Fig. 4. Tunability of the magnetic moment of bound states through controlling the size of triangular S vacancies.

a, b Intensity plot of field dependent dI/dV spectra (top) and corresponding energy shift of primary peak position with magnetic field (bottom) for triangular vacancy of N = 3 (a) and N = 10 (b). A linear function is applied to fit the energy shift of peak position, with the slope marked. c STM image (top) and corresponding line profile (bottom), showing a narrow Co₃Sn terrace confined by the step edges of adjacent S terraces. d Intensity plot of field dependent dI/dV spectra (top) and corresponding energy shift of peak position with magnetic field (bottom) of the bound states at narrow Co₃Sn terrace in (c), revealing a magnetic moment of approximately 0.19 meV/T = 3.28 µ_B for the bound state near Fermi level. e Evolution of the magnetic moment with the atomic number of vacancies, showing that the magnetic moments extend from localized magnetic moment around vacancies (spin–orbit polarons, SOPs) to flat band negative magnetism from Co₃Sn kagome layer. The colored curve is a visual guide to the trend in the evolution of the moment with increasing atomic number N. The error bars in (e) are determined by linear fitting as shown in bottom panel in (a), (b) and (d). The red circling arrows in (e) indicate the circulating current in kagome lattice. STM parameters: (a): V_s = −250 mV, I_t = 500 pA; (b) V_s = −50 mV, I_t = 500 pA; (d) V_s = 20 mV, I_t = 500 pA; V_mod = 0.2 mV; (c) V_s = −400 mV, I_t = 50 pA.