Neutron diffraction and $\mu \mathrm{SR}$ studies of two polymorphs of nickel niobate ${\mathrm{NiNb}}_2{\mathrm{O}}_6$

Neutron diffraction and muon spin relaxation ($\mu \mathrm{SR}$) studies are presented for the newly characterized polymorph of ${\mathrm{NiNb}}_2{\mathrm{O}}_6 (\beta -{\mathrm{NiNb}}_2{\mathrm{O}}_6)$ with space group ${P4}_2/n$ and $\mu \mathrm{SR}$ data only for the previously known columbite structure polymorph with space group $Pbcn$. The magnetic structure of the ${P4}_2/n$ form was determined from neutron diffraction using both powder and single-crystal data. Powder neutron diffraction determined an ordering wave vector $\vec{k}=(\frac{1}{2},\frac{1}{2},\frac{1}{2})$. Single-crystal data confirmed the same $\vec{k}$ vector and showed that the correct magnetic structure consists of antiferromagnetically coupled chains running along the $a$ or $b$ axis in adjacent ${\mathrm{Ni}}^{2+}$ layers perpendicular to the $c$ axis, which is consistent with the expected exchange interaction hierarchy in this system. The refined magnetic structure is compared with the known magnetic structures of the closely related trirutile phases, ${\mathrm{NiSb}}_2{\mathrm{O}}_6$ and ${\mathrm{NiTa}}_2{\mathrm{O}}_6$. $\mu \mathrm{SR}$ data finds a transition temperature of $T_N\sim 15\mathrm{K}$ for this system, while the columbite polymorph exhibits a lower $T_N=5.7\left(3\right)$ K. Our $\mu \mathrm{SR}$ measurements also allowed us to estimate the critical exponent of the order parameter $\beta$ for each polymorph. We found $\beta =0.25\left(3\right)$ and 0.16(2) for the $\beta$ and columbite polymorphs, respectively. The single-crystal neutron scattering data give a value for the critical exponent $\beta =0.28\left(3\right)$ for $\beta -{\mathrm{NiNb}}_2{\mathrm{O}}_6$, in agreement with the $\mu \mathrm{SR}$ value. While both systems have $\beta$ values less than 0.3, which is indicative of reduced dimensionality, this effect appears to be much stronger for the columbite system. In other words, although both systems appear to be well described by $S=1$ spin chains, the interchain interactions in the $\beta$ polymorph are likely much larger.

Figure 1

Two polymorphs of ${\mathrm{NiNb}}_2{\mathrm{O}}_6$. The blue (dark) octahedra contain nickel; the green (light) octahedra contain niobium. Images created with vesta[11]. (a) A $\mathit{bc}$ plane view of the columbite structure showing the zigzag chains of edge-sharing Ni-O octahedra along $c$. Data from [1]. (b) An $\mathit{ac}$ plane view of the ${P4}_2/n$ polymorph showing the absence of the edge-sharing Ni-O octahedra.

Figure 2

A comparison of the nickel sites in (a) the $\beta$ polymorph of nickel niobate and (b) the trirutile nickel tantalate. In (a), the cell of the same dimensions as the tantalate is outlined, demonstrating that for both materials the nickel sublattice has the same body-centered-tetragonal symmetry.

Figure 3

Ni (blue/small) and oxide ion (red and orange/large) positions in the ${\mathrm{K}}_2{\mathrm{NiF}}_4$, TR (${\mathrm{NiTa}}_2{\mathrm{O}}_6$ and ${\mathrm{NiSb}}_2{\mathrm{O}}_6$), and ${\mathrm{NiNb}}_2{\mathrm{O}}_6$ structures shown along a (001) square plane defined by the Ni ions. For ${\mathrm{K}}_2{\mathrm{NiF}}_4$, the oxide ions and the Ni ions are in the same plane. In ${\mathrm{NiTa}}_2{\mathrm{O}}_6$ and ${\mathrm{NiNb}}_2{\mathrm{O}}_6$, one set of O ions (red) is either exactly in the plane of the Ni ions (Ta) or only slightly out of the plane by 0.096 Å (Nb), while the other set (orange) is either 1.55 Å (Ta) or 1.57 Å (Nb) from the plane.

