Nanoscale phase competition accompanies colossal magnetoresistance

Colossal magnetoresistance is aptly named. By subjecting a piece of appropriately doped manganite to a strong magnetic field and a moderately low temperature, one can raise its electrical conductivity by orders of magnitude.

Despite its prodigious magnitude, CMR has not led to any commercial devices since its discovery 15 years ago. Cooling a sample by the requisite few tens of kelvin isn’t hard, but it is inconvenient for manufacturers. Worse, CMR shows up only at the mighty, tesla-scale magnetic fields used in magnetic resonance imaging scanners.

To physicists, however, CMR remains intriguing. Unlike its already commercialized cousins, giant magnetoresistance and tunneling magnetoresistance, CMR doesn’t rely on the nanoscale layering of different materials. It’s an intrinsic property of a single substance. Depending on the doping level and external conditions, a CMR material can be a ferromagnetic metal, a paramagnetic insulator, or an antiferro-magnetic insulator in which the valence electrons arrange themselves in stripes and other kinds of charge order. (See Physics Today, October 1996, page 19 .)

Moreover, pairs of those other phases can coexist in CMR manganites whenever and wherever the temperature, magnetic field, or mechanical strain reduces the energy differences between them. (See Neil Mathur and Peter Littlewood’s article, Physics Today, January 2003, page 25 .)

The CMR effect itself arises when the paramagnetic insulating phase yields to the ferromagnetic metallic phase. Now, Jing Tao of Brookhaven National Laboratory and her collaborators have found evidence that a charge-ordered, possibly antiferromagnetic phase plays a role too. ¹ As her sample approached the CMR transition, patches of charge order appeared as if to forestall and thereby intensify the onset of metallic behavior.

Tao derived her results using a new technique, scanning electron nano-diffraction (SEND). The technique combines electron diffraction’s ability to reveal the presence of ordered structures with scanning microscopy’s ability to reveal those structures’ real-space distribution.

Competing phases

The broad labels ferromagnetic, paramagnetic, and antiferromagnetic don’t fully describe the richness of manganite phases. Spin-up and spin-down electrons may arrange themselves in stripes or in a checkerboard pattern; the occupancy of atomic orbitals may alternate. Those and other arrangements arise when doping turns on the interplay between a manganite’s crystal structure, shown in figure 1, and its spin, charge, and orbital degrees of freedom.

Like other undoped manganites, LaMnO₃, to pick an example, is an insulator at all temperatures and magnetic fields. Replacing some of the trivalent lanthanum ions with divalent calcium ions not only removes electrons, it also engenders lattice distortions because Ca ions are smaller than La ions.

The valence electrons whose mobility—or lack of it—manifests CMR come from the two most energetic of manganese’s 3d orbitals. Just below them in energy are three more 3d orbitals, each degenerate and occupied by one electron. Those electrons are too tightly bound to take part in conduction; they behave together like a single spin-3/2 particle, a so-called core spin.

When the doping is moderate (that is, in La_x-1Ca_xMnO₃ when 0.15 < x < 0.5), the core spins align ferromagnetically at a temperature that can be raised by applying a strong magnetic field. Thanks to that alignment, the valence electrons, whose spins are also polarized, can lower their energy by hopping between Mn atoms via intervening oxygen atoms. The process is known as double exchange. Raising the temperature, lowering the magnetic field, or doing both reduces the core spins’ ferromagnetic order and the valence electrons’ hopping ability. The material becomes a paramagnetic insulator.

Double exchange can account for the existence of a magnetoresistive effect in La_x-1Ca_xMnO₃ and other manganites, but not for the effect’s magnitude. The Ca ions also influence the valence electrons’ mobility through the Jahn–Teller effect: If the valence electrons confine themselves to their Mn atom, they can lower their energy by inducing a distortion in the oxygen cage that surrounds them.

