# The spin-1/2 coupled tetramer system Ba(TiO)Cu$_4$(PO$_4$)$ _4$ probed by magnetization, specific heat, and $^{31}$P-NMR

## TL;DR

This study synthesizes and investigates the magnetic and structural properties of the 2D layered spin-1/2 tetramer system Ba(TiO)Cu$_4$(PO$_4$)$_4$ using various experimental techniques, revealing magnetic ordering and hyperfine interactions.

## Contribution

It provides a comprehensive experimental analysis of BTCPO, highlighting its layered structure, magnetic anomalies, and hyperfine coupling parameters, which were not previously characterized.

## Key findings

- Magnetic susceptibility shows a broad maximum at 16.5 K.
- Heat capacity exhibits a sharp anomaly at 9.5 K indicating magnetic ordering.
- $^{31}$P NMR confirms magnetic transition and reveals hyperfine coupling details.

## Abstract

We present the synthesis and a detailed investigation of structural and magnetic properties of polycrystalline Ba(TiO)Cu$_{4}$(PO$_{4}$)$_{4}$ (BTCPO) via x-ray diffraction, magnetic susceptibility, heat capacity, and $^{31}$P Nuclear Magnetic Resonance (NMR) measurements. BTCPO has a 2D layered structure with interlinked Cu$_{4}$O$_{12}$ tetramer units. A broad maximum is observed around 16.5 K in our magnetization data accompanied by a sharp anomaly around $T$ = 9.5 K in the heat capacity. An anomaly at $T$ = 9.5 K is also found in the temperature dependence of the $^{31}$P NMR spin-lattice relaxation rate $1/T_1$. A power law behavior for the heat capacity as well as for the $^{31}$P $1/T_1$ below the ordering temperature could be obtained. The $^{31}$P NMR lineshape is asymmetric and the NMR shift tracks the bulk spin-susceptibility. We estimated the isotropic and axial components of the hyperfine coupling tensor to be as the $A^{iso}_{hf} \backsimeq 6794$ $\rm{Oe/\mu_{B}}$ and $A^{ax}_{hf} \backsimeq 818$ $\rm{Oe/\mu_{B}}$, respectively.