Figure 4

Rietveld refinement of neutron powder diffraction data at 20 K for $\beta -{\mathrm{NiNb}}_2{\mathrm{O}}_6$. The red circles are the data, the black line is the model, the blue line (below model) is the difference plot, and the green tick marks locate the Bragg peaks. The wavelength is 1.33 Å.

Figure 5

A difference plot (3.5–20 K) showing three magnetic reflections indexed on $\vec{k}=(\frac{1}{2},\frac{1}{2},\frac{1}{2}$). The neutron wavelength is 1.33 Å. The fits are to single Gaussians.

Figure 6

Four possible spin configurations for $\beta -{\mathrm{NiNb}}_2{\mathrm{O}}_6$ shown on the chemical unit cell. Figure made using vesta [11].

Figure 7

A plot of the $T$ dependence of the magnetic $\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$ Bragg peak. A power-law fit gives a value of the critical exponent $\beta =0.28\left(3\right)$.

Figure 8

Refinements of single crystal neutron diffraction data for $\beta -{\mathrm{NiNb}}_2{\mathrm{O}}_6$ are presented here. The calculated and observed values of $F^2$, the residuals, ${\chi }^2$ and the R factor for the (a) ${\mathrm{\Gamma }}_1$, (b) ${\mathrm{\Gamma }}_3$, and (c) ${\mathrm{\Gamma }}_3+{\mathrm{\Gamma }}_7$ models are shown.

Figure 9

The full magnetic structure of $\beta -{\mathrm{NiNb}}_2{\mathrm{O}}_6$ in the ${\mathrm{\Gamma }}_3+{\mathrm{\Gamma }}_7$ basis. Figure made using vesta [11].

Figure 10

A comparison of the magnetic structures for (a) ${\mathrm{NiSb}}_2{\mathrm{O}}_6$ [25], (b) ${\mathrm{NiTa}}_2{\mathrm{O}}_6$ [25], and (c) $\beta -{\mathrm{NiNb}}_2{\mathrm{O}}_6$ projected along the $c$ axis and with two adjacent layers shown. In (c), the larger chemical cell is indicated by the darker solid lines and the smaller TR-like chemical cell by the lighter solid lines. In all three diagrams, the dashed lines indicate the magnetic unit cell.

Figure 11

Selected data and internal field fits from zero-field $\mu \mathrm{SR}$ measurements performed on the $\beta -{\mathrm{NiNb}}_2{\mathrm{O}}_6$ polymorph. (a) Fits of $\mu \mathrm{SR}$ data from 2 to 20 K for $\beta -{\mathrm{NiNb}}_2{\mathrm{O}}_6$. Each asymmetry plot is offset by +0.05 for clarity. There is a distinct reduction in the local field with increasing temperature, followed by a transition to the paramagnetic state above 15 K. (b) The internal magnetic field strength at two different muon sites in $\beta -{\mathrm{NiNb}}_2{\mathrm{O}}_6$.

Figure 12

Selected data and internal field fits from zero-field $\mu \mathrm{SR}$ measurements performed on the columbite polymorph of ${\mathrm{NiNb}}_2{\mathrm{O}}_6$. (a) Fits of $\mu \mathrm{SR}$ data from 2 to 20 K for the columbite polymorph of ${\mathrm{NiNb}}_2{\mathrm{O}}_6$. Each asymmetry plot is offset by +0.05 for clarity. There is a distinct decrease in the local field with increasing temperature, followed by a transition to the paramagnetic state above 5.7 K. (b) The internal magnetic field strength at two different muon sites in the columbite polymorph of nickel niobate.