Charge disproportionation and collinear magnetic order in the frustrated triangular antiferromagnet ${\text{AgNiO}}_2$

We report a high-resolution neutron diffraction study of the crystal and magnetic structure of the orbitally degenerate frustrated metallic magnet ${\text{AgNiO}}_2$. At high temperatures the structure is hexagonal with a single crystallographic Ni site, low-spin ${\text{Ni}}^{3+}$ with spin 1/2 and twofold orbital degeneracy, arranged in an antiferromagnetic triangular lattice with frustrated spin and orbital order. A structural transition occurs upon cooling below 365 K to a tripled hexagonal unit cell containing three crystallographically distinct Ni sites with expanded and contracted ${\text{NiO}}_6$ octahedra, naturally explained by spontaneous charge order on the Ni triangular layers. No Jahn-Teller distortions occur, suggesting that charge order occurs in order to lift the orbital degeneracy. Symmetry analysis of the inferred Ni charge order pattern and the observed oxygen displacement pattern suggests that the transition could be mediated by charge fluctuations at the Ni sites coupled to a soft oxygen optical phonon breathing mode. At low temperatures the electron-rich Ni sublattice (assigned to a valence close to ${\text{Ni}}^{2+}$ with $S=1$) orders magnetically into a collinear stripe structure of ferromagnetic rows ordered antiferromagnetically in the triangular planes. We discuss the stability of this uncommon spin order pattern in the context of an easy-axis triangular antiferromagnet with additional weak second-neighbor interactions and interlayer couplings.

Figure 1

(Color online) Nominal crystal structure of $2H{\text{-AgNiO}}_2$ deduced from x-ray measurements in Ref. 15 (space group $P{6}_3/mmc,D_{6h}^4$). (a) There are two ${\text{NiO}}_2$ layers per unit cell related by a mirror plane reflection through the ${\text{Ag}}^{+}$ layer at $z=1/4$. (b) Basal plane showing the triangular network of Ni ions (large red balls) coordinated by oxygens (small blue balls). The thick solid line contour shows the unit cell and the dashed line shows the unit cell tripling in the distorted structure.

Figure 2

(Color online) (a) Room temperature (300 K) neutron diffraction pattern obtained using HRPD (resolution $\Delta Q/Q\sim {10}^{-3}$, 15 h counting on an 11 g powder sample). The solid curve through the data points is a fit to the distorted $P{6}_{3}22$ space group. Vertical bars indicate Bragg peak positions and the bottom curve shows the difference between the fit and the data. Zoomed-in regions showing weak supercell peaks are plotted in Fig. 3. (b) Detail of the (111) peak line shape expected to split in the case of a structural distortion to an orthorhombic or monoclinic structure. No splitting could be detected, and the line shape at both 300 (open symbols) and 2 K (filled circles) could be well described by a resolution-convolved profile for the hexagonal $P{6}_{3}22$ space group (solid lines) with lattice parameters adjusted for thermal contraction upon cooling.

Figure 3

(Color online) Zoomed-in regions of the 300 K neutron diffraction pattern (a), (b), (e), and (h) showing a number of the weak supercell reflections disallowed in the ideal $P{6}_3/mmc$ structure and associated with a tripling of the unit cell in the $ab$ plane. Solid lines are the calculated profile for the distorted $P{6}_{3}22$ structure in Fig. 4 and dashed lines show the estimated local background including the resolution tails of nearby main structural peaks (data in some panels are shifted vertically by indicated amounts for clarity). Paired panels (b),(c), (e),(f), and (h),(i) show how the supercell peaks are displaced in $Q$ following the lattice contraction upon cooling (the base temperature data have a higher overall background as they were collected in a cryostat). Supercell peaks are not observed in the x-ray data in (d), (g), and (j), consistent with the structural modulation involving mainly displacements of the light oxygen ions.

Figure 4

(Color online) (Top) Schematic diagram of the ${\text{NiO}}_2$ layer at $z=1/4$ showing how the displacements (small arrows) of the oxygen ions (small balls) lead to a periodic arrangement of expanded (large circle, Ni1) and contracted (small circles, Ni2,3) ${\text{NiO}}_6$ octahedra. Thick hexagonal contour shows the honeycomb network of contracted sites. The origin of the coordinate system is at the circled Ni2 site. (Bottom) The expanded site Ni1 has a staggered zigzag arrangement between even and odd layers stacked along the $c$ axis. Layer 2 in the unit cell ($z=3/4$ and $-1/4$) is obtained from layer 1 by 180° rotation around the central $\left(1/2,1/2,z\right)$ axis followed by a $\mathit{c}/2$ translation.

