# Singlet ground state in the spin-$1/2$ weakly coupled dimer compound NH$_4$[(V$_2$O$_3$)$_2$(4,4$^\prime$-$bpy$)$_2$(H$_2$PO$_4$)(PO$_4$)$_2$]$\cdot$0.5H$_2$O

## TL;DR

This study synthesizes and characterizes a vanadium-based compound exhibiting a singlet ground state with a small spin gap, confirmed through multiple magnetic and spectroscopic techniques, highlighting its potential for high-field magnetic research.

## Contribution

The paper reports the discovery and detailed analysis of a new weakly coupled spin-1/2 dimer compound with a well-characterized small spin gap and distinct P-site hyperfine interactions.

## Key findings

- The compound has a spin gap of approximately 26 K from susceptibility data.
- NMR results confirm the singlet ground state with activated behavior at low temperatures.
- The estimated spin gap from NMR matches the susceptibility analysis, indicating consistency across methods.

## Abstract

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.