  Cu(pz)2(ClO4)2 (with pz denoting pyrazine, C4H4N2) is among the best
realizations of a two-dimensional spin-1/2 square-lattice antiferromagnet.
Below T_N = 4.21 K, its weak interlayer couplings induce a 3D magnetic order,
strongly influenced by external magnetic fields and/or hydrostatic pressure.
Previous work, focusing on the [H, T] phase diagram, identified a spin-flop
transition, resulting in a field-tunable bicritical point. However, the
influence of external pressure has not been investigated yet. Here we explore
the extended [p, H, T] phase diagram of Cu(pz)2(ClO4)2 under pressures up to 12
kbar and magnetic fields up to 7.1 T, via magnetometry and 35Cl nuclear
magnetic resonance (NMR) measurements. The application of magnetic fields
enhances T_XY , the crossover temperature from the Heisenberg to the XY model,
thus pointing to an enhancement of the effective anisotropy. The applied
pressure has an opposite effect [dT_N/dp = 0.050(8) K/kbar], as it modifies
marginally the interlayer couplings, but likely changes more significantly the
orbital reorientation and the square-lattice deformation. This results in a
remodeling of the effective Hamiltonian, whereby the field and pressure effects
compensate each other. Finally, by comparing the experimental data with
numerical simulations we estimate T_BKT, the temperature of the
Berezinskii-Kosterlitz-Thouless topological transition and argue why it is
inaccessible in our case.
