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We present an experimental study of the two-dimensional S=1/2 square-latticeantiferromagnet Cu(pz)$_2$(ClO$_4$)$_2$ (pz denotes pyrazine - $C_4H_4N_2$)using specific heat measurements, neutron diffraction and cold-neutronspectroscopy. The magnetic field dependence of the magnetic orderingtemperature was determined from specific heat measurements for fieldsperpendicular and parallel to the square-lattice planes, showing identicalfield-temperature phase diagrams. This suggest that spin anisotropies inCu(pz)$_2$(ClO$_4$)$_2$ are small. The ordered antiferromagnetic structure is acollinear arrangement with the magnetic moments along either thecrystallographic b- or c-axis. The estimated ordered magnetic moment at zerofield is m_0=0.47(5)mu_B and thus much smaller than the available single-ionmagnetic moment. This is evidence for strong quantum fluctuations in theordered magnetic phase of Cu(pz)$_2$(ClO$_4$)$_2$. Magnetic fields appliedperpendicular to the square-lattice planes lead to an increase of theantiferromagnetically ordered moment to m_0=0.93(5)mu_B at mu_0H=13.5T -evidence that magnetic fields quench quantum fluctuations. Neutron spectroscopyreveals the presence of a gapped spin excitations at the antiferromagnetic zonecenter, and it can be explained with a slightly anisotropic nearest neighborexchange coupling described by J_1^{xy}=1.563(13)meV andJ_1^z=0.9979(2)J_1^{xy}.

The Two-Dimensional Square-Lattice S=1/2 Antiferromagnet Cu(pz)$_2$(ClO$_4$)$_2$