The more Ca ions are present, the more room the cage has to flex and the stronger the Jahn–Teller effect is. When 0.15 < x <0.5, the Jahn–Teller effect is too weak to overcome double exchange and stifle conduction. The Jahn–Teller effect does, however, contribute significantly to the resistance in the paramagnetic state. Indeed, it’s responsible for the “C” in CMR.

But when x > 0.5, the Jahn–Teller effect starts defeating double exchange. Conduction ceases, the core spins align antiferromagnetically, and the valence electrons arrange themselves in stripes or another charge- or orbital-ordered pattern.

That clear-cut picture of doping-determined behavior was established within a year of CMR’s discovery, but it soon proved inadequate. Various experiments revealed that phases could coexist at values of x that favor one phase over its competitor. Even when the competition is balanced, odd behavior appears.

In 2002 James Loudon, Neil Mathur, and Paul Midgley of Cambridge University applied electron microscopy to a sample of La_0.5Ca_0.5MnO₃. They found regions of ferromagnetic order and charge order, as one might expect given the fine balance at x = 0.5 between the two phases. But they also found a single region where the phases appeared to coincide to form a new phase, at least at the 20-nm resolution of their magnetic probe. ²

The Cambridge result was consistent with earlier simulations by Elbio Dagotto of Oak Ridge National Laboratory and his collaborators. ³ At a few nanometers across, the regions of charge-ordered phase that form amid the ferromagnetic phase are indeed below the resolution limit. Moreover, those charge-ordered regions, argued Dagotto, Adriana Moreo, and Seiji Yunoki, are not inconsequential bystanders in the CMR transition but active participants. ⁴

Scanning diffraction

Four years ago, Tao set herself the goal of directly observing the phase coexistence and determining its role in CMR. The clearest signature of charge order comes from the diffraction spots caused by the Jahn–Teller distortion. Tao realized that if the beam of a transmission electron microscope could be made narrow enough and if it could be scanned across the sample, the charge order could be mapped on the nanoscale.

Standard TEMs have a beam size of about 4 nm. Tao shrank the beam on her microscope to 1.7 nm using optics developed at the University of Illinois at Urbana-Champaign, where she did her PhD work. She also took advantage of adaptations that her former group had made to scanning hardware and image reconstruction software.

Tao used La_0.67Ca_0.33MnO₃ as her sample. At that doping, applying a 4-T magnetic field at 253 K causes the material’s resistivity to drop by 50%. (Other manganites show a bigger CMR effect.) By scanning the SEND beam across the sample, Tao obtained a sequence of diffraction patterns. The brightest spots in each pattern corresponded to the undistorted lattice. Whenever the beam passed over a region of charge-ordered phase, additional faint spots appeared.

Figure 2 shows the maps Tao constructed from the intensity distributions of the charge-ordered spots. The regions of charge-ordered phase are indeed nanoscale. And they proliferate and spread as the CMR transition temperature of 253 K is approached from either direction. At their greatest extent, the charge-ordered phase occupies 22% of the sample volume.

Doping is inherently inhomogeneous: An x value of 0.5 doesn’t imply that every Mn ion is surrounded by exactly four Ca ions and four La ions. Given that Ca ions promote the charge-ordered phase, could local overdoping account for the maps in figure 2? Tao repeated the scans over her sample. Each run yielded the same overall behavior but with a different distribution of regions. Immobile dopants would have yielded the same distribution.

That the charge-ordered phase appears to be intimately associated with the CMR transition is consistent with Dagotto’s most recent simulations. ⁵ Weak, charge-ordered correlations are present in the insulating paramagnetic state. As the temperature is reduced toward the transition temperature, the correlations strengthen, creating regions of charge order. “Then, at the transition itself,” Dagotto says, “the ferromagnetic state abruptly emerges, as if its lower energy defeats the charge-ordered state’s higher entropy.”

Support for that picture, which is based on simulating clusters of up to 256 Mn atoms, may come when Tao extends her investigation to other doping values.