Predicting Magnetic Behavior in Copper Oxide Superconductors

New theoretical techniques predict experimental observations in superconducting materials.

Image courtesy of Physical Review X

a) Crystal structure of the parent compound of a calcium-strontium-based cuprate superconductor [(Ca/Sr)2CuO3]. (b) Calculated energies for different magnetic states (FM = ferromagnetic; AFM = antiferromagnetic). (c) The critical property compared is the energy of the magnetic coupling or exchange between neighboring atoms, denoted by “J” in the figure. Closed circles are data calculated from fundamental physics, in good agreement with experimental measurements from the literature (yellow shaded area). Open circles are data derived from a prior model. U is a parameter which is varied to find the state with the lowest energy which corresponds to the theoretical prediction.

The Science

Theoretical calculations were successfully used to predict magnetic properties of the complex electron behavior in metal oxide systems – combinations of metals such as iron, cobalt, nickel or copper with oxygen, which possess a wealth of useful properties.  Enabled by high performance computing, the magnetic couplings in model systems for copper-containing cuprate high temperature superconductors were accurately calculated for the first time.

The Impact

Accurate theoretical calculations could open the door for discovery of new materials in this class with even better properties than those currently in use.  This research demonstrates the power of advanced high-performance computing in enabling accurate calculations of important materials properties.  Effective magnetic models of superconductivity allow predictions of magnetic properties (previously reliant solely on experimentally measured data) for new systems from theory, which could lead to better fundamental predictions of superconductor behavior.


Theory has long had difficulty predicting the behavior of transition metal oxides. These materials, combinations of metals such as iron, cobalt, nickel or copper with oxygen, display a wealth of important properties such as magnetism, temperature dependent phase transitions from electrically insulating to conducting, and superconductivity – a property that allows materials to conduct electricity with perfect efficiency. Accurate theoretical calculations could open the door for discovery of new materials in this class with even better properties than those currently in use. The problem with describing them theoretically is the phenomenon of electron correlation, the fact that the motion of individual electrons depends on the motion of all the others. Theories that treat electron correlation have been known for a number of years but required orders of magnitude greater computer resources than were available. In this research, accurate calculations of magnetic energies were performed at the ORNL leadership class computer for calcium copper oxide (Ca2CuO3) a material containing nearly one-dimensional (1D) chains of copper, a one-dimensional counterpart of the famous high temperature superconducting cuprates. Like other cuprates the pure material is a magnetic insulator but becomes superconducting with changes in composition – in this case by increasing the oxygen concentration. Standard theory predicts the pure material (and other cuprates) to be a metal in contrast to the experiments. In this research, the 1D character of the materials permitted detailed comparison between theory and experiments, and showed good agreement between the theoretical data and those obtained from neutron scattering and magnetic susceptibility measurements. The research used highly accurate Quantum Monte Carlo (QMC) calculations. QMC methods accurately describe many-body systems, but at a high computational cost. High-performance computers, such as those at the Oak Ridge Leadership Computing Facility, allow application of QMC to problems that have remained unsolved for decades. This achievement could lead to better predictions of superconductor behavior derived from fundamental laws of physics.


F. Reboredo and K. Foyevtsova
Oak Ridge National Laboratory


Department of Energy, Office of Science, Basic Energy Sciences program supported the research including use capabilities in the Center for Nanophase Materials Sciences. Computational resources included the Oak Ridge Leadership Computing Facility supported by the Office of Science, Advanced Scientific Computing Research program.


K. Foyevtsova, J. T. Krogel, J. Kim, P. R. C. Kent,  E. Dagotto, and F. A. Reboredo, “Ab initio quantum Monte Carlo calculations of spin superexchange in cuprates: the benchmarking case of Ca2CuO3,” PHYS. REV. X 4, 031003 (2014)

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