Sr 2 Cu 3 O 4 Cl 2 has Cu I and Cu II subsystems, forming interpenetrating S 1͞2 square lattice Heisenberg antiferromagnets. The classical ground state is degenerate, due to frustration of the intersubsystem interactions. Magnetic neutron scattering experiments show that quantum fluctuations cause a two dimensional Ising ordering of the Cu II 's, lifting the degeneracy, and a dramatic increase of the Cu I out-of-plane spin-wave gap, unique for order out of disorder. The spin-wave energies are quantitatively predicted by calculations which include quantum fluctuations. PACS numbers: 75.30.Ds, 75.10.Jm, 75.25. + z, 75.45. + j The classical ground states of many magnetic systems are degenerate due to frustration. Quantum or thermal fluctuations often lift this degeneracy, yielding order due to disorder [1][2][3][4]. For example, when a system can be separated into two Heisenberg antiferromagnetic (AFM) sublattices, so that the molecular field of the spins in each sublattice vanishes on the spins of the other, then classically the sublattices order independently of each other, the ground state is degenerate, and the excitation spectrum contains two distinct sets of zero energy (Goldstone) modes, reflecting the fact that these subsystems can be rotated independently without cost in energy. As shown by Shender, quantum spin-wave (SW) interactions prefer collinearity of the spins in the two sublattices [2]. Concomitantly, this also generates a fluctuation driven gap in the SW spectrum. Indeed, such a gap was hypothesized in the garnet Fe 2 Ca 3 ͑GeO 4 ͒ 3 [5]. Since a similar gap could also arise from crystalline magnetic anisotropy, the final identification was rather complex.In parallel to these developments, the discovery of high temperature superconductivity triggered much work on the magnetism in lamellar copper oxides. These materials contain CuO 2 planes, whose two-dimensional (2D) spin fluctuations can be modeled well by the S 1͞2 square lattice quantum Heisenberg antiferromagnet (SLQHA) [6].The above two advances combine in the isostructural compounds Sr 2 Cu 3 O 4 Cl 2 and Ba 2 Cu 3 O 4 Cl 2 (2342). In the present paper, we show that these materials offer a dramatic and clear demonstration of ordering due to fluctuations. As shown in Fig. 1(a), the CuO 2 plane is replaced in 2342 by a Cu 3 O 4 one, which contains an additional Cu 21 II ion at the center of every second plaquette of the original Cu I O 2 square lattice [7]. The configuration in the neighboring plane is obtained by translating the whole plane by ͑ a 2ā 2 ͒. In the plane, the Cu I and Cu II subsystems form interpenetrating S 1͞2 SLQHA's with exchange interactions J I and J II . The isotropic interaction J I-II between these subsystems is frustrated; that is, its molecular field vanishes as described above, and one needs nontrivial theories to explain their ordering and SW gaps. Experimentally, 2342 exhibits AFM order of the Cu I 's and Cu II 's below the Néel temperatures T N,I and T N,II , respectively [8,9]. For temperatures T . T N,II , the...

The effect of quenched random ferromagnetic bonds on the antiferromagnetic correlation length, ξ 2D , of a two-dimensional Heisneberg model is studied, applying the renormalization group method to the classical non-linear sigma model with quenched random dipole moments. It is found that the antiferromagnetic long range order is destroyed for any non-zero concentration, x, of the dipolar defects, even at zero temperature. Below a line T ∝ x, where T is the temperature, ξ 2D is independent of T , and decreases exponentially withx. At higher temperatures, it decays exponentially with ρ eff s /T , with an effective stiffness constant ρ eff s , which decreases with x/T . The results are used to estimate the three-dimensional Néel temperature, which decays linearly withx at small concentrations, and drops precipitously at a critical concentration.These predictions are compared with experiments on doped copper oxides, and are shown to reproduce successfully some of the prominent features of the data.

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We report a neutron scattering study on the tetragonal compound Sr 2 Cu 3 O 4 Cl 2 , which has two-dimensional ͑2D͒ interpenetrating Cu I and Cu II subsystems, each forming a Sϭ1/2 square lattice quantum Heisenberg antiferromagnet ͑SLQHA͒. The mean-field ground state is degenerate, since the intersubsystem interactions are geometrically frustrated. Magnetic neutron scattering experiments show that quantum fluctuations lift the degeneracy and cause a 2D Ising ordering of the Cu II subsystem. Due to quantum fluctuations a dramatic increase of the Cu I out-of-plane spin-wave gap is also observed. The temperature dependence and the dispersion of the spin-wave energy are quantitatively explained by spin-wave calculations which include quantum fluctuations explicitly. The values for the nearest-neighbor superexchange interactions between the Cu I and Cu II ions and between the Cu II ions are determined experimentally to be J I-II ϭϪ10(2) meV and J II ϭ10.5(5) meV, respectively. Due to its small exchange interaction J II , the 2D dispersion of the Cu II SLQHA can be measured over the whole Brillouin zone with thermal neutrons, and a dispersion at the zone boundary, predicted by theory, is confirmed. The instantaneous magnetic correlation length of the Cu II SLQHA is obtained up to a very high temperature, T/J II Ϸ0.75. This result is compared with several theoretical predictions as well as recent experiments on the Sϭ1/2 SLQHA.