Yi-feng Yang is a 2007-2009 ICAM Postdoctoral Fellow who has been combining theoretical work on heavy-electron materials under the supervision of David Pines, at UC Davis, with an extended visit to an experimental group led by J. D. Thompson at Los Alamos National Laboratory.  As a direct result of this exchange, Yang, Pines, and Thompson, together with their ICAM colleague Zachary Fisk of UC Irvine, and Thompson’s postdoc Han-Oh Lee,  devised a conceptual framework for the study of all heavy-electron compounds.  Their results were published in the July 31 issue of Nature and will be named by Discover magazine in its January 2009 issue as one of the top 100 scientific research discoveries of 2008.  Yang’s part in this success story was quite recently recognized by Los Alamos, which has awarded him one of its prestigious Director’s Funded Postdoctoral Fellowships.

The behavior of the heavy-electron compounds has perplexed physicists since their discovery almost forty years ago.  They are known to  possess a lattice of localized electron spins (a Kondo lattice) embedded in a sea of mobile electrons;  the two components behave independently near room temperature, but as the temperature is lowered, they change their character dramatically, with the materials exhibiting a rich spectrum of ordered states at very low temperatures.  Yang, Fisk, Lee, Thompson, and Pines reviewed years of experimental data on many materials and worked out a simple equation for calculating the temperature at which a new quantum state of matter first emerges, one in which the lattice of localized spins changes its behavior from individual to collective and the mobile electrons begin to become “heavy.”  Their equation makes it possible to predict the behavior of a Kondo lattice from studies of the behavior of a single localized spin in a mobile electron sea, and paves the way for future investigations of the interplay at low temperatures between superconductivity, antiferromagnetism, and quantum critical behavior in these fascinating materials. 

ICAM’s initial impact on this work, which also received NSF and DOE support, goes back some four years, to discussions during and immediately following a December 2003 ICAM Exploratory Workshop that focused on the newly discovered family of 115 (In MCoCeMIn_5, where M is Co, Rh, or Ir) heavy-electron materials.  These led Fisk and Pines, together with Satoru Nakatsuji (then at Kyoto University, now at ISSP, Tokyo University), to propose that the mobile electrons form a new quantum state of matter, a Kondo liquid, and to show that it emerges below a distinct onset temperature T*.  The quasiparticle excitations of this liquid do not follow the Fermi-liquid behavior articulated by Landau; they are emergent and coherent rather than elementary, since their effective mass increases logarithmically with decreasing temperature [S. Nakatsuji, D. Pines, and Z. Fisk, “Two-Fluid Description of the Kondo Lattice,” Phys. Rev. Lett. 92, 016401 (2004)].  Their work was soon extended in an ICAM collaboration between Nick Curro, David Pines, and Ben-li Young, who were all then at Los Alamos and Joerg Schmalian at Iowa State [N. Curro, B. Young, J. Schmalian, and D. Pines, “Scaling in the Emergent Behavior of Heavy-Electron Materials,” Phys. Rev. B 70, 235117 (2004)] that identified T* with the onset of anomalous magnetic behavior measured in what are known as Knight-shift experiments.

The next chapter in this “emergent” understanding of the Kondo liquid took place almost  three years later, following Yang’s appointment as an ICAM Fellow, and can be traced to discussions during and after a talk that  Pines gave at an  August 2007 ICAM followup workshop on the 115 materials.  These led Yang and Pines to argue that the Kondo liquid arises from the collective entanglement of localized f-electron spins with the background conduction electrons, and to show that for a broad spectrum of heavy-electron materials, and in response to many different experimental probes, the order parameter and quasiparticle effective mass for the  Kondo liquid display universal behavior for which the scale is set by T* between T* and a lower cutoff temperature T^0 [Y. Yang and D. Pines, “Universal Behavior in Heavy-Electron Materials,” Phys. Rev. Lett. 100, 096404 (2008)].

The next  question to be settled in the  phenomenological description  of a Kondo liquid was the physical origin of T*.  This was pursued by Yang, working with Pines, Fisk, Thompson, and Lee.  He looked systematically at the many ways the Kondo lattice “emergence” temperature T* and the single-ion Kondo temperature T_K can be obtained for a given heavy-electron material, reviewing the experimental literature for over 25 materials.  What emerged was the discovery of an unexpectedly simple relationship  between T* and the single-ion temperature T_K for the same background material.   Just as was the case for T_K, T* was found to depend only on the characteristic energy J that measures the local Kondo coupling between single spins and mobile electrons, with T* being determined by an induced interaction between nearest-neighbor f-electron spins that is simply related to the square of J.

 This work enabled them to update the famous Doniach diagram that had  explained the behavior of heavy-electron materials on an either/or basis— either local spin behavior dominates, leading to antiferromagnetism, or mobile electron behavior dominates, with the possibility of the material’s becoming superconducting.  Their new approach suggested that this competition is instead one between two quantum ordered states of the heavy, but mobile, Kondo liquid, and showed that, in all materials thus far investigated, T* is large compared to T_K.   Their results were published in the July 31, 2008 issue of Nature [Y. Yang, Z. Fisk, H. Lee, J. D. Thompson, and D. Pines, “Scaling the Kondo Lattice,” Nature 454, 611-613 (2008)] and in the online supplementary materials that accompanied it. 

For his part, Yang found working with experimentalists quite a change from his previous theoretical work.  It required a phenomenological approach, an attempt to deduce from experiment a detailed physical picture of what is going on, rather than a search for a soluble mathematical model.  Ultimately, however, this new perspective— and examining more than 30 years’ worth of experimental data—led him and his collaborators to the solution for TM*.  The novel character of the ICAM collaboration was recognized by Nature, which published an article on it in the “Making the Paper” segment of its July 31 issue.  This kind of combined attack—a marriage of theory and experiment—is, according to David Pines, the key to solving problems on the frontier of emergent behavior and is an example of what ICAM exists to encourage.

By Karie Friedman, ICAMNews October 2008