Oxygen-vacancy-induced ferromagnetism in CeO 2 from first principles Xiaoping Han, 1 Jaichan Lee, 1, * and Han-Ill Yoo 2 1 School of Advanced Materials Science and Engineering, SungKyunKwan University, Suwon 440-746, Korea 2 Department of Materials Science and Engineering, Seoul National University, Seoul 151-744, Korea Received 14 October 2008; revised manuscript received 8 January 2009; published 10 March 2009 The electronic and magnetic properties of CeO 2 with various concentrations of oxygen vacancies have been studied by first-principles calculations within the LSDA+ U method and were found to remarkably depend on the oxygen vacancy concentration. With increasing oxygen deficiency, the electrons left behind by oxygen removal not only localize on Ce 4 f orbitals but also on the vacancy sites. This leads to the magnetic mecha- nism with both superexchange and polarization in the cases of heavy doping, effectively enhancing the stability of ferromagnetism. The study reveals the magnetic properties and associated magnetic mechanisms of CeO 2 with the different oxygen deficiencies. DOI: 10.1103/PhysRevB.79.100403 PACS numbers: 75.50.Pp, 61.72.Bb, 71.15.Mb Global environment and energy issues have led to great interest in ceria CeO 2 and related compounds, which can be applied to environmentally friendly power generation, such as solid oxide fuel cell and catalytic applications. 14 CeO 2 is known to be an oxygen vacancy reservoir with a high capacity for storing and releasing oxygen vacancies. Such a high oxygen vacancy storage capacity is essential in a wide variety of applications. To this end, oxygen vacancy often plays a vital role in changing materials properties, fur- ther influencing oxide-based device characteristics and reli- ability. For example, the high performance of CeO 2 as an oxygen buffer and active support for noble metals in cataly- sis relies on an efficient supply of lattice oxygens at reaction sites governed by oxygen vacancy formation. 5,6 Moreover, CeO 2 is widely used for ionic conducting oxides due to the role of oxygen vacancy. It is well known that the stoichiometrical CeO 2 is para- magnetic. When an oxygen atom is released from CeO 2 , two electrons are left behind and are believed to strongly localize at the f -level traps on two Ce atoms, which causes the formal valence of two neighboring Ce atoms to change from +4 to +3. This will give rise to net spin in the Ce f states, inducing the magnetism. However, little effort has been done to study the magnetic properties of oxygen-deficient CeO 2 . Further- more, most previous studies have been limited to slightly reduced CeO 2 , while CeO 2 is known to be an effective oxy- gen vacancy reservoir. In fact, high oxygen deficiency in CeO 2 is a very likely situation in a wide range of applica- tions since the oxides are often exposed to various environ- ments, such as a highly reducing atmosphere or a high- temperature condition. In this study, we therefore have examined the localization behavior of CeO 2 with various de- grees of oxygen deficiency as well as the associated mag- netic properties and their origins. This study reveals that the electrons are localized not only on the Ce 4 f state but also on the oxygen vacancy site i.e., the electron localization ten- dency on the Ce 4 f state weakenswhen the oxygen defi- ciency becomes large. These electrons remaining on the oxy- gen vacancy site are polarized by the reduced ions, eventually leading to the evidently enhanced ferromagnetic ordering in highly oxygen deficient CeO 2 . First-principles methods, implemented in the Vienna ab initio simulation package VASP, 7 were used to study the electronic and magnetic properties of CeO 2-x , particularly, the effects of oxygen vacancy doping concentration x = 3.13%, 6.25%, 12.5%, and 25% corresponding to 2 2 2, 1 2 2, 1 1 2, and 1 1 1 supercells with one oxygen vacancy, respectively. In all calculations, the projec- tor augmented wave method PAWRef. 8with the frozen- core approximation was used for the ion-electron interac- tions. Exchange correlation interactions were described by the PAW local spin density approximation LSDA. Due to the strong Coulomb interaction of the localized Ce 4 f elec- trons, the standard density-functional theory DFTcalcula- tions were inadequate for a satisfactory electronic structure prediction. Many recent reports 912 have proven that DFT calculation with the correction of Hubbard U parameter DFT+ Uis effective for CeO 2-x and related compounds. Dudarev’s spherical LDA+ U methods 13 were employed in this study. The optimal combination of U =8 eV and J =1 eV for Ce 4 f orbitals was found to improve the predic- tion of the electronic structure. The Brillouin-zone BZin- tegration was performed on a well-converged Monkhorst- Pack k-point grid. The plane-wave kinetic energy cutoff was set to be 400 eV. Atomic positions and lattice parameters were optimized until the atomic forces were smaller than 0.02 eV / Å. First, a CeO 1.969 supercell was used to model a low dop- ing concentration case x = 0.0313, where one oxygen atom is removed from a 96-atom 2 2 2 supercell of pure CeO 2 . Figure 1ashows the total density of states DOSof CeO 1.969 . The peak just below the Fermi level represents the localized f states, which are mainly on two Ce ions that are the nearest neighbors to the O vacancy. The gap between the O2p valence-band edge and occupied f state is 1.4 eV, which agrees well with the experimental value of 1.2–1.5 eV. 14 Figures 1b1dshow the total DOSs of CeO 2-x x = 0.0625, 0.125, and 0.25. The existence of the gap states in these figures reveals the electron localization. These local- ized states are also due to the 4 f states of the reduced Ce ion, originating from the electrons by oxygen removal. The inte- gration analysis using Bader analysis 15 shows that each of the two reduced Ce ions has 0.98, 0.97, 0.93, and 0.91 elec- trons for the cases of x = 0.0313, 0.0625, 0.125, and 0.25, PHYSICAL REVIEW B 79, 100403R2009 RAPID COMMUNICATIONS 1098-0121/2009/7910/1004034©2009 The American Physical Society 100403-1