Crystal growth and magnetic properties of the coupled alternating $S=1$ spin chain ${\mathrm{Sr}}_2\mathrm{Ni}{\left(\mathrm{Se}{\mathrm{O}}_3\right)}_3$

The structural, magnetic, and thermodynamic properties of a quasi-one-dimensional (1D) $S=1$ alternating spin chain compound ${\mathrm{Sr}}_2\mathrm{Ni}{\left(\mathrm{Se}{\mathrm{O}}_3\right)}_3$ are investigated by using synchrotron x-ray powder diffraction, magnetic susceptibility $\chi (H,T)$, and heat capacity $C_{\mathrm{P}}(H,T)$ measurements together with density functional theory (DFT) calculations. The $\chi (H,T)$ and $C_{\mathrm{P}}(H,T)$ data reveal long-range antiferromagnetic order at $T_{\mathrm{N}}=3.4\left(3\right)$ K and short-range order at $T_{\mathrm{m}}\approx 7.8\mathrm{K}$. The short-range magnetic order together with 95% of spin entropy release above $T_{\mathrm{N}}$ signifies the importance of 1D spin correlations persisting to $\sim 8T_{\mathrm{N}}$. Theoretical DFT calculations with generalized gradient approximation determine leading exchange interactions, suggesting that interchain interactions are responsible for the observed long-range magnetic ordering. In addition, the temperature-field phase diagram of ${\mathrm{Sr}}_2\mathrm{Ni}{\left(\mathrm{Se}{\mathrm{O}}_3\right)}_3$ is determined based on the $\chi (T,H)$ and $C_{\mathrm{P}}(T,H)$ data. Interestingly, a nonmonotonic phase boundary of $T_{\mathrm{m}}$ is found for an external field applied along a hard axis. Our results suggest that the ground state and magnetic behavior of ${\mathrm{Sr}}_2\mathrm{Ni}{\left(\mathrm{Se}{\mathrm{O}}_3\right)}_3$ rely on the interplay of single-ion anisotropy, bond alternation, and interchain interactions.

Figure 1

(a) Schematic illustration of the three-dimensional crystal structure of ${\mathrm{Sr}}_2\mathrm{Ni}{\left(\mathrm{Se}{\mathrm{O}}_3\right)}_3$. (b) Distorted octahedra of ${\mathrm{NiO}}_6$ with Ni-O distances. [(c)–(d)] and (e) Exchange interaction paths mediating Ni ions and their network connectivity.

Figure 2

X-ray diffraction pattern of ${\mathrm{Sr}}_2\mathrm{Ni}{\left(\mathrm{Se}{\mathrm{O}}_3\right)}_3$ single crystals measured at room temperature. The inset shows a photographic image of as-grown single-crystal morphology.

Figure 3

Synchrotron x-ray powder diffraction (SXRD) patterns of pulverized single crystals of ${\mathrm{Sr}}_2\mathrm{Ni}{\left(\mathrm{Se}{\mathrm{O}}_3\right)}_3$ at (a) $T=300$ K and (b) $T=105$ K. The observed, calculated, and difference patterns are denoted by the red crosses and green and purple lines, respectively. The diffraction peaks are marked with black lines at the bottom of the figures.

Figure 4

(a) Magnetic susceptibility $\chi \left(T\right)$ of ${\mathrm{Sr}}_2\mathrm{Ni}{\left(\mathrm{Se}{\mathrm{O}}_3\right)}_3$ single crystal as a function of temperature measured at $H=100$ Oe for $H\parallel a$ and $H\perp a$. The inset zooms in the low-temperature $\chi \left(T\right)$ vs $T$ (left axis) and $d\chi /dT$ vs $T$ (right axis). (b) Temperature dependence of the inverse magnetic susceptibility $1/\chi$ (left axis) and $\chi T$ (right axis). The solid and dashed lines correspond to linear fits in the low-$T$ and high-$T$ regimes, respectively.

Figure 5

Temperature and field dependence of the magnetic susceptibility under a different magnetic field applied along the (a) $H\perp a$ and (b) $H\parallel a$ directions.

Figure 6

(a) Magnetization of ${\mathrm{Sr}}_2\mathrm{Ni}{\left(\mathrm{Se}{\mathrm{O}}_3\right)}_3$ single crystal vs field measured for $H\parallel a$ and $H\perp a$ at 2 K. (b) (left axis) Magnetization vs magnetic field for single-crystal powder measured at 2 K up to 130 kOe and its derivative on the right axis ($dM/dT$ vs $H$).

Figure 7

(a) Specific heat capacity ($C_{\mathrm{P}}$) data of ${\mathrm{Sr}}_2\mathrm{Ni}{\left(\mathrm{Se}{\mathrm{O}}_3\right)}_3$ single crystal at zero magnetic field and (b) an enlarged view at low temperatures. The inset shows a fit to the equation $C_{\mathrm{mag}}=\tilde{n}R{(\mathrm{\Delta }/T)}^2{e}^{-\mathrm{\Delta }/T}$. (c) Magnetic specific heat divided by temperature $C_{\mathrm{mag}}/T$ vs temperature (left axis) and their corresponding magnetic entropy $S_{\mathrm{mag}}$ (right axis). (d) Temperature and field dependence of the $C_{\mathrm{P}}$ data.

Figure 8

(a) Calculated electronic band structure and (b) density of states (DOS) of ${\mathrm{Sr}}_2\mathrm{Ni}{\left(\mathrm{Se}{\mathrm{O}}_3\right)}_3$. The top of the valence band is set to zero.

Figure 9

$H\text{−}T$ phase diagram constructed from $\chi (T,H)$ and $C_{\mathrm{P}}\left(T,H\right)$ for ${\mathrm{Sr}}_2\mathrm{Ni}{\left(\mathrm{Se}{\mathrm{O}}_3\right)}_3$. The solid black curves are fits of the $H\text{−}T$ phase boundary to the expression $H=H_0{\left[1–T_{\mathrm{N}}\left(H\right)/T_{\mathrm{N}}\left(H=0\right)\right]}^{1/2}$.