Magnetism of chromia from first-principles calculations

Abstract

The electronic structure and magnetism of chromia ͑corundum-type Cr 2 O 3 ͒ are studied using full-potential first-principles calculations. The electronic correlations are included within the LSDA+ U method. The energies of different magnetic configurations are very well fitted by the Heisenberg Hamiltonian with strong exchange interaction with two nearest neighbors and additional weak interaction up to the fifth neighbor shell. These energies are insensitive to the position of the oxygen states, indicating that magnetism in Cr 2 O 3 is dominated by direct exchange. The Néel temperature is calculated using the pair-cluster approximation for localized quantum spins of magnitude 3/2. Very good agreement with experiment is found for all properties including the equilibrium volume, spectral density, local magnetic moment, band gap, and the Néel temperature for the values of U and J that are close to those obtained within the constrained occupation method. The band gap is of the Mott-Hubbard type.

Microscopic origin of the structural phase transitions at the Cr2O3(0001) surface

“…The identification of sites A and B as the most favorable agrees with LEED measurements and molecular dynamics simulations of Ref. 6, as well as with surface x-ray diffraction data, 7 but recent LEED 10 and surface x-ray diffraction (SXRD) 11 22 the reduced coordination could make it more important at the surface. To estimate its role, we calculated the energy difference between surface models A and B in the presence of spin-orbit coupling (taking the structures relaxed without it).…”

“…Further, first-principles calculations by Rohrbach et al 16 based on the GGA+U method have shown that this termination has the lowest surface energy (compared to all others considered) over the entire range of oxygen chemical potential where Cr 2 O 3 is stable. Note that earlier results based on the GGA method, which leads to grossly incorrect electronic and magnetic properties, 22 were quite different. 15 In this work we only consider the Cr 2 O 3 (0001) surface terminated by a single layer of Cr.…”

“…We considered 1 × 1, 1 × 2, 1 × 3, and √ 3 × √ 3 surface supercells (where 1 × 1 corresponds to the hexagonal unit cell of bulk Cr 2 O 3 ). The lateral dimensions of the unstrained supercell were fixed to the calculated equilibrium bulk values; 22 for the strained case these values were used as a reference. Apart from these constraints, the ionic positions were relaxed until the Hellmann-Feynman forces were converged to less than 0.01 eV/Å.…”

“…The fitted parameters differ significantly from the bulk couplings, which is a result of large ionic relaxations near the polar surface. (The parameters calculated as if the bulk exchange parameters 22 do not change near the surface are listed in the last column of Table III. ) To calculate the temperature dependence of magnetizations for surface sites A and B, we used the mean-field approximation applied to the quantum spin-3/2 version of the Heisenberg model (6).…”

Excited Cr impurity states in Al2O3from constraint density functional theory

“…Moreover, recent LSDA+U calculations 21 and combined DFT calculations with the configuration interaction method 22 pointed out the importance of electron correlation effects in the localized Cr 3d-orbitals in ruby. Even in the case of pure Cr 2 O 3 , which has less localized character compared to the impurity states, the LSDA+U calculations give great improvements for structural ground-state properties of the bulk and at surfaces [23][24][25] .…”