Singlet ground state in the spin-$\frac{1}{2}$ weakly coupled dimer compound ${\mathrm{NH}}_4[{\left({\mathrm{V}}_2{\mathrm{O}}_3\right)}_2{(4,4^{\prime }-bpy)}_2\left({\mathrm{H}}_2{\mathrm{PO}}_4\right){\left({\mathrm{PO}}_4\right)}_2]·0.5{\mathrm{H}}_2\mathrm{O}$

We present the synthesis and a detailed investigation of structural and magnetic properties of polycrystalline ${\mathrm{NH}}_4\left[{\left({\mathrm{V}}_2{\mathrm{O}}_3\right)}_2{(4,4^{\prime }-bpy)}_2\left({\mathrm{H}}_2{\mathrm{PO}}_4\right){\left({\mathrm{PO}}_4\right)}_2\right]·0.5{\mathrm{H}}_2\mathrm{O}$ by means of x-ray diffraction, magnetic susceptibility, electron spin resonance, and ${}^{31}\mathrm{P}$ nuclear magnetic resonance measurements. Temperature-dependent magnetic susceptibility could be described well using a weakly coupled spin-$\frac{1}{2}$ dimer model with an excitation gap $\mathrm{\Delta }/k_{\mathrm{B}}\simeq 26.1$ K between the singlet ground state and triplet excited states and a weak interdimer exchange coupling $J^{\prime }/k_{\mathrm{B}}\simeq 4.6$ K. A gapped chain model also describes the data well with a gap of about 20 K. The electron spin resonance intensity as a function of temperature traces the bulk susceptibility nicely. The isotropic Landé $g$ factor is estimated to be about $g\simeq 1.97$, at room temperature. We are able to resolve the ${}^{31}\mathrm{P}$ NMR signal as coming from two inequivalent P sites in the crystal structure. The hyperfine coupling constant between ${}^{31}\mathrm{P}$ nucleus and ${\mathrm{V}}^{4+}$ spins is calculated to be $A_{\mathrm{hf}}\left(1\right)\simeq 2963$ Oe/${\mu }_{\mathrm{B}}$ and $A_{\mathrm{hf}}\left(2\right)\simeq 1466$ Oe/${\mu }_{\mathrm{B}}$ for the P(1) and P(2) sites, respectively. Our NMR shift and spin-lattice relaxation rate for both the ${}^{31}\mathrm{P}$ sites show an activated behavior at low temperatures, further confirming the singlet ground state. The estimated value of the spin gap from the NMR data measured in an applied field of $H=9.394$ T is consistent with the gap obtained from the magnetic susceptibility analysis using the dimer model. Because of a relatively small spin gap, ${\mathrm{NH}}_4\left[{\left({\mathrm{V}}_2{\mathrm{O}}_3\right)}_2{(4,4^{\prime }-bpy)}_2\left({\mathrm{H}}_2{\mathrm{PO}}_4\right){\left({\mathrm{PO}}_4\right)}_2\right]·0.5{\mathrm{H}}_2\mathrm{O}$ is a promising compound for further experimental studies under high magnetic fields.

Figure 1

Left panel: crystal structure of VP-$bpy$ viewed along the [110] direction. Vanadium phosphate layers are connected by the long $4,4^{\prime }$-bipyridine ligands. Middle panel: a section of the vanadium phosphate layer composed of weakly coupled dimers in the $ab$ plane is shown. The solid line represents the dimer units while the dotted line represents the direction of alternating cross chains. Right panel: two dimer units with intradimer coupling ($J$) via V(2)-P-O-P-V(2) path and interdimer coupling ($J^{\prime }$) via V(2)-O-V(1)-P-O-V(2) path are shown by solid and dotted lines, respectively.

Figure 2

Powder x-ray diffraction patterns (open circles) at $T=300$ K (top panel) and 22.5 K (bottom panel) for VP-$bpy$. The solid red line represents the calculated pattern using Le-Bail fit, with the vertical bars showing the expected Bragg peak positions and the lower solid blue line representing the difference between the observed and calculated intensities.

Figure 3

Upper panel: $\chi \left(T\right)$ measured at $H=0.5$ T. The solid and dotted lines represent the fit of $\chi \left(T\right)$ and ${\chi }_{\mathrm{spin}}\left(T\right)$ using Eqs. (2) and (4), respectively. Lower panel: $1/\chi \text{vs}T$ and the solid line is the CW fit using Eq. (1).

Figure 4

Temperature-dependent ESR intensity, $I_{\mathrm{ESR}}\left(T\right)$, obtained by integration of the ESR spectra of the polycrystalline VP-$bpy$ sample. The solid line represents the fit described in the text. The upper inset shows a typical spectrum (symbols) together with the fits using a single Lorentzian function (dashed line) and a powder-averaged Lorentzian shape (solid line) for a uniaxial $g$-factor anisotropy. The bottom inset shows the $I_{\mathrm{ESR}}\text{vs}\chi$ in the temperature range 15 to 295 K.

Figure 5

Temperature-dependent frequency sweep ${}^{31}\mathrm{P}$ NMR spectra of VP-$bpy$ measured at $H=9.394$ T. The double Gaussian fit to the spectrum is shown at $T=12.6$ K. The dotted and dashed lines correspond to the P(1) and P(2) sites, respectively. The solid line represents the total fit. The ratio of areas under P(1) and P(2) spectra is nearly 2:1. The vertical dashed line corresponds to the ${}^{31}\mathrm{P}$ resonance position of the reference ${\mathrm{H}}_3{\mathrm{PO}}_4$ sample.

Figure 6

Upper panel: temperature-dependent ${}^{31}\mathrm{P}$ NMR shift ($K_1$ and $K_2$) for both the ${}^{31}\mathrm{P}$ sites as a function of temperature. The solid lines are the fits of $K\left(T\right)$ by Eq. (5). Inset: $K\text{vs}\chi$ (measured at 9 T) with temperature as an implicit parameter. The solid lines are the linear fits. Lower panel: $(K-K_0)T^{1/2}\text{vs}1/T$ for both the P sites. The solid lines indicate the activation law $(K-K_0)T^{1/2}\propto e^{-\mathrm{\Delta }/k_{\mathrm{B}}T}$.

Figure 7

Upper panel: $1/T_1$ ($1/T_{1\mathrm{S}}$ and $1/T_{1\mathrm{L}})$ is plotted as a function of temperature. Inset: Recovery of longitudinal magnetization as a function of waiting time $t$ at three different temperatures. Solid lines are the fits using Eq. (6). Lower panel: $1/T_1$ is plotted against $1/T$. The solid lines are the fits in the low-temperature region as discussed in the text.