For the past six decades, researchers have been striving to find out how manganese oxide (MnO) attains its long-range magnetic order of alternating up and down electron spins. Currently, a group of researchers have used their newly created mathematical approach to examine the short-range magnetic interactions that they hope would drive this long-range order.
By making a comparison of measurements of the local magnetic interactions in manganese oxide with those estimated by competing hypothetical models, the researchers found that the antiparallel electron spin alignment is caused by the magnetic interaction of the adjacent Mn ions via an intermediary nonmagnetic oxygen ion. This process is known as superexchange.
The study was explained in a paper reported on May 11 in the Physical Review Letters journal by a group of scientists from the U.S. Department of Energy's (DOE) Brookhaven National Laboratory, Columbia University, DOE's Oak Ridge and Los Alamos National Laboratories, Institut Laue-Langevin in France, and the University of Warwick in England. The mathematical approach, known as magnetic pair distribution function (mPDF) analysis, was created at Columbia University and Brookhaven Lab. It is a potential tool for understanding the magnetic properties of transition metal oxides, superconductors, and other materials with strong electron-electron interaction.
"This research demonstrates that our technique can be used to study fluctuating local magnetism and yield important scientific insights about a material's magnetic properties, which are closely related to its ability to conduct electricity without resistance (superconductivity), change electrical resistance under an applied magnetic field (magnetoresistance), and transition from a conducting to an insulating state," said Brookhaven Lab physicist and Columbia University School of Engineering Professor Simon Billinge, lead author on the paper and co-developer of mPDF. "If we can understand how materials get these properties, we can make power transmission more efficient, increase data-storage capacity, and build smaller electrical components."
Magnetism in Manganese Oxide
The electron spins or, magnetic moments, of adjacent Mn ions spontaneously assemble in an ordered, alternating up-down-up-down pattern at low temperatures. As the temperature is raised, the magnetic moments begin to vibrate and turn out to be less ordered. The long-range antiparallel order tends to vanish completely beyond a critical temperature of 118K, with the magnetic moments fluctuating at random.
Even above the critical temperature, researchers have noticed fleeting, short-ranged leftovers of magnetic order in the randomly fluctuating magnetic moments, which are supposed to have crucial data pertaining to the nature of the magnetic interactions. However, these short-ranged correlations have been extremely difficult to study as traditional measurement methods do not have the capability to record the details of the correlations, for instance, how the magnetic moments are positioned on the nanometer scale. mPDF is designed to address this problem.
The ultimate goal of our research is to understand what causes these magnetic moments to line up.
Professor Simon Billinge
The MnO structure has Mn-O-Mn chains, wherein the O ion can act as a "bridge" for the second-nearest neighbor Mn ions for exchanging magnetic data through electron hops—a mechanism known as superexchange. Conversely, Mn ions could exchange magnetic data directly through the first-nearest neighbor ions that are diagonal from each another through direct electron hops via space. Both the interactions are known to take place, but which is one is a dominant mechanism remains a mystery.
"Determining which of these two interactions—those between nearest neighbor spins or second-nearest neighbor spins—is primarily responsible for the ordering of the magnetic moments is key to understanding how the material gets its magnetic properties," said Benjamin Frandsen, a Columbia University graduate student in Billinge's group and the major developer of mPDF.
Studying the short-range magnetic correlations that are present beyond the critical temperature provides key insights in to the magnetic interactions, a driving factor for the long-range correlations at low temperature.
As the temperature is increased, the magnetic correlations over long ranges are lost. Five neighbors over from an Mn ion, the electron spins are completely random," said Billinge. "But there are remnants of what the locally ordered state looked like. Using mPDF, we can measure patches of remaining magnetic order, even when these patches are fluctuating and short-range ordered only, and compare predictions of competing models based on superexchange versus direct-exchange interactions.
Professor Simon Billinge
Magnetic and Nuclear Scattering Data Analysis
To determine the correlations, the group initially carried out neutron scattering experiments to acquire data required to apply its method. The researchers directed neutron beams at a sample of MnO powder for a temperature range of 15-300K and determined the energy and angle at which the neutrons were scattered subsequent to the sample interaction. They captured two types of scattering signals: magnetic, i.e., the interaction mechanism of the magnetic moments of the neutrons with that of the Mn ions, and nuclear, i.e, the interaction mechanism of the neutrons with atomic nuclei of the sample.
How Magnetic Moments in MnO Fluctuate at Different Temperatures
These signals enabled the group to concurrently compute the magnetic and atomic pair distribution functions (PDF), and mathematical equations to express the correlations within a sample. The atomic PDF is the possibility of detecting any two atoms that are separated by a specific distance. Although similar to the atomic PDF, the magnetic PDF can also provide data about the relative orientations of the electron spins.
These experimental measurements were then compared with the PDF signals measured by magnetic and structural models of MnO. They were also fitted to models of magnetic order and atomic structure by iteratively altering parameters like the position of Mn ions or the direction of electron spins on every Mn ion until reaching agreement between the calculated PDF and the measured PDF. The mPDF has both of these modeling capabilities.
At temperatures beyond 118K, the measurements proved that the MnO’s local atomic structure was slightly deformed from cubic to rhombohedral, but the long-range regular structure retained the cubic form. The mPDF signal analysis corroborated the presence of short-range magnetic correlations at these temperatures. However, the correlations are slightly different from those observed in the long-range magnetic structure.
The local structure exhibits a slightly different type of magnetic order than that found in the low-temperature average structure—for example, the second-nearest neighbor spins have significantly stronger local correlations than would be expected from the low-temperature structure. Our experimental mPDF signals do not match the signals generated by the known long-range magnetic order.
Julie Staunton from the University of Warwick headed the group to compare the experimental results with competing hypothesis for magnetic exchange by computing the magnetic correlations at elevated temperatures for a range of magnetic exchange ratios between first- and second-nearest neighbors. Theoretically, the value of these ratios is expected to be higher for interactions dominated by direct exchange and lower for superexchange. The researchers then determined the mPDF using the calculated magnetic correlations and compared the ensuing value with the experimental data. The experimentally observed and predicted ratios were in good agreement, supporting a superexchange model of magnetic interactions in MnO.
The study results helped the researchers to confirm that the dominant mechanism is superexchange for magnetic exchange in MnO. Determining the reason behind this phenomenon is their next step. Billinge and Frandsen are also wanted to analyze the magnetic interactions in other materials using their technique.
"Our technique provides a new diagnostic tool for studying the physics of strongly correlated electron systems. If we can understand the physics of these systems—how their magnetic, electronic, and structural properties relate—we can design new materials for specific applications," said Billinge.
DOE's Office of Science and the National Science Foundation supported this study.