Figure 5

(Color online) (a) Comparison between 300 K (open symbols, lower trace) and 420 K data (filled symbols, upper trace) showing the absence of the triple-cell peaks (021), (212), and (314) at high temperature. Solid lines are fits to the distorted (300 K) and ideal (420 K) structures, respectively, and dashed lines show the estimated background level. The high-temperature data have been shifted vertically by the indicated offsets for clarity. (b) Temperature dependence of the lattice parameters: $c$ left axis, $a$ right axis. Solid (dashed) lines for the $c$ parameter are straight line fits to the data below (above) $T_S=365\text{K}$. Filled and open symbols are data from different instruments. Inset: temperature dependence of the oxygen displacement parameter $ϵ$; the solid line is a guide to the eye.

Figure 6

(Color online) Charge order pattern described by Eq. (2) to be compared with Fig. 4. Labels $-1$ and $+0.5$ indicate charges in units of $\sigma$. Thick hexagonal contours indicate the honeycomb network of the electron-depleted Ni2,3 sites and dashed line contour is the unit cell of the charge ordered structure. The light shaded area is the unit cell of the ideal structure with all Ni sites equivalent.

Figure 7

(Color online) (a) Inverse magnetic susceptibility $\left(1/\chi \right)$ fitted to a Curie-Weiss law Eq. (1) (solid line) gives a large negative intercept indicating dominant antiferromagnetic interactions. Inset shows suppression of susceptibility below 20 K attributed to onset of antiferromagnetic order. (b) Temperature dependence of the specific heat observing a sharp lambda-like peak near the magnetic transition temperature.

Figure 8

(Color online) Difference pattern 4 K–300 K from OSIRIS showing peaks of magnetic origin, indexed by the propagation vector $\mathit{k}=\left(1/2,0,0\right)$. The circles represent the observed intensities; the solid curve is a fit to the magnetic structure depicted in Fig. 10 and vertical bars indicate the magnetic Bragg peak positions. The bottom curve shows the difference between the fit and the data.

Figure 9

(Color online) Observed intensity of several magnetic Bragg peaks as a function of reduced temperature $T/T_N$. Data points are from elastic neutron powder scattering measurements using IN6. Lines are guides to the eye.

Figure 10

(a) Magnetic structure of the Ni1 sublattice consisting of alternating rows (dashed lines) of ferromagnetically aligned spins. $\pm$ symbols indicate the projection of the spin moment along the $c$ axis; dots represent the unordered (Ni2 and Ni3) Ni sites in the unit cell (solid contour). Thick black symbols indicate the moments in the bottom ${\text{NiO}}_2$ plane $\left(z=1/4\right)$ whereas faint gray symbols correspond to the moments in the upper plane $\left(z=3/4\right)$ obtained by shifting the pattern by an in-plane offset ${\mathit{a}}_0$. The arrowed line labeled $J^{″}$ indicates one of the three interlayer exchange paths. The drawn structure has propagation vector $\mathit{k}=\left(1/2,0,0\right)$ (Bragg peaks indicated by black stars in Fig. 11); equivalent structures are obtained by $\pm 60°$ rotation around the $\left(2/3,1/3,z\right)$ axis. (b) In a single layer the ordered sites form a triangular lattice of spacing $a$. Short and long arrowed lines indicate the nearest- and next-nearest-neighbor exchanges $J$ and $J^{\prime }$ in a minimal model proposed to explain the stability of the observed structure.

Figure 11

Reciprocal basal plane showing locations of structural (filled circles) and magnetic reflections (stars). Large filled circles and large bold hexagon indicate the zone centers and Brillouin zone of the ideal, undistorted structure $\left(P{6}_3/mmc\right)$, whereas small filled circles and thin line hexagons are, respectively, structural supercell peaks and the Brillouin zone of the distorted crystal structure $\left(P{6}_{3}22\right)$. Filled stars are the magnetic Bragg peak positions from the magnetic structure with propagation wave vector $\mathit{k}=\left(1/2,0,0\right)$ shown in Fig. 10; open stars are peaks from domains rotated by $\pm 60°$.