Quantum magnetism of ferromagnetic spin dimers in $\alpha$-KVOPO$_4$.

Magnetism of the spin-$\frac12$ $\alpha$-KVOPO$_4$ is studied by thermodynamic measurements, $^{31}$P nuclear magnetic resonance (NMR), neutron diffraction, and density-functional band-structure calculations. Ferromagnetic Curie-Weiss temperature of $\theta_{\rm CW}\simeq 15.9$ K and the saturation field of $\mu_0H_s\simeq 11.3$ T suggest the predominant ferromagnetic coupling augmented by a weaker antiferromagnetic exchange that leads to a short-range order below 5 K and the long-range antiferromagnetic order below $T_{\rm N}\simeq 2.7$ K in zero field. Magnetic structure with the propagation vector $\mathbf k=(0,\frac12,0)$ and the ordered magnetic moment of 0.58 $\mu_B$ at 1.5 K exposes a non-trivial spin lattice where strong ferromagnetic dimers are coupled antiferromagnetically. The reduction in the ordered magnetic moment with respect to the classical value (1 $\mu_{\rm B}$) indicates sizable quantum fluctuations in this setting, despite the predominance of ferromagnetic exchange. We interpret this tendency toward ferromagnetism as arising from the effective orbital order in the folded chains of the VO$_6$ octahedra.