Orbital Degeneracy Removed by Charge Order in Triangular Antiferromagnet ${\mathrm{AgNiO}}_2$

We report a high-resolution neutron diffraction study on the orbitally degenerate spin-$1/2$ hexagonal metallic antiferromagnet ${\mathrm{AgNiO}}_2$. A structural transition to a tripled unit cell with expanded and contracted ${\mathrm{NiO}}_6$ octahedra indicates $\sqrt{3}\times \sqrt{3}$ charge order on the Ni triangular lattice. This suggests charge order as a possible mechanism of lifting the orbital degeneracy in the presence of charge fluctuations, as an alternative to the more usual Jahn-Teller distortions. A novel magnetic ground state is observed at low temperatures with the electron-rich $S=1$ Ni sites arranged in alternating ferromagnetic rows on a triangular lattice, surrounded by a honeycomb network of nonmagnetic and metallic Ni ions. We also report first-principles band-structure calculations that explain microscopically the origin of these phenomena.

Figure 1

(a) 300 K neutron powder diffraction pattern and (b)–(d) zoomed-in regions showing some of the prominent supercell peaks which indicate a distortion of the high-symmetry $P{6}_3/mmc$ structure where all Ni sites are equivalent. (e)–(g) Supercell peaks are not observed in x-ray data, indicating that the distortion involves mainly displacements of oxygen ions. Solid lines in all panels are fits to the model with periodic arrangement of expanded and contracted ${\mathrm{NiO}}_6$ octahedra shown in Fig. 2, and peak indexing is in the triple unit cell (space group $P{6}_{3}22$).

Figure 2

Bottom $\mathrm{Ni}{\mathrm{O}}_2$ layer showing the expanded $\mathrm{Ni}1{\mathrm{O}}_6$ octahedra (large circle) surrounded by a honeycomb network (thick lines) of contracted Ni2 and Ni3 sites (small circles). The small balls are oxygen ions, and the small arrows indicate the displacements from the ideal structure.

Figure 3

(a) Magnetic diffraction pattern (difference 4–300 K) indexed by wave vector $\mathit{k}=(1/2,0,0)$. The solid line is a fit to the spin order depicted in (b). In one layer, ordered spins (Ni1) form alternating ferromagnetic rows, $\pm$ symbols indicate spin projection along the $c$ axis, and gray balls are unordered sites (Ni2 and Ni3). The diamond-shaped box is the unit cell. (c) 3D view of the magnetic order along the $c$ axis. Band-structure calculations indicate that the effective FM interlayer coupling between the strongly magnetic Ni1 spins (large arrows) occurs via AFM couplings to a very small moment at the Ni3 site (small white arrow). The inset in (a) shows the 2D hexagonal Brillouin zone with locations of magnetic Bragg peaks [solid stars for the stripe domain in (b), open stars for equivalent domains rotated by $\pm 60°$].

Figure 4

Ferromagnetic band structure of $2H\mathrm{\text{−}}{\mathrm{AgNiO}}_2$ along symmetry directions in the Brillouin zone. Blue/red (light/dark) correspond to the up/down spin directions, and circles indicate the relative weight of the Ni1 states. Inset: Partial densities of states for the three Ni sites in states/eV/triple cell. Top/bottom: Spin majority (up)/minority (down).