Quantum spins placed on the corners of a square lattice can dimerize and form singlets, which then can be transformed into a magnetic state as the interactions between dimers increase beyond threshold. This is a strictly 2D transition in theory, but real-world materials often need the third dimension to stabilize long-range order. We use high pressures to convert sheets of Cu 2+ spin 1/2 dimers from local singlets to global antiferromagnet in the model system SrCu 2 (BO 3 ) 2 . Single-crystal neutron diffraction measurements at pressures above 5 GPa provide a direct signature of the antiferromagnetic ordered state, whereas high-resolution neutron powder and X-ray diffraction at commensurate pressures reveal a tilting of the Cu spins out of the plane with a critical exponent characteristic of 3D transitions. The addition of anisotropic, interplane, spin-orbit terms in the venerable Shastry-Sutherland Hamiltonian accounts for the influence of the third dimension.condensed matter physics | quantum magnetism | phase transition | dimensional cross-over | neutron and X-ray scattering T wo-dimensional systems lie at the boundary between the order-destroying effects of fluctuations in lower dimension and the emergence of true long-range order in higher dimension. How ordered states form and remain stable at finite temperature is a fundamental question that cuts across the sciences. In physics, surfaces, quantum wells, and layered compounds all have provided insights into the peculiar nature of 2D phases, phase transitions, and dimensional cross-over effects. Of particular interest for quantum phase transitions is the theoretically tractable case of interacting magnetic spins placed on a 2D square lattice, the Shastry-Sutherland model (1). The geometry prevents simultaneous satisfaction of all spin-spin coupling terms, leading to a frustrated state that in turn enhances the effects of quantum fluctuations. As the coupling terms are tuned, magnetic order can emerge, but its nature and the potential influence of other sheets of spins in a real physical system have not been probed directly.The Shastry-Sutherland model can be described by the Hamiltonian:where a set of S = 1/2 spins sits on a square lattice and interacts via a regular array of diagonal bonds. This creates a network of dimers with antiferromagnetic intradimer coupling J and interdimer coupling J′. The ground state depends on the ratio of J′=J = x. For x < 0.7, the ground state consists of S = 0 singlets, whereas for x > 0.9 a global antiferromagnetic phase is expected.For intermediate values of x, a variety of locally ordered states has been predicted (2). The first known experimental realization of the ShastrySutherland lattice is SrCu 2 (BO 3 ) 2 (SCBO) (3). The magnetism in SCBO consists of S = 1/2 Cu 2+ ions in well-separated planes whose nearest-neighbor interactions are mediated by in-plane oxygen bonds; layered Cu-O compounds of this kind are of broad interest due to their role in driving phenomena such as high-temperature superconductivity. At ambient...