Fig. 2: XAS and XMCD spectra of GdMn₆Sn₆ samples at Gd M_{4, 5} edges, Mn L_{2, 3} edges and Sn M_{4, 5} edges.

a–c Experimental and calculated x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) spectra of Gd, Mn and Sn element. I⁺ (red circles) and I⁻ (blue circles) represent the absorption intensities measured under positive and negative magnetic fields, respectively. The XMCD data which shown as green circles are obtained by calculating the difference between I⁺ and I⁻ absorption spectra. d Schematic of the experimental setup. The absorption intensity of the sample under positive (+B, black) and negative (−B, red) magnetic fields corresponds to left-circular (red) and right-circular (black) polarized light, respectively. The XMCD intensity is defined as \(\Delta I={I}^{+}-{I}^{-}\). e, f Schematic of the microscopic magnetic structure in GdMn₆Sn₆ showing that magnetic moments on Mn are anti-parallel coupled with those on Sn and Gd. Different atoms are labeled with different colors, with Sn1, Sn2, and Sn3 shown in yellow, red, and green, respectively. Arrows indicate the magnitude and direction of the magnetic moments of the different atoms.