We have investigated the element specific magnetic characteristics of single-crystal ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ using x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD). We have found that the Fe $L_{2,3}$-edge XAS spectra do not exhibit clear multiplet structures, indicating strong hybridization between the Fe $3d$ and S $3p$ orbitals, leading to delocalized rather than localized electronic states. The Fe $3d$ and Cr $3d$ spin moments are antiferromagnetically coupled, consistent with the Goodenough-Kanamori rule. The orbital magnetic moments of Fe and Cr are determined to be −0.23 and −0.017 ${\mu }_{\mathrm{B}}$ /ion, respectively. The large orbital magnetic moment of Fe is due to the $d^6$ configuration under the relatively weak tetrahedra crystal field at the Fe site, and the delocalized Fe electrons maintain the orbital degree of freedom in spite of their itinerant nature. To understand phenomena such as the gigantic Kerr rotation, it is essential to consider not only the orbital degrees of freedom but also the role of spin-orbit coupling, which induces a finite orbital magnetic moment through $t_2$ and $e$ level hybridization under the tetrahedral crystal field. This finite orbital moment serves as a direct indicator of spin-orbit interaction strength and links element-specific orbital magnetism to the large Kerr rotation. On the other hand, the octahedral crystal-field splitting of the Cr $3d$ level is large enough to result in the quenching of the orbital moment of the Cr ion in ${\mathrm{FeCr}}_2{\mathrm{S}}_4$.

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• Electronic structure of atoms & molecules
• Micromagnetism
• Spintronics
• Ferrimagnets
• Magnetic semiconductors
• X-ray absorption spectroscopy
• X-ray magnetic circular dichroism