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.
Eight-pole electromagnet installed at ALS Beamline 4.0.2 provides magnetic fields of up to 0.8 T in arbitrary directions, crucial for the study of the XMLD angular dependence.
The Ni^{2+ }moments in NiFe_{2}O_{4} 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 *L*_{2,3} 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 [100] 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 *L*_{2} 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.
Angular dependence of the Ni *L*_{2,3} XMLD in NiFe_{2}O_{4}/SrTiO_{3}(011). The inset depicts the experimental geometry of field **H** (black arrows) and linear polarization **E** (yellow arrows) at angle to the [100] axis (dashed line). Top: X-ray absorption (XA) spectrum. Bottom: XMLD spectra. Symbols indicate the experimental data and (red) lines give the results of the modeled angular dependence. The pronounced angular dependence of the XMLD signal is obvious.
Theoretical expressions for XMLD angular dependence can be obtained from symmetry considerations. The knowledge of only two "fundamental spectra,'' *I*_{0} and *I*_{45}, is needed for a correct description of the entire angular dependence. There is excellent agreement between the experimental data for *I*_{0} and *I*_{45} 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 3*d*^{8} → 2*p*^{5}3*d*^{9} in an octahedral crystal field. Agreement of the calculated I_{0} and *I*_{45} 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.
Top: Measured Ni *L*_{2,3} XA spectrum for NiFe_{2}O_{4}/SrTiO_{3}. Bottom: Comparison of the experimentally obtained fundamental XMLD spectra (dots) together with results from atomic multiplet calculations (lines).
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 Ni^{2+} x-ray magnetic linear dichroism: Interfacial coupling revisited," *Phys. Rev. Lett.* **98**, 197201 (2007). |