It is well-known that the experimental observation of characteristic Berezinskii-Kosterlitz-Thouless (BKT) behavior in real quasi two-dimensional easy-plane systems is hindered, when the 2D critical temperature is approached, by the onset of 3D ordering. However, the 3D transition is triggered by the diverging 2D correlation length, so that if it would be possible to vary the BKT critical temperature and the 3D transition varies accordingly, one could conclude that BKT behavior is present. This is the case of the 2D Heisenberg ferromagnet in a Zeeman field. Indeed, the field competes with the exchange and the energy is minimized when the spins cant in its direction [1], the so-called `spin-flop' phase, where the longitudinal spin fluctuations are quenched and the system becomes XY-like. What is remarkable is that the critical temperature is ruled by the field strength: the predictable behavior T_c(H) can therefore be used as a signature of BKT behavior in an experiment. Due to the required strong field, this is possible only in real compounds displaying a tiny exchange. One of them is the S=5/2 layered compound Mn(HCOO)_22H_2O (manganese-formate di-hydrate, or Mn-f-2H) [2], for which in 1983 Takeda and Koyama drew a 'phase diagram' in the H-T plane by considering the peaks of the specific heat and of the uniform susceptibility. We investigated the spin-flop phase of the 2D quantum Heisenberg antiferromagnet by means of the pure-quantum self-consistent harmonic approximation [3], a semiclassical approach that works through a classical effective Hamiltonian with renormalized interaction parameters. In this way one can study systems with S>1/2, where quantum Monte Carlo [4] is unpractical. The quantitative phase diagram can be easily drawn from its classical [1] counterpart. As the data for Mn-f-2H agree fairly well with the curve T_c(H) for S=5/2, we conclude that characteristic BKT behavior was indeed observed in the experiment.

[1] D. P. Landau and K. Binder, Phys. Rev. B 24, 1391 (1981).

[2] K. Takeda and K. Koyama, J. Phys. Soc. Jap. 52, 648 and 656 (1983).

[3] A. Cuccoli, R. Giachetti, V. Tognetti, R. Vaia, and P. Verrucchi, J. Phys.: Condens. Matter 7, 7891 (1995).

[4] A. Cuccoli, T. Roscilde , R. Vaia, and P. Verrucchi, Phys. Rev. B 68, 060402 (2003).