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Register a new userExtreme Suppression of Antiferromagnetic Order and Critical Scaling in a Two-Dimensional Random Quantum Magnet
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Sr$_2$CuTeO$_6$ is a square-lattice Neel antiferromagnet with superexchange between first-neighbor $S=1/2$ Cu spins mediated by plaquette centered Te ions. Substituting Te by W, the affected impurity plaquettes have predominantly second-neighbor interactions, thus causing local magnetic frustration. Here we report a study of Sr$_2$CuTe$_{1-x}$W$_x$O$_6$ using neutron diffraction and $mu$SR techniques, showing that the Neel order vanishes already at $x = 0.025 pm 0.005$. We explain this extreme order suppression using a two-dimensional Heisenberg spin model, demonstrating that a W-type impurity induces a deformation of the order parameter that decays with distance as $1/r^2$ at temperature $T=0$. The associated logarithmic singularity leads to loss of order for any $x>0$. Order for small $x>0$ and $T>0$ is induced by weak interplane couplings. In the nonmagnetic phase of Sr$_2$CuTe$_{1-x}$W$_x$O$_6$, the $mu$SR relaxation rate exhibits quantum critical scaling with a large dynamic exponent, $z approx 3$, consistent with a random-singlet state.
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We study the Neel-paramagnetic quantum phase transition in two-dimensional dimerized $S=1/2$ Heisenberg antiferromagnets using finite-size scaling of quantum Monte Carlo data. We resolve the long standing issue of the role of cubic interactions arising in the bond-operator representation when the dimer pattern lacks a certain symmetry. We find non-monotonic (monotonic) size dependence in the staggered (columnar) dimerized model, where cubic interactions are (are not) present. We conclude that there is an irrelevant field in the staggered model that is not present in the columnar case, but, at variance with previous claims, it is not the leading irrelevant field. The new exponent is $omega_2 approx 1.25$ and the prefactor of the correction $L^{-omega_2}$ is large and comes with a different sign from that of the formally leading conventional correction with exponent $omega_1 approx 0.78$. Our study highlights the possibility of competing scaling corrections at quantum critical points.
Theoretical studies of quantum phase transitions have suggested critical points with higher symmetries than those of the underlying Hamiltonian. Here we demonstrate a surprising emergent symmetry of the coexistence state at a strongly discontinuous phase transition between two ordered ground states. We present a quantum Monte Carlo study of a two-dimensional $S=1/2$ quantum magnet hosting the antiferromagnetic (AFM) and plaquette-singlet solid (PSS) states recently detected in SrCu$_2$(BO$_3$)$_2$. We observe that the O(3) symmetric AFM order and the Z$_2$ symmetric PSS order form an O(4) vector at the transition. The control parameter $g$ (a coupling ratio) rotates the vector between the AFM and PSS sectors and there are no energy barriers between the two at the transition point $g_c$. This phenomenon may be observable in SrCu$_2$(BO$_3$)$_2$.
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Frustrated magnetic interactions in a quasi-two-dimensional [111] slab of pyrochlore lattice were studied. For uniform nearest neighbor (NN) interactions, we show that the complex magnetic problem can be mapped onto a model with two independent degrees of freedom, tri-color and binary sign. This provides a systematic way to construct the complex classical spin ground states with collinear and coplanar bi-pyramid spins. We also identify `partial but extended zero-energy excitations amongst the ground states. For nonuniform NN interactions, the coplanar ground state can be obtained from the collinear bi-pyramid spin state by collectively rotating two spins of each tetrahedron with an angle, $alpha$, in an opposite direction. The latter model with $alpha sim 30^circ$ fits the experimental neutron data from SCGO well.
For a number of quantum critical points in one dimension quantum field theory has provided exact results for the scaling of spatial and temporal correlation functions. Experimental realizations of these models can be found in certain quasi one dimensional antiferromagnetc materials. Measuring the predicted scaling laws experimentally presents formidable technical challenges. In many cases it only became possible recently, thanks to qualitative progress in the development of inelastic neutron scattering techniques and to the discovery of new model compounds. Here we review some of the recent experimental studies of this type.
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