Spin-polarized ground states and ferromagnetic order induced by low-coordinated surface atoms and defects in nanoscale magnesium oxide

We investigate the effect of surface defects and the related low-coordinated surface atoms on the defect-induced magnetism in MgO nanocrystallites using hybrid density functional theory calculations. It has been demonstrated that when Mg vacancies are introduced at the surface or near surface of cubelike MgO clusters, a magnetic state ($S$ $\ge$ 1) becomes lower in total energy than the nonmagnetic singlet state ($S$ = 0) by several electron volts, resulting in the robust spin-polarized ground state. The total spin $S$ of the clusters in their ground state is equal to the number of the surface Mg vacancies introduced. The resulting spin density is not only located at the surrounding O atoms neighbor to the Mg vacancy site but is also extended to the low-coordinated surface O atoms along the $〈110〉$ direction, forming ferromagneticlike domains. This directional spin delocalization allows a remote (∼1 nm or longer) vacancy-vacancy interaction, eventually leading to a long-range ferromagnetic interaction.

Figure 1

(a) Schematic view of a ($4\times 4\times 4$)-atom block of the MgO cluster. An Mg (or O) atom, indicated by an arrow, is removed to create an Mg- (or O-) deficient cluster.

Figure 2

Schematic views of (a) ($4\times 4\times 4$)-, (b) ($6\times 4\times 3$)-, (c) ($7\times 4\times 3$)-, and (d) ($8\times 4\times 3$)-atom blocks of the MgO clusters. Two corner Mg atoms indicated by arrows are removed from each cluster to create the corresponding Mg deficient cluster with two Mg vacancies.

Figure 3

Comparison of the relative total energies of the ($4\times 4\times 4$)-based clusters with (a) one O vacancy and (b) one Mg vacancy located at different sites. For the O-deficient clusters, the energy is referenced to that of the cluster with a corner O vacancy in the spin-restricted singlet state. For the Mg-deficient clusters, the energy is referenced to that of the cluster with a corner Mg vacancy in the triplet state.

Figure 4

Spin-density isosurface (0.001 $e$/Bohr${}^3$) projected from the [111] direction of the ($4\times 4\times 4$)-based cluster with one corner Mg vacancy calculated for (a) the spin-unrestricted singlet state and (b) the spin triplet state. Large and small circles represent Mg and O atoms, respectively. The corner Mg vacancy is located at the forward most position along the [111] direction. The blue (dark) and red (light) isosurfaces represent spin up and down values, respectively.

Figure 5

Spin-density map on one of the {100} planes for the Mg${}_{31}$O${}_{32}$ cluster in the spin-triplet state. The Mg vacancy is located (a) at the corner and (b) in the plane. In (c), the Mg vacancy resides at the subsurface or one layer below the oxygen atom indicated by the white arrow. Large and small circles represent Mg and O atoms, respectively. The values indicated are Mulliken atomic spin densities; the values below 0.001 are omitted.

Figure 6

Spin-density map on the (100) plane containing two corner Mg vacancies calculated for the (a) ($4\times 4\times 4$)-, (b) ($6\times 4\times 3$)-, (c) ($7\times 4\times 3$)-, and (d) ($8\times 4\times 3$)-based clusters in the spin-quintet ($S$ = 2) state. Large and small circles represent Mg and O atoms, respectively. The values indicated are Mulliken atomic spin densities; the values below 0.001 are omitted.

Figure 7

Spin-density map on the (100) plane containing two corner Mg vacancies calculated for the (a) ($4\times 4\times 4$)- and (b) ($6\times 4\times 3$)-based clusters in the spin-unrestricted singlet state. Large and small circles represent Mg and O atoms, respectively. The values indicated are Mulliken atomic spin densities; the values below ±0.1 are omitted.

Figure 8

Spin-density map on one of the {100} planes for the Mg${}_{28}$O${}_{32}$ cluster in the spin-nonet ($S$ = 4) state. The values indicated are Mulliken atomic spin densities; the values below 0.001 are omitted.

Figure 9

Molecular orbital energy-level diagrams of occupied molecular orbitals (solid lines) and unoccupied molecular orbitals (dotted lines) calculated for the ($4\times 4\times 4$)-based clusters with one O or one Mg vacancy at the corner. (a) O-deficient Mg${}_{32}$O${}_{31}$ cluster in the spin-singlet state, (b) Mg-deficient Mg${}_{31}$O${}_{32}$ cluster in the spin-singlet state, and (c) Mg-deficient Mg${}_{31}$O${}_{32}$ cluster in the spin-triplet state.

Figure 10

Cross section of the LUMO orbital of the ($4\times 4\times 4$)-based clusters with (a) one O vacancy and (b) one Mg vacancy at the corner calculated for the spin-restricted singlet state.