X-Ray Directional Dichroism of a Polar Ferrimagnet

Abstract

In a polar ferrimagnet GaFeO3, we have found a novel magneto-optical effect, termed x-ray nonreciprocal directional dichroism (XNDD), that the x-ray absorption at around the K edge of an Fe ion depends on whether the x-ray propagation vector is parallel or antiparallel to the outer product of the magnetization and electric-polarization vectors. The XNDD spectroscopy as demonstrated here can be a useful tool to probe the local magnetism in noncentrosymmetric systems such as magnetic interfaces and nanostructures.

Detection of electromagnetic multipoles by x-ray spectroscopies

“…Even though we basically agree with the general interpretation given by the authors of Ref. [ 7] itself, their analysis is just semi-quantitative and here we are able to provide a more comprehensive description of the experiment, which can frame the measured signal within the global picture described above. The aim of this subsection is to relate the XNDD signal to the dipole-quadrupole magnetic tensors F (i−) (E1 − E2) (i=1,2,3) introduced above, discuss the physical meaning of each term, and substantiate the description by calculating the XNDD through an abinitio numerical code.…”

“…This possibility was realized in Ref. [ 7], in which a beautiful experiment was performed under the name of x-ray non-reciprocal directional dichroism (XNDD) whereby a time-reversal and parity-odd signal was detected. Even though we basically agree with the general interpretation given by the authors of Ref.…”

“…Of course, a much more cogent test to demonstrate the detectability of such quantities is represented by a convergent description of theory and experiment. Such an experiment has already been performed with a dichroic technique in absorption, 7 and in the next section we shall provide its quantitative interpretation in terms of the three time-reversal and parity-odd quantities…”

“…[ 7,35], the unit cell is orthorhombic, with an electric polarization along the screw b axis, and a net magnetization, below T c , along the c axis.…”

“…[ 7] four absorption spectra were measured, all with the x-ray wavevector directed along the a-axis: in two cases the electric polarization was directed along the c-axis, and in two cases along the b-axis. For each of these two subcases, the magnetic moment was selected to be either parallel or antiparallel to the easy c-axis, by means of an applied external magnetic field.…”