Field-dependent antiferromagnetism and ferromagnetism of the two copper sublattices inSr2Cu3O

Abstract

The Cu 3 O 4 layer in Sr 2 Cu 3 O 4 Cl 2 is a variant of the square CuO 2 lattice of the high-temperature superconductors, in which the center of every second plaquette contains an extra Cu 2ϩ ion. The ions that make up the conventional CuO 2 network, called CuI, have CuI-CuI exchange energy Ϸ130 meV, and order antiferromagnetically at about 380 K; the CuII-CuII exchange is only Ϸ10 meV, and the CuII's order at Ϸ40 K. A study is reported here of the dependence of the magnetization on field, temperature, and crystallographic orientation for this interesting system. We show that the small permanent ferromagnetic moment, that appears when the CuI spins order, and the unusual spin rotation transitions seen most clearly for one particular direction of the magnetic field, are the result of several small bond-dependent anisotropic terms in the spin Hamiltonian that are revealed because of the frustration of the isotropic Heisenberg interaction between CuI and CuII spins. These include a term which favors collinearity of the CuI and CuII spins, which originates from quantum fluctuations, and also the pseudodipolar interaction. Some of these small interactions also come into play in other lamellar cuprates, connected with the high-T c superconductivity materials, and in many spin-chain and spin-ladder compounds.

Quantum fluctuations in the frustrated antiferromagnetSr2Cu3O4

“…͑12͒, the perpendicular field acting on an e spin is 4␦J 12 ͒, is a classical effect which already appeared within mean field theory. 3,4 The other in-plane anisotropies only have an effect when we consider fluctuations. However, since the effect of ␦J 12 is rather small, we do not consider the effects of fluctuation corrections to it.…”

“…1. For T II ϽTϽT I a very small residual anisotropic exchange interaction causes the Cu II spins to have a small ferromagnetic moment, the study of which 4 led to the determination of the magnetic structure which has recently been confirmed by neutron diffraction. 7 The study of the statics also led to the determination of several coupling constants in the Hamiltonian used to model this system.…”

“…2 Recently, a variant of this system Sr 2 Cu 3 O 4 Cl 2 ͑2342͒ has been shown to display very interesting magnetic properties. [3][4][5] The structure of this system 6 is one in which an additional Cu ion ͑which we refer to as a Cu II ion͒ is inserted at the center of alternate Cu plaquettes of the usual copper lattice, whose ions we refer to as Cu I 's. Although all the Cu ions are chemically equivalent, they play very different roles insofar as magnetism is concerned.…”

Possibility of soft-matter effects in solids

“…It should be stressed that in contrast to pure AFMs, the configurations with (M F , L) and (M F , −L) are inequivalent, due to anisotropic pseudodipolar interactions (described by the constant J pd ). Figure 5 illustrates the field-induced variation of equilibrium magnetic configurations (represented by X-projections of M F and L vectors) obtained from the numerical minimization of expression (17) with the data taken from [1,4,6].…”

“…The most interesting case on which we concentrate our attention in the present paper, lies in-between: i.e., in multiferroics with the domains of different nature some types of domains can easily nucleate and show soft-like behaviour while the others could have high nucleation barrier and reveal themselves as solids. In particular, we consider a multiferroic (like Sr 2 Cu 3 O 4 Cl 2 or Ba 2 Cu 3 O 4 Cl 2 ) that simultaneously shows ferromagnetic (FM) and AFM ordering on different systems of copper ions [1].…”