A detailed theory of this effect is presented, which applies where the magnetic ordering is spontaneous (magnetic phase transitions), as well as where it is obtained by applying external magnetic fields to a paramagnetic compound. It is shown that an electric field gradient is induced by the magnetic ordering via the spin-orbit coupling. Utilizing the crystal-field approach, the magnetic ordering is described by adding a magnetic term to the Hamiltonian, using the molecular-field approximation. For cases where the magnetic term can be treated as a perturbation—which requires that it should be small compared to the spin-orbit interaction—closed expressions are obtained for the induced electric field gradient and for the magnetic hyperfine field at the site of the nucleus. The procedure required for other cases is outlined. The form of the resulting Mössbauer spectrum is discussed. It is shown that the quadrupole interaction is positive if the magnetic axis is parallel to a $〈111〉$ direction, and that is it of equal magnitude, but negative, when the axis is parallel to a $〈100〉$ direction. This fact may be utilized to determine the direction of the magnetic axis from Mössbauer measurements on a powder sample. Experimental evidence and possible applications of the theory are discussed.