Influence of Topological Spin Fluctuations on Charge Transport

Layered transition metal oxides are the focus of intense research efforts because they might clarify the superconducting mechanism of cuprate high-temperature superconductors (HTSCs). A case in point is Na_xCoO₂ with x = 0.7, which is a parent compound for a family of cobaltites that exhibits superconductivity. This class of materials is also thought to be ideal for detecting the long-sought resonating valence bond (RVB) state of matter proposed by Philip Anderson of Princeton University in 1973. Researchers from Princeton University and ALS are the first to use angle-resolved photoemission spectroscopy (ARPES) to demonstrate the strongly electron correlated nature of this material and to provide evidence that charge transport is strongly influenced by topological spin frustration.

Triangular Blues

The almost two-decades-long search for an answer to the question: what gives ceramic cuprate compounds (so-called because they are copper-based) their miraculous ability to conduct electricity without resistance at much higher temperatures than superconducting metals and alloys is taking on the proportions of a Homeric odyssey. One sign is that physicists are driven to attack the problem by studying other materials that are like but not exactly the same as the cuprates in the hope of narrowing the options from among the many possibilities. For example, if cuprates and their near twins shared some characteristics but not others, that might lead physicists to focus more intently on the similarities.

A case in point is the family of materials called cobaltites (because they are cobalt-based), which have many similarities to cuprates, including superconductivity (but at a relatively low temperature) and electronic activity confined to two-dimensional layers. But there are also important differences, such as the symmetry of the atomic arrangement of the cobalt atoms in the layers, which is triangular rather than square, as for copper atoms in the cuprates. Hasan et al. have applied to the cobaltites an x-ray photoemission technique that has been very successful in the study of the cuprates. They are the first to use this technique to demonstrate both the strongly correlated nature of the electrons (the property that makes the problem so difficult) and the influence of magnetic effects (spin fluctuations).

The family of sodium cobalt oxides or oxyhydrates (cobaltites) Na_xCoO₂ (with variable x) is similar to cuprate HTSCs. The parent compounds are Mott insulators, in which a strong electrostatic repulsion blocks charge transport; they have layered crystal structures with electronic two-dimensionality; and they can be chemically doped by altering the sodium concentration, thereby changing the electron concentration in the electronically active cobalt-oxygen layers. There is one very important difference, however. While the electronically active copper-oxygen planes in HTSCs have square symmetry, in cobaltites, the symmetry is triangular, a configuration that geometrically frustrates formation of the antiferromagnetically ordered Néel state present in HTSCs and results in a less well ordered "quantum spin liquid" state.

Atomic structure models of Na_xCoO₂ before and after exposure to water adds H₂O to the sodium spacer layers between the electronically active cobalt-oxygen layers, whose electron concentration is controlled by the sodium fraction x.

The interplay of charge and spin degrees of freedom is indeed exciting in cobaltites and leads to a bouquet of changing electronic properties with doping. With increasing sodium concentration, the material progresses from a paramagnetic metal that is superconducting at low-temperature for 1/4 < x 3/4.


Photoemission intensity (bright regions are highest intensity) maps of the valence excitations at T = 10 K along the two symmetry directions (Γ–M and Γ–K) in a two-dimensional hexagonal Brillouin zone. Solid curves are from mean-field calculations [D. J. Singh, Phys. Rev. B 61, 13397 (2000)]. Co t_2g and O 2p indicate the origin of the bands is predominantly from these states.		The difference (green) between photoemission energy distribution curves (EDCs) taken at T = 18 K in resonance with the cobalt 3p → 3d transition (red) and out of resonance (blue) shows a resonance enhancement of the correlation satellite centered near 11 eV.

The Princeton/ALS group performed a detailed investigation of low-energy electronic structure and charge dynamics of the parent cobaltite compound Na_0.7CoO₂ at ALS Beamlines 7.0.1 and 12.0.1. This technique is sensitive to an electron’s quantum correlations because it directly probes the electron distribution function over a complete Brillouin zone (unit cell in momentum space) with good resolution.


An energy distribution curve (EDC) showing a quasielectron feature (blue curve) after background (red curve) subtraction locates the peak position for a particular momentum, giving one point on an energy–momentum dispersion curves.		Energy–momentum dispersion curves for the quasielectron after correction for the background along Γ–M (left) and Γ–K (right) directions. In both directions, the quasielectron bandwidth, confined to 100 meV, is extremely narrow. Red dots are extrapolations to the Brillouin zone boundary (dotted line).

ARPES spectra taken in the energy range of valence (loosely bound) electrons are in good agreement with the results of mean-field (first principles) calculations and map the dispersion (energy–momentum relationship) of several distinct bands. Most exciting, ARPES spectra also reveal an additional satellite feature centered at a much higher binding energy near 11 eV. Separation of this correlation satellite from the valence band gives an estimate of a strong on-site Coulomb repulsion (Hubbard U) between electrons of about 5 eV, which is in the same range as the Hubbard U for the cuprates and provides strong evidence for the highly correlated nature of electrons.

In addition, the researchers discovered a tiny feature (quasielectron) adjacent to the Fermi energy (zero binding energy) that was dwarfed by the presence of the valence band. This feature is essentially flat in momentum space with a dispersion less than 100 meV, which is a factor of 5 smaller than in cuprates and an order of magnitude below the mean-field (first principles) calculations. Accompanying the small bandwidth is a very weak nearest-neighbor single-particle hopping energy t of about 10 meV. That t is of the same order of magnitude as the spin exchange coupling J for this family implies that the charge dynamics are strongly perturbed by spin fluctuations.


Quasiparticle distribution in momentum space. The occupied area (blue) in the Brillouin zone (red line) forms a single large hexagonal pocket around the center of the Brillouin zone. The Fermi surface is the inner edge of the pocket.		Quasiparticles lose their coherence above 150K (well below room temperature) and a coherent-to-incoherent cross-over is observed. A combination of very small hopping and magnetic exchange energies causes the low coherence temperature.

Temperature-dependent ARPES measurements revealed that quantum coherent quasielectrons exist only at low temperatures and linearly disappear as their motion becomes incoherent beyond 150 K. This value, which is well below the decoherence temperature of tens of thousands of degrees in conventional metals, is of the order of t and J, making geometrical frustration of antiferromagnetic interactions in triangular cobalt lattice planes the leading cause of quasielectron’s quantum decoherence.

Research conducted by M.Z. Hasan (Princeton University, Princeton Materials Institute, and ALS); Y.-D. Chuang (Princeton University and ALS); D. Qian, Y.W. Li, and Y. Kong (Princeton University); A. Kuprin, A.V. Fedorov, R. Kimmerling, E. Rotenberg, K. Rossnagel, Z. Hussain, and H. Koh, (ALS); and N.S. Rogado, M.L. Foo, and R.J. Cava (Princeton Materials Institute and Princeton University).

Research funding: National Science Foundation, Princeton University, and U.S. Department of Energy, Office of Basic Energy Sciences (BES). Operation of the ALS is supported by BES.

Publication about this research: M.Z. Hasan, Y.-D. Chuang, D. Qian, Y.W. Li, Y. Kong, A. Kuprin, A.V. Fedorov, R. Kimmerling, E. Rotenberg, K. Rossnagel, Z. Hussain, H. Koh, N.S. Rogado, M.L. Foo, and R.J. Cava, “Fermi surface and quasiparticle dynamics of Na_0.7CoO₂ investigated by angle-resolved photoemission spectroscopy,” Phys. Rev. Lett. 92, 246402 (2004).