Slow Dynamics of Orbital Domains in Manganite

At the ALS, an international team of researchers has used low-energy coherent x rays to extract new knowledge about the correlated motion of groups of self-assembled, outer-lying electrons in the extremely complex electronic system found in manganites. The manganite family of materials has puzzled physicists for years by defying standard models for the motion of electrons in crystals. By controlling the properties of the incident x rays, the researchers were able to map the complexity of a "half-doped" manganite into a far-field speckle diffraction pattern to study the manganite's domain dynamics. Their results suggest the material undergoes a transition characterized by the competition between a pinned orbital domain topology that remains static and mobile domain boundaries that exhibit slow, temporal fluctuations.

Speckles in Time

Radar is familiar to anyone who has received a speeding ticket. A radar gun can be used to determine the speed of a car by reflecting a radio wave of known frequency aimed toward the car while detecting the change in the reflected wave. This allows one to probe the speed of an object by how it reflects the radio wave back to the observer. Because electrons, or rather, groups of electrons—called "domains"—are about a billion times smaller than automobiles, we must use a radar-type technique with photons of light that have wavelengths a billion times smaller than radio waves in order to study their domain motion. By using these soft x rays generated at the ALS, one of the brightest source of photons at this energy in the world, we can measure complex interference patterns created from the reflection of x rays from the domains of electrons. These special patterns, called "speckle" patterns, are imaged with a digital camera for x rays called a charge-coupled device (CCD). By measuring how these patterns change from image to image, we can understand the movement of the electronic domain structure.

A typical image from a digital camera for x rays (CCD) showing a soft x-ray speckle pattern. The close-up structure shows the large intensity variation due to interference of scattered x rays from different domains.

One conundrum involving the manganites is colossal magnetoresistance, a hot topic in correlated electron physics with promising applications in electronics, energy conservation, and nanodevice switching. Scientifically, this family of materials is also exciting because of the enormous range of phenomena it exhibits. Charge, orbital, lattice, and magnetic order are all intertwined to create an array of patterns, all interrelated in a nontrivial way. Orbital ordering occurs when specific electron wave functions self-organize. Interactions between these electron shells determine the patterns formed by the orbitals and, among other things, will even affect the system's magnetism.

A cartoon diagram of the orbital ordering is shown in purple and red, emphasizing the anti-phase domain wall. Any points where the wave functions are out of phase with each other can act as an orbital domain boundary.

To perform this study, the researchers used the coherent magnetic scattering endstation at ALS Beamline 12.0.2, which is specifically designed to deliver "laser-like" x rays that propagate in unison, like musicians in a marching band. It includes an 11-flanged vacuum chamber (dubbed the "flangosaurus" after its resemblance to a prehistoric creature) that allows signal detection over a broad range of scattering angles.

These coherent x rays are also resonant. This means they are tuned precisely to a specific absorption edge of a particular atomic species in the crystal to enhance the sensitivity to the local environment. In other words, by changing the energy of the x rays to particular values, they can "see" things that are invisible at all other energies.

The researchers measured a diffraction peak that is due solely to the orbital ordering of the d-electron shells in a single crystal of half-doped manganite, Pr_0.5Ca_0.5MnO₃. Because of the coherent illumination, constructive and deconstructive interference occurs between waves scattered from different domains, and the peak exhibits a "speckle" pattern, a unique characteristic pattern that acts as a fingerprint of the microscopic domain structure. Just as it is not easy to directly connect the fingerprint of a person to the face, extracting the domain structure from the speckle pattern is not straightforward. However, to better understand the orbital domain physics, one can measure the dynamics of the domains by noting that any small changes in this unique speckle pattern indicate changes in the domain configuration, the same way that a different fingerprint uniquely correlates to a different person.

Overall, the speckle patterns did not change significantly over time. However, near a transition temperature of about 232 K, small-amplitude fluctuations "turned on" before the domains completely melted. The domain walls are pinned except for close to the transition, where they execute small-amplitude motion. This behavior contrasts with that of most systems, where things usually behave in one of two ways: fluid-like, where everything is dynamic, or solid-like, where everything is static. Here a mixture of the two was found. Another surprising finding was that the fraction of the sample that was dynamic moved quite slowly, slower than typical electron domain behavior in other types of systems. The cause is unclear, but something is impeding the motion of the domain walls, up to a time scale on the order of several minutes. These slow dynamics may even be the reason the manganites form these disordered states in the first place.

Comparisons of adjacent speckle patterns for different temperatures. Yellow is attributed to speckle patterns that have not changed, while the other colors indicate that the speckle—and hence the domain configuration—is changing in time, with blue the most drastic. Time is represented on the vertical axis while momentum is on the horizontal.

Research conducted by J.J. Turner (University of Oregon and ALS), K.J. Thomas and J.P. Hill (Brookhaven National Laboratory), M.A. Pfeifer (La Trobe University, Australia), K. Chesnel (National Pulsed Magnetic Field Laboratory [LNCMP], France), Y. Tomioka and Y. Tokura (National Institute of Advanced Industrial Science and Technology, Japan), and S.D. Kevan (University of Oregon).

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

Publication about this research: J.J. Turner, K.J. Thomas, J.P. Hill, M.A. Pfeifer, K. Chesnel, Y. Tomioka, Y. Tokura, and S.D. Kevan, "Orbital domain dynamics in a doped manganite," New J. Phys. 10, 053023 (2008).