Magnetic frustration in three dimensions (3D) manifests itself in the spin-$frac12$ insulator Li$_2$CuW$_2$O$_8$. Density-functional band-structure calculations reveal a peculiar spin lattice built of triangular planes with frustrated interplane coup
lings. The saturation field of 29 T contrasts with the susceptibility maximum at 8.5 K and a relatively low Neel temperature $T_Nsimeq 3.9$ K. Magnetic order below $T_N$ is collinear with the propagation vector $(0,frac12,0)$ and an ordered moment of 0.65(4) $mu_B$ according to neutron diffraction data. This reduced ordered moment together with the low maximum of the magnetic specific heat ($C^{max}/Rsimeq 0.35$) pinpoint strong magnetic frustration in 3D. Collinear magnetic order suggests that quantum fluctuations play crucial role in this system, where a non-collinear spiral state would be stabilized classically.
We present a detailed investigation of the magnetic properties of complex vanadium phosphates M(VO)2(PO4)2 (M = Ca, Sr) by means of magnetization, specific heat, 31P NMR measurements, and band structure calculations. Experimental data evidence the pr
esence of ferro- and antiferromagnetic interactions in M(VO)2(PO4)2 resulting in a nearly vanishing Curie-Weiss temperature theta_{CW} < 1 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 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(VO)2(PO4)2 compounds are essentially three-dimensional with the frustration caused by competing ferro- and antiferromagnetic interactions. Both calcium and strontium compounds undergo antiferromagnetic long-range ordering at T_N = 1.5 K and 1.9 K, respectively. The spin model reveals an unusual example of controllable frustration in three-dimensional magnetic systems.
