Systematic study of the physical origin of ferromagnetism in CeO2−δ nanoparticles

Abstract

We have carried out a Schrieffer-Wolff transformation on a general tight-binding Hamiltonian and obtained a $4f$-one-band effective Hubbard Hamiltonian to study the physical origin of ferromagnetism in ${\mathrm{CeO}}_{2\ensuremath{-}\ensuremath{\delta}}$ nanoparticle systems. For a low temperature regime and low concentrations of oxygen vacancies, isolated vacancies have previously been showed to form on the ${100}$ and ${110}$ surfaces and our studies indicate these will be in singlet and triplet states, respectively. This is sustained by a superexchange interaction between the $4f$ electrons of the two cerium atoms, which are the nearest neighbors of the vacancy, and ferromagnetism and antiferromagnetism can coexist. Moreover, increasing the vacancy concentration we found that pairs of vacancies, which have been previously shown to form on the ${111}$ surfaces, produce Nagaoka ferromagnetism and isolated vacancies in the bulk produce an antiferromagnetic sign. Furthermore, further oxygen vacancy increases are previously known to favor the formation of oxygen vacancy clusters. In this case, our results showed a weakening of the magnetic correlations with respect to temperature. Thus, at a fixed temperature, the magnetic moment is reduced when the concentration of vacancies is increased, which is in agreement with experimental results reported in the literature. Interestingly, at a room-temperature regime, the antiferromagnetic order is destroyed and only the ferromagnetic couplings, produced mainly by isolated vacancies on the ${110}$ surfaces, survive. Finally, as temperature is increased further, the paramagnetic behavior of $4f$ electrons dominates.