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