Room temperature d⁰ ferromagnetism in PbS films: nonuniform distribution of Pb vacancies

Because of the importance of ferromagnetism at room temperature, we search for new materials that can exhibit a non-vanishing magnetic moment at room temperature and at the same time can be used in spintronics. The experimental results indicate that d0 ferromagnetism without any magnetic impurities takes place in PbS films made of close-packed lead sulfide nanoparticles of 30 nm. To explain the existence of the d0 ferromagnetism, we propose a model where various PbS bulk and surface configurations of Pb-vacancies are analyzed. The bulk configurations have a zero magnetic moment while the two surface configurations with Pb vacancies with the same non-vanishing magnetic moments and lowest ground state energies contribute to the total magnetization. Based on the experimental value of the saturation magnetization, 0.2 emu g-1, we have found that the calculated Pb vacancy concentration should be about 3.5%, which is close to typical experimental values. Besides being very important for applications, there is one feature of PbS d0 ferromagnetism that makes this material special for fundamental research: PbS ferromagnetism can exhibit topologically driven spatial magnetic moment distributions (e.g., magnetic skyrmions) due to large spin-orbit coupling.