  Crystal structure, electronic structure, and magnetic behavior of the
spin-1/2 quantum magnet Na1.5VOPO4F0.5 are reported. The disorder of Na atoms
leads to a sequence of structural phase transitions revealed by synchrotron
x-ray powder diffraction and electron diffraction. The high-temperature
second-order alpha <--> beta transition at 500 K is of the order-disorder type,
whereas the low-temperature beta <--> gamma+gamma' transition around 250 K is
of the first order and leads to a phase separation toward the polymorphs with
long-range (gamma) and short-range (gamma') order of Na. Despite the complex
structural changes, the magnetic behavior of Na1.5VOPO4F0.5 probed by magnetic
susceptibility, heat capacity, and electron spin resonance measurements is well
described by the regular frustrated square lattice model of the
high-temperature alpha-polymorph. The averaged nearest-neighbor and
next-nearest-neighbor couplings are J1 ~ -3.7 K and J2 ~ 6.6 K, respectively.
Nuclear magnetic resonance further reveals the long-range ordering below TN =
2.6 K in low magnetic fields. Although the experimental data are consistent
with the simplified square-lattice description, band structure calculations
suggest that the ordering of Na atoms introduces a large number of inequivalent
exchange couplings that split the square lattice into plaquettes. Additionally,
the direct connection between the vanadium polyhedra induces an unusually
strong interlayer coupling having effect on the transition entropy and the
transition anomaly in the specific heat. Peculiar features of the
low-temperature crystal structure and the relation to isostructural materials
suggest Na1.5VOPO4F0.5 as a parent compound for the experimental study of
tetramerized square lattices as well as frustrated square lattices with
different values of spin.
