Magnetic Properties of Low-Dimensional Cuprates

Abstract

The interest in quasi low-dimensional cuprates originated from the discovery of high-Tc superconductors typically consisting of intermediate valence (“doped”) copper oxide planes with strongly correlated d-electrons. For understanding the mechanism of superconductivity in these materials their magnetic properties, even in the non-doped state, have to be considered. The magnetism of the cuprates mainly originates from the d-electrons of copper in the oxidation states Cu’, Cull or Cum. In an ionic approximation the Cu species are described by charge states, e.g. Cull by Cue+. According to this approximation the ground state of Cu’ compounds has no magnetic moment and they exhibit diamagnetism or van Vleck paramagnetism. Cue+has an odd number of d-electrons resulting in so called Kramersdegeneracy. Its paramagnetic moment is well approximated by the spin-only value of 1.73 Bohr magnetons. Depending on its anionic surrounding the paramagnetic moment of Cu’ corresponds to the high-spin value of 2.83 Bohr magnetons (as in K3CuF6) or it may be zero (low spin) as usually in cuprates. In the ionic approximation a certain overlap of wave functions results in exchange interactions of the magnetic moments which may lead to antiferromagnetic or ferromagnetic long-range order. In the case of cuprates the dominating type of interaction is superexchange via oxygen anions. In a more realistic description covalence or, more generally, overlapping electron-wave functions combined with electron correlation have to be taken into account in order to explain effects as (i) the existence of well localized magnetic moments (in spite of delocalized wave functions), (ii) the real electric charge of the species usually being much smaller than following from the formal valency, (iii) the metallic or insulating behavior of particular compounds as e.g. LaCuO3 or La2CuO4, respectively, and (iv) the special crystallographic structures which in the case of Cu’ compounds usually contain O-Cu-O dumbbells. In most cases the Cull cuprates contain quasi two-dimensional or quasi one-dimensional networks of CuO4 plaquettes and they mostly behave like quantum spin-1/2 antiferromagnets of low dimensionality (d = 1 or d = 2). Usually a crossover to three-dimensional behavior occurs in these compounds at sufficiently low temperatures because, actually, they are three-dimensional solids.