#### Abstract

Crystal structure and magnetic properties of the layered vanadium phosphate $\text{PbZnVO}{\left({\text{PO}}_{4}\right)}_{2}$ are studied using x-ray powder diffraction, magnetization and specific-heat measurements, as well as band-structure calculations. The compound resembles $A{A}^{\prime}\text{VO}{\left({\text{PO}}_{4}\right)}_{2}$ vanadium phosphates and fits to the extended frustrated square-lattice model with the couplings ${J}_{1},\text{\hspace{0.5em}}{J}_{1}^{\prime}$ between nearest neighbors and ${J}_{2},\text{\hspace{0.5em}}{J}_{2}^{\prime}$ between next-nearest neighbors. The temperature dependence of the magnetization yields estimates of averaged nearest-neighbor and next-nearest-neighbor couplings, ${\overline{J}}_{1}\simeq -5.2\text{\hspace{0.5em}}\text{K}$ and ${\overline{J}}_{2}\simeq 10.0\text{\hspace{0.5em}}\text{K}$, respectively. The effective frustration ratio $\alpha ={\overline{J}}_{2}/{\overline{J}}_{1}$ amounts to $-1.9$ and suggests columnar antiferromagnetic ordering in $\text{PbZnVO}{\left({\text{PO}}_{4}\right)}_{2}$. Specific-heat data support the estimates of ${\overline{J}}_{1}$ and ${\overline{J}}_{2}$ and indicate a likely magnetic ordering transition at 3.9 K. However, the averaged couplings underestimate the saturation field, thus pointing to the spatial anisotropy of the nearest-neighbor interactions. Band-structure calculations confirm the identification of ferromagnetic ${J}_{1},\text{\hspace{0.5em}}{J}_{1}^{\prime}$ and antiferromagnetic ${J}_{2},\text{\hspace{0.5em}}{J}_{2}^{\prime}$ in $\text{PbZnVO}{\left({\text{PO}}_{4}\right)}_{2}$ and yield $\left({J}_{1}^{\prime}-{J}_{1}\right)\simeq 1.1\text{\hspace{0.5em}}\text{K}$ in excellent agreement with the experimental value of 1.1 K, deduced from the difference between the expected and experimentally measured saturation fields. Based on the comparison of layered vanadium phosphates with different metal cations, we show that a moderate spatial anisotropy of the frustrated square lattice has minor influence on the thermodynamic properties of the model. We discuss relevant geometrical parameters, controlling the exchange interactions in these compounds and propose a strategy for further design of strongly frustrated square-lattice materials.

2 More- Received 12 October 2009

DOI:https://doi.org/10.1103/PhysRevB.81.174424

©2010 American Physical Society