We present a detailed investigation of the magnetic properties of complex vanadium phosphates $M{\left(\text{VO}\right)}_2{\left({\text{PO}}_4\right)}_2$ ($M=\text{Ca}$ and Sr) by means of magnetization, specific heat, ${}^{31}\text{P}$ NMR measurements, and band-structure calculations. Experimental data evidence the presence of ferromagnetic and antiferromagnetic interactions in $M{\left(\text{VO}\right)}_2{\left({\text{PO}}_4\right)}_2$, resulting in a nearly vanishing Curie-Weiss temperature ${\theta }_{\text{CW}}\le 1\text{K}$ that contrasts with the maximum of magnetic susceptibility at 3 K. Specific heat and NMR measurements also reveal weak exchange couplings with the thermodynamic energy scale $J_c=10–15\text{K}$. Additionally, the reduced maximum of the magnetic specific heat indicates strong frustration of the spin system. Band-structure calculations show that the spin systems of the $M{\left(\text{VO}\right)}_2{\left({\text{PO}}_4\right)}_2$ compounds are essentially three-dimensional with the frustration caused by competing ferromagnetic and antiferromagnetic interactions. Both calcium and strontium compounds undergo antiferromagnetic long-range ordering at $T_N=1.5$ and 1.9 K, respectively. The spin model reveals an unusual example of controllable frustration in three-dimensional magnetic systems.

• Received 29 April 2008

DOI:https://doi.org/10.1103/PhysRevB.78.024418