Spin structures of tetragonal lamellar copper oxides.

The spin Hamiltonian of tetragonal lamellar antiferromagnets is shown to contain several novel anisotropies. Symmetry allows bond-dependent anisotropic exchange interactions, which lead to (a) interplane mean-field coupling and (b) an in-plane anisotropy which vanishes classically but arises from quantum zero point energy (QZPE). A similar QZPE involving the interplane isotropic interaction prefers collinear spins. Adding also diploar anisotropy, the competition between all these effects explains for the first time the spin structures of many cuprates. Disciplines Physics | Quantum Physics This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/473 VOLUME 72, NUMBER 23 PHYSICAL REVIEW LETTERS 6 3UXE 1994 Spin Structures of Tetragonal Lamellar Copper Oxides T. Yildirim, A. B. Harris, O. Entin-Wohlman, and Amnon Aharony 'Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 1910$ 6-996 2 School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 6'9978, Israel (Received 24 January 1994) The spin Hamiltonian of tetragonal lamellar antiferromagnets is shown to contain several novel anisotropies. Symmetry allows bond-dependent anisotropic exchange interactions, which lead to (s) interplsne mean-field coupling snd (b) sn in-plane snisotropy which vanishes classically but arises from quantum zero point energy (QZPE). A similar QZPE involving the interplsne isotropic interaction prefers collinear spins. Adding also dipolar anisotropy, the competition between all these effects explains for the Grst time the spin structures of many cuprates. PACS numbers: 75.30.Et, 75.25.+z, 75.30.Ds The discovery of high-temperature superconductivity [1] initiated intense interest in the properties of the doped lamellar copper oxide systems. Hopefully, a step towards the understanding of the superconductivity of these systems would be to understand the simpler undoped systems, which are antiferromagnetic. In this Letter we consider two structural families of such tetragonal systems, the "123" compounds, which are isomorphic to YBa2CusOs (YBCO) [2], and the "214" compounds, isostructural to LazCu04 (LCO) [3], as shown in Fig. 1. The magnetic structure of members in the latter family has been studied for more than twenty years. Famous examples [4] include KzNiF4, in which the spins order perpendicular to the basal plane, and RbzMnF4, where they order in that plane. The latter is also true of many cuprates, including orthorhombic LCO, and the tetragonal systems SrzCuClzOz [5], PrzCu04 [6], and Nd2Cu04 [6]. The magnetic properties of all these systems are very well described by an isotropic Heisenberg model in two dimensions, as demonstrated by the striking comparison between the theoretical predictions [7] for the temperature evolution of the correlation length and the corresponding experimental values at high temperatures [8—10]. However, some of the magnetic properties of these systems depend on more subtle interactions and are less well understood. In particular, the two dimensional isotropic Heisenberg model would not have a phase transition at a finite temperature. In orthorhombic LCO, the transition was explained by the finite coupling between planes and by the antisymmetric spin exchange anisotropy [3]. However, in tetragonal systems the latter snisotropy is absent, and earlier calculations gave only isotropic Heisenberg exchange [11]. The interplane coupling, which tetragonally averages out in the mean-Geld sense, has also not been expected to contribute. Phenomenologically, the transitions were explained to result from a crossover to an XY model, due to some small easy plane anisotropy, followed by a crossover to three dimensional long range order, due to some very weak interplanar coupling [6,8]. The easy plane anisotropy has only recently [12,13] been explained to result from the interplay of spin-orbit and Coulomb exchange interactions, and its calculated [13] magnitude was consistent with the out-of-plane spin-wave gaps in all the cuprates. However, (a) the relative ordering of spins in different planes, and (b) the low-temperature directions of the spins within the easy planes, which indicate a breaking of the in-plane XY rotational invariance, remained unexplained. The latter is particularly mysterious for the cuprates, where the spin 1/2 eliminates any single ion anisotropy. The issue becomes even more intriguing when one notes suggestions in the literature for the different spin directions in 123 and 214 systems (see Fig. 1). These issues, which we show to be interrelated, are addressed and explained in this Letter. Topic (a) has been addressed for the case of isotropic Heisenberg interactions. In that case, for the 214 systems, there is a classical degeneracy, in that the mean field exerted by one layer on an adjacent layer vanishes for tetragonal symmetry. As first shown by Shender [14], such degeneracies are partially removed by the spin-wave quantum zero point energy (QZPE), and the lowest energy state is one with the spins collinear. Denoting the ground state spin direction at site i in the anth plane by n o, , where o, = +1 and n = xcos8 + ysin8 FIG. 1. IJnit cells of 214 (left) snd 123 (&ight) lliieiisr coPper oxide tetragonal systems, with spin directions suggested for LCO [3] snd YBCO [2], respectively. 3710 003 1-9007l94/72 (23)f37 10 (4)$06.0