Two distinctive features of materials known as quantum double-exchange ferromagnets are purely due to quantum spin effects and multiorbital physics, with no need for the lattice vibrations previously invoked to explain them. This theoretical result could lead to new insights into these technologically important materials, as it suggests that some of their properties may arise from interactions hitherto regarded as less important.
Quantum double-exchange ferromagnets have interested scientists since the late 1980s, when physicists led by Albert Fert and Peter Grünberg found that their electrical resistance depends strongly on the magnitude of an external magnetic field. This phenomenon is known as giant magnetoresistance (GMR), and its discovery led to an enormous increase in the storage capacity of modern hard-disk drives, which incorporate GMR structures into their magnetic field sensors. It also led, in 2007, to a Nobel Prize for Fert and Grünberg.
Modelling strategies
Despite these successes, however, physicist Jacek Herbrych of the Institute of Theoretical Physics at Wrocław University of Science and Technology in Poland, who led the new research effort, says that these materials remain somewhat mysterious. “They are theoretically complex, and even today, there is no exact solution to fully solve these systems,” he says.
The key question, Herbrych continues, is how Coulomb interactions between many individual electrons lead to the electron spins in these ferromagnets becoming aligned. “Physicists broadly distinguish two mechanisms,” he explains. “For insulating ferromagnets, the Goodenough-Kanamori rules (based on electron shell occupancy and geometrical arguments) can predict spin alignment. For metallic ferromagnets, the double-exchange mechanism is more appropriate.”
In this latter case, Herbrych explains, the electrons’ motion and the alignment of their spins are intrinsically linked, and the electrons often occupy multiple orbitals. This means they need to be modelled in a fundamentally different way.
The approach Herbrych and his colleagues took, which they describe in Rep. Prog. Phys., was conceptually simple, using a basic yet realistic model of interacting electrons to predict the quantum behaviour of electron spins. “In quantum mechanics, ‘simple’ can quickly become complex, however,” Herbrych notes. “Materials in which the double-exchange mechanism dominates typically exhibit multiorbital behaviour, as mentioned. A minimal model must therefore include electron mobility (or ‘itinerancy’), Coulomb interactions and orbital degrees of freedom.”
Two distinctive features
Herbrych and colleagues identified the two-orbital Hubbard-Kanamori model and the Kondo lattice model with interactions as fitting these requirements. They then used these models to explore two distinctive features of quantum double-exchange ferromagnets.
Both features involve magnons, which are collective oscillations of the materials’ spin magnetic moments. In basic “toy” models of ferromagnets, magnons exhibit a well-defined energy-momentum correspondence known as the dispersion relation. Quantum double-exchange ferromagnets, however, experience a phenomenon known as magnon mode softening: at short wavelengths, their magnons become nearly dispersionless, or momentum independent. “This implies that there are fundamental differences between long- and short-distance spin dynamics,” Herbrych says. “Magnons can travel over long distances but appear localized at short scales.”
The second distinctive feature is called magnon damping. This occurs when magnons lose coherence, meaning that the standard picture of spin flips propagating through the material’s lattice breaks down. “It was previously thought that Jahn-Teller phonons (lattice vibrations) were responsible for these features, and that a classical spin model with phonons would do, but our work challenges this view,” says Herbrych. “We show that these phenomena can arise purely from quantum spin effects and multiorbital physics, without requiring lattice vibrations.”
This is, he tells Physics World, “a remarkable result” as it suggests that some experimental features of quantum double-exchange ferromagnets may arise from interactions previously considered secondary.
Limitations and extensions
The researchers’ present work is restricted to one dimension, and they acknowledge that extending it to two or three dimensions will be a challenge. “Still, our approach offers a conceptual framework that can be approximately extended to higher dimensions,” Herbrych says. “The results not only provide insights into the physics of strongly correlated systems, but also into the interplay of competing phases, such as ferromagnetism, orbital order and superconductivity, observed in these materials.”
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