Title: Competing magnetic interactions in spin-1/2 square lattice: hidden order in Sr$_2$VO$_4$,
Abstract: With decreasing temperature Sr$_2$VO$_4$ undergoes two structural phase
transitions, tetragonal-to-orthorhombic-to-tetragonal, without long-range
magnetic order. Recent experiments suggest, that only at very low temperature
Sr$_{2}$VO$_{4}$ might enter some, yet unknown, phase with long-range magnetic
order, but without orthorhombic distortion. By combining relativistic density
functional theory with an extended spin-1/2 compass-Heisenberg model we find an
antiferromagnetic single-stripe ground state with highly competing exchange
interactions, involving a non negligible inter-layer coupling, which places the
system at the crossover between between the XY and Heisenberg picture. Most
strikingly, we find a strong two-site "spin-compass" exchange anisotropy which
is relieved by the orthorhombic distortion induced by the spin stripe order.
Based on these results we discuss the origin of the hidden order phase and the
possible formation of a spin-liquid at low temperatures.