Possible charge disproportionation in $3R{\text{-AgNiO}}_2$ studied by neutron powder diffraction

Using neutron-scattering techniques, we have investigated the nuclear and the magnetic structures of the triangular antiferromagnet $3R{\text{-AgNiO}}_2$. The symmetry analysis based on the group theory suggests that the $\sqrt{3}\times \sqrt{3}$ charge order proposed for $2H{\text{-AgNiO}}_2$ [E. Wawrzyńska et al., Phys. Rev. Lett. 99, 157204 (2007)] will have a monoclinic symmetry if present in the trigonal lattice of $3R{\text{-AgNiO}}_2$. The Rietveld refinement shows that symmetry reduction in the ${\text{NiO}}_2$ layer is consistent with the prediction of the group theory. The pair density function consistently shows that the nearest-neighbor Ni-O bonds split into two groups separated by approximately $0.1\text{Å}$. The antiferromagnetic Bragg peaks observed below $T_N=25\text{K}$ can be described by the propagation vector $\mathbf{k}=\left(0,1,0\right)$ of the monoclinic unit cell. The similarities of the local structure and the antiferromagnetic order strongly suggest that the novel charge order observed in $2H{\text{-AgNiO}}_2$ also exists in $3R{\text{-AgNiO}}_2$.

Figure 1

(a) Top view of the three ${\text{NiO}}_2$ layers in $3R{\text{-AgNiO}}_2$. In each layer, large and small spheres represent charge-rich (Ni1) and charge-poor (Ni2) sites, respectively, of the proposed $\sqrt{3}\times \sqrt{3}$ order. (b) The relation between the basal planes of the trigonal $\left({\mathbf{a}}_t\times {\mathbf{b}}_t\right)$ and the monoclinic $\left(\mathbf{a}\times \mathbf{b}\right)$ unit cells of $3R{\text{-AgNiO}}_2$. Also shown in the basal plane of the ${\text{NaNiO}}_2$ unit cell $\left(\mathbf{a}\times {\mathbf{b}}^{\prime }\right)$.

Figure 2

The expected oxygen displacements in the case of $\sqrt{3}\times \sqrt{3}$ charge order that is consistent with the basis vector ${\Gamma }_1$ in Table . The gray shaded areas represent the $R\overline{3}m$ unit cell.

Figure 3

Experimental (open dots) and calculated (solid lines) neutron powder diffraction profiles and their differences of $3R{\text{-AgNiO}}_2\left(\text{a},\text{b}\right)$ and $3R{\text{-AgFeO}}_2$ at $T=10\text{K}$. The profiles were calculated based on [(a) and (c)] the nominal $R\overline{3}m$ model or (b) the monoclinic $C2/m$ model. The vertical marks represent the Bragg peak positions, and the star symbols are the impurity peaks. The insets show the region where superlattice peaks are expected for the monoclinic structure.

Figure 4

Experimental (open circles) and calculated (solid lines) pair density functions of $3R{\text{-AgNiO}}_2$ [(a) and (b)] and $3R{\text{-AgFeO}}_2$ (c) at $T=10\text{K}$. The profiles were calculated based on [(a) and (c)] the nominal $R\overline{3}m$ structure or (b) the monoclinic model with one third of ${\text{NiO}}_6$ octahedra expanded. The dash-dotted lines are the difference between the experimental and the calculated functions, which are displaced vertically for clarity.

Figure 5

[(a)–(c)] The nearest-neighbor peak in the experimental (open circles) and calculated (solid lines) pair density functions that are shown in Fig. 4. The lower parts show the calculated partial pair density functions for the Ni-O and the Ag-O pairs. (d) The Ni-O partial pair density functions calculated for the $R\overline{3}m$ (dashed lines) and the monoclinic (solid lines) models. The vertical lines mark the two average Ni-O bond distances obtained from the monoclinic model. (e) Temperature dependence of the calculated Ni-O partial pair density function.

Figure 6

(a) Low-field dc magnetization of $3R{\text{-AgNiO}}_2$ at $B=1\text{T}$. The inset shows $H/M$ and the linear fitting to the paramagnetic region. (b) Temperature dependence of the integrated intensity of the magnetic reflection at $Q=0.716{\text{Å}}^{-1}$. (c) The difference intensity, $I\left(<4\text{K}\right)-I\left(40\text{K}\right)$, measured using the BT1 powder diffractometer (empty circles) and the SPINS triple axis spectrometer (filled circles), respectively. The solid line through the BT1 data is the calculation based on the model shown in Fig. 7a. The filled downward and the upward triangles mark the positions of nuclear and magnetic Bragg peaks, respectively.

Figure 7

(Color online) (a) The proposed antiferromagnetic structure of $3R{\text{-AgNiO}}_2$. The thick solid lines show the outline of the monoclinic unit cell. [(b) and (c)] Arrangements of two Ni layers in (a) $2H{\text{-AgNiO}}_2$ and (b) $3R{\text{-AgNiO}}_2$. In $3R{\text{-AgNiO}}_2$, the hatched areas are triangles formed by three Ni sites, whose centers coincide with the in-plane coordinates of Ni sites on the adjacent layers. Thick black lines indicate (the shorter) Ni2-O bonds while thick gray lines indicate (the longer) Ni1-O bonds. Other lines are guides to the eyes to find Ni-O or Ag-O bonds.