Effect of covalent bonding on magnetism and the missing neutron intensity in copper oxide compounds

Abstract

Theories involving highly energetic spin fluctuations are among the leading contenders for explaining high-temperature superconductivity in the cuprates 1 . These theories could be tested by inelastic neutron scattering (INS), as a change in the magnetic scattering intensity that marks the entry into the superconducting state provides a precise quantitative measure of the spin-interaction energy involved in the superconductivity 2-11 . However, the absolute intensities of spin fluctuations measured in neutron scattering experiments vary widely, and are usually much smaller than expected from fundamental sum rules, resulting in 'missing' INS intensity 2-5,12,13 . Here, we solve this problem by studying magnetic excitations in the one-dimensional related compound, Sr 2 CuO 3 , for which an exact theory of the dynamical spin response has recently been developed. In this case, the missing INS intensity can be unambiguously identified and associated with the strongly covalent nature of magnetic orbitals. We find that whereas the energies of spin excitations in Sr 2 CuO 3 are well described by the nearestneighbour spin-1/2 Heisenberg Hamiltonian, the corresponding magnetic INS intensities are modified markedly by the strong 2p-3d hybridization of Cu and O states. Hence, the ionic picture of magnetism, where spins reside on the atomic-like 3d orbitals of Cu 2+ ions, fails markedly in the cuprates.Over the past 20 years, the magnetic properties of cuprates have been studied extensively by theorists and experimentalists alike. These systems are usually described within the antiferromagnetic Mott insulator model, in which the unpaired electrons are localized on the Cu 2+ ions because of the overwhelming cost in the on-site Coulomb interaction energy, U , associated with the charge transfer between the Cu sites, a strong correlation phenomenon. Virtual electron hopping, which in the one-band Hubbard model of a Mott insulator often adopted for cuprates 14 is quantified by the transition matrix element, t , results in antiferromagnetic exchange. For t U , electronic spins form the only low-energy electronic degrees of freedom. Their properties are well approximated by the spin-1/2 Heisenberg Hamiltonian on the lattice 15 , H = J i(nn)j S i S j , with the nearest-neighbour exchange coupling J ≈ 4t 2 /U . This description conveniently splits the problem of electronic magnetism in the Mott insulator into two parts 15 . The first deals with the electron transfer between the neighbouring sites of the crystal lattice, which is determined by the overlap integral (∼t ) of the wavefunctions occupied by the unpaired electrons, and leads to the Hubbard model, or the Heisenberg spin Hamiltonian. The second concerns the form of the electronic Wannier wavefunctions, that is, the shape of the spin magnetization cloud associated with 1 ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, UK, 2 Department of Physics, University College London, Gower Street, London WC1E 6BT, UK, 3 London Centre for Nanotechnology, 17-19 Go...

Heisenberg necklace model in a magnetic field

“…The mass gap Λ serves as the ultraviolet cut-off for the sigma model (14). The corrections to the sigma model generated by the last term in (15) carry higher power of gradients of the n-field and therefore can be discarded for momenta < Λv −1 .…”

“…These materials have crystal structure composed of chains of corner-sharing CuO 4 square plaquettes, where strong Cu-O hybridization results in an exceptionally strong in-chain superexchange, J ∼ 2500 − 2800 K, [13,14]. Small orbital overlaps between the planar CuO 4 plaquettes on neighbor chains lead to an extremely small inter-chain coupling,…”

Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain

“…The main sources of uncertainty come from the need to normalize the neutron scattering intensity to that of a reference Vanadium standard and from the role of other intrinsic and extrinsic sources of bias such as covalency, self-absorption, atomic zero point and thermal motion, and the limits of the dipole approximation used in the interpretation of the neutron crosssection. The recent most accurate study, on the cuprate compound Sr 2 CuO 3 , finds only 80% of the predicted spectral intensity 41 . Here we present a totally different approach to quantifying the full correlator, including two-and higher-spinon contributions.…”

“…The qualitative characteristics of two-spinon excitations, a continuum-like spectrum with linearly dispersing low-energy onset, are evidenced by inelastic neutron scattering on numerous compounds [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] . Among them, there are various quantitative attempts of an absolute comparison to theory 30,37,41 . However, none was sufficiently accurate to distinguish between an excitation continuum made of only two-spinon states and that composed of two-and higher-order spinon states, bearing a ∼30% larger spectral weight.…”

What is the Valence of Mn inGa1−xMnxN?

“…(The other two electrons reside in the spin-majority effective e g WOs.) This effective d 4 picture also gives a local moment of 4µ B that is really the one fluctuating at low energy, with a form factor [57,58] extending to neighboring N ions in real space.…”