|Unexpected Angular Dependence of X-Ray Magnetic Linear Dichroism|
Using spectroscopic information for magnetometry and magnetic microscopy obviously requires detailed theoretical understanding of spectral shape and magnitude of dichroism signals. A research team at ALS Beamline 4.0.2 has now shown unambiguously that, contrary to common belief, spectral shape and magnitude of x-ray magnetic linear dichroism (XMLD) are not only determined by the relative orientation of magnetic moments and x-ray polarization, but their orientation relative to the crystallographic axes must be taken into account for accurate interpretation of XMLD data.
The Ni2+ moments in NiFe2O4 films are coupled ferromagnetically and can be aligned in any in-plane direction by external magnetic fields of about 0.5 T. The angular dependence of the XMLD signal across the Ni L2,3 edges was determined by rotating the orientation of x-ray polarization E and external magnetic field H relative to the crystalline axes. E makes an angle relative to the  crystal axis. XMLD spectra were determined with H and hence the Ni moments parallel and perpendicular to E, varying the orientation of E relative to the crystal lattice. A strong anisotropy of the XMLD signal can clearly be observed. In particular, the Ni L2 XMLD signal reversed sign between = 0º and 45º and disappeared almost completely for = 90º. This demonstrates that the spectral shape of the XMLD signal depends strongly on the orientations of E and H relative to the crystalline axes. This must be taken into account for a correct interpretation of the XMLD for magnetometry and microscopy applications.
Theoretical expressions for XMLD angular dependence can be obtained from symmetry considerations. The knowledge of only two "fundamental spectra,'' I0 and I45, is needed for a correct description of the entire angular dependence. There is excellent agreement between the experimental data for I0 and I45 and the modeled angular dependence. Additional confirmation was obtained from atomic multiplet calculations. The researchers fit the experimental spectra using the calculated dipole transitions Ni 3d8 → 2p53d9 in an octahedral crystal field. Agreement of the calculated I0 and I45 when compared with the experimental data is remarkable. All experimentally observed features are reproduced by the calculation. Only the intensity of the XMLD feature at 855.5 eV appears overestimated.
The XA spectra are determined by electric-dipole selection rules restricting the set of final states reachable from the ground state. This gives different transition probabilities from the exchange-split core levels to the crystal-field-split empty d states. The calculations show that the angular dependence of the XMLD signal disappears when the crystal field splitting goes to zero. Therefore, anisotropic XMLD is a property of the cubic wavefunctions for the d states with respect to the spin quantization axis, not the anisotropic spin-orbit interaction.
Research conducted by E. Arenholz (ALS), G. van der Laan (Daresbury Laboratory), R.V. Chopdekar (Cornell University and University of California, Berkeley), and Y. Suzuki (University of California, Berkeley).
Research funding: U.S. Department of Energy, Office of Basic Energy Sciences (BES). Operation of the ALS is supported by BES.
Publication about this research: E. Arenholz, G. van der Laan, R.V. Chopdekar, and Y. Suzuki, "Angle-dependent Ni2+ x-ray magnetic linear dichroism: Interfacial coupling revisited," Phys. Rev. Lett. 98, 197201 (2007).