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.

Magnetism and X Rays

The ancient Greeks and also the Chinese knew about strange and rare stones with the power to attract iron. Moreover, when freely suspended these objects pointed north-south. Throughout the past, we have used this phenomenon—magnetism—for navigation and more recently for power production and digital information storage, all while trying to explore and understand its origins. In 1986 researchers at a facility similar to the ALS observed for the first time that the absorption of x rays depends not only on the composition of a material—that is, if it contains iron, nickel, or other elements—but also on its magnetism. The effect is unique in that it allows us to distinguish which atomic species magnetism originates from and provides information about their local atomic environment—for example, whether a magnetic species is surrounded by 4 or 6 oxygen atoms. A research team at the ALS has now shown that the relationship between magnetic order and absorption of x rays is even more complex and exciting than has been assumed for the past 20 years, leading to a reassessment of previous results.

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 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 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 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.

Angular dependence of the Ni L_2,3 XMLD in NiFe₂O₄/SrTiO₃(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,'' 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.

Top: Measured Ni L_2,3 XA spectrum for NiFe₂O₄/SrTiO₃. 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 Ni²⁺ x-ray magnetic linear dichroism: Interfacial coupling revisited," Phys. Rev. Lett. 98, 197201 (2007).