Emergence of long-range order in sheets of magnetic dimers

Abstract

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...

Magnetic nanopantograph in the SrCu 2 (BO 3 ) 2 Shastry–Sutherland lattice

“…In simpler words, our results also suggest that pressures of the order of a few gigapascals might be used to control the J′=J parameter through the pantograph effect and therefore to drive SCBO out of the spin dimer ground state into plaquette or Néel order. Magnetic susceptibility vs. pressure and very recent neutron diffraction under pressure results (30,31) support these ideas. We also note that low temperature active Raman modes have been identified as being correlated with the spin gap in SrCu 2 (BO 3 ) 2 (32).…”

4-spin plaquette singlet state in the Shastry–Sutherland compound SrCu2(BO3)2

“…In an X-ray diffraction investigation the temperature dependence of the lattice parameters was analysed as an indirect proxy for the singlet triplet gap leading to the suggestion that it closes at 20 kbar 23 . At even higher pressures neutron and X-ray diffraction experiments observed a transition above 45 kbar from the ambient I42M tetragonal space group to monoclinic [24][25][26] .…”

“…The magenta line shows the tetragonal to monoclinic structural transition 25 . The corresponding monoclinic space groups are indicated 26,27 . The dashed line in the plaquette phase is the extrapolated energy gap using Ref.…”

Order–disorder effects on the elastic properties of CuMPt6 (M=Cr and Co) compounds

“…Pressure is a tool of choice to tune magnetic couplings and thereby enables to explore the Shastry-Sutherland phase diagram for which SrCu 2 (BO 3 ) 2 is the only known spin S ¼ 1=2 realization. Previous studies [17][18][19][20] have indicated that pressure actually drives the compound even closer to a magnetic quantum phase transition.…”

“…Strong magnetoelastic effects are observed upon entering the spin-gap regime (T $ 35 K) [22]. These magneto-elastic effects have been used in combined pressure and temperature dependent X-ray diffraction measurements to detect signs of quantum phase transitions [20]. There, a change in the compressibility of the a-axis was recorded around 4.5 GPa at 4 K. Applying an additional external magnetic field of 7 T magnetic ordering has been reported below 4 K at 2.4 GPa by NMR measurements [18].…”