Spin and charge are inseparable traits of an electron, but in one-dimensional solids, a 40-year-old theory predicts their separation into "collective" modes—as independent excitation quanta called spinons and holons. Angle-resolved photoemission spectroscopy (ARPES) should provide the most direct evidence of this spin–charge separation, as the single quasiparticle peak splits into a spinon–holon two-peak structure. However, despite extensive ARPES experiments, the unambiguous observation of the two-peak structure has remained elusive. Working at the ALS, a team of researchers from Korea, Japan, and the U.S. has now observed electron spin–charge separation in a one-dimensional solid. These results hold implications for future developments in several key areas of advanced technology, including high-temperature superconductors, nanowires, and spintronics.

The idea behind spin–charge separation is that electrons behave differently when their range of motion is restricted to a single dimension. Ordinarily, the removal of an electron from a crystal creates a hole, a vacant positively charged energy space. This hole can move freely throughout the crystal in two or three dimensions, carrying with it information on both the electron's spin and charge, as observed in a single peak of an ARPES spectrum. When restricted to one dimension, however, it becomes theoretically possible for the hole (carrying a positive charge) to propagate in one direction while the spin propagates in the opposite direction, or at a different speed. If this spin–charge separation occurs, the hole is said to decay into a spinon and a holon, and two peaks in the ARPES spectrum would be observed.

Schematic view of electron removal in the case of a one-dimensional system with antiferromagnetic correlation. Removal of a spin-up electron results in a positively charged hole (holon) that moves along the chain as neighboring electrons fill the empty space. The "closing up" of the initial hole leaves two spin-down electrons adjacent to each other. This magnetic disorder can be thought of as a quasiparticle (spinon) that propagates along the chain, independently of the holon, through the flipping of successive spins.

ARPES is an excellent tool for observing spin–charge separation and other collective effects involving electrons. By measuring the energy and momentum of emitted electrons, ARPES provides a detailed picture of the electron energy spectrum and important information about electron dynamics, such as the speed of the electrons and their effective mass. However, despite extensive studies of various one-dimensional systems, previous efforts to observe the two-peak spectrum proved unsuccessful or ambiguous. The materials in these earlier studies were complex enough to allow for alternative explanations for the peaks, and independent estimates of the spinon and holon energy scales—a valuable check on the interpretation of the data—were not available.

The current observations are direct and the results are unambiguous because they were obtained from a simple material that left little room for misinterpretation. The researchers examined the ARPES spectrum of SrCuO₂, which has a double Cu-O chain structure but is an ideal one-dimensional compound because of very weak interchain coupling. Furthermore, the values of its spinon and holon energy scales can be estimated from optical and neutron data as well as band theory. The observations were made at the Electronic Structure Factory endstation at ALS Beamline 7.0.1, which is able to survey a relatively large range of momentum and energy values to locate the interesting correlated effects. The data not only show a clear separation of ARPES peaks, but the spinon and holon energy scales of ~0.43 and 1.3 eV, respectively, are in quantitative agreement with theoretical predictions. In addition, deviation of the data from a simple two-peak structure (shaded green in figure) is also predicted by theory.

Two discrete peaks in the ARPES data form the signature of a spin–charge separation event. The raw data (black dots) are fitted with gaussian peaks for the holon (blue) and the spinon (red) with an integrated background (dashed line). The solid black line is the sum of the two gaussian peaks and the background. The inset compares the data with the calculated spectral function, and the shaded green area indicates the extra intensity predicted by theory. The red bar shows that the spinon peak is wider than the holon peak.

The researchers credit their breakthrough to the use of high photon energies that suppressed the effects of the main valence band, whose spectral "tail" obscured the holon peak in previous efforts. The only aspect of the data that remains unexplained is the broadness of the peaks; one clue may lie in the fact that the spinon peak is wider than the holon peak. The clear-cut nature of this landmark study not only strengthens and deepens our understanding of the collective behavior of a system of particles, it also points the way to future investigations.

Research conducted by B.J. Kim and S.-J. Oh (Seoul National University, Korea), H. Koh and E. Rotenberg (ALS), H. Eisaki (National Institute of Advanced Industrial Science and Technology, Japan), N. Motoyama and S. Uchida (University of Tokyo, Japan), T. Tohyama (Tohoku University, Japan), S. Maekawa (Tohoku University and Japan Science and Technology Agency), Z.-X. Shen (Stanford Synchrotron Radiation Laboratory), and C. Kim (Yonsei University, Korea).

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

Publication about this research: B.J. Kim, H. Koh, E. Rotenberg, S.-J. Oh, H. Eisaki, N. Motoyama, S. Uchida, T. Tohyama, S. Maekawa, Z.-X. Shen, and C. Kim, "Distinct spinon and holon dispersions in photoemission spectral functions from one-dimensional SrCuO₂," Nature Physics 2, 397 (2006).