Tickling the underpinnings of a weak antiferromagnet


Unusual electronic phases of crystalline condensed matter, whose microscopic origins are often a challenge to identify, has expanded as an area of high activity of research into quantum matter. Weak ferromagnetism presented one enigma: the two well understood mechanisms of magnetic order, (i) a strong intraatomic repulsion (“Hubbard U”) and (ii) the quantum exchange mechanism leading to the Stoner instability, both lead to magnetic moments of usual size, with just a handful of “weak ferromagnets” having been discovered. Weak antiferromagnets (wAFMs) are extremely rare.

Presently, TiAu is the most heavily studied (and perhaps only) wAFM. New theoretical conundrums have arisen. The Stoner instability promoted by the huge density of electronic carriers should result in ferromagnetism; Fermi surface nesting that induces spin density waves (incommensurate wAFMs) does not apply in TiAu. A proposed new mechanism — mirroring of pairs of zero electron velocity regions in momentum space — accounts very nicely as the mechanism underlying the wAFM state.

Recent studies replacing Ti with Sc (which has one less electron) led to identification of a critical concentration – where magnetic order vanishes — of 1/8 Sc on the Ti sublattice. The changes introduced by this alloying should be (a) reducing the Fermi level thereby moving it away from the van Hove singularities (zero velocity) peak, (b) strongly reducing the exchange interaction on Ti and thus its tendency to become magnetic, and (c) altering the interatomic RKKY coupling through the electronic system. To quantify the alloy behavior, its resistivity, susceptibility, and other physical properties have been characterized near and above the quantum critical point. The observed disorder effects however remained a challenge to understand, and researchers have been poking around for alternative methods to understand hole-doped TiAu.

To this note, University of California Davis researchers Milena Mathew (a high school senior) and Dr. Wen Fong Goh, led by Professor Warren Pickett from the Department of Physics, invoked numerical simulations of a variety of Sc (hole) concentrations, up to and beyond the critical concentration beyond which AFM order vanished. Specifically, the simulations involved substituting the Ti with Sc in real-space supercells, and can be found in Journal of Physics: Condensed Matter.

The expected behavior would follow numerous seemingly similar alloys with itinerant magnetism. TiAu is a binary intermetallic compound with a simple (but unusual) crystal structure. Sc is another metal atom adjacent to Ti in the periodic table. The magnetism of TiAu has all the signs of itinerant character. The virtual crystal (itinerant electron) picture should give a realistic approximation: Ti and Sc are replaced by a concentration dependent average atom – call it Ts – and then one does the simulation for TsAu. The change in the electronic and magnetic behaviors evolve smoothly with the concentration of Sc.

The real-space simulations, with separate Ti or Sc atoms on the Ti sublattice, give strikingly different results, which are local-moment like rather than itinerant-moment like. Roughly speaking, the results were that the Ti atom retained it magnetic moment well beyond the quantum critical point concentration of 1/8, and Sc never developed a moment. This behavior indicates that the basic model underpinning the alloy’s magnetism should be local rather than itinerant, in spite of the seeming itinerant behavior before doping. The simulations, though crucial, are only a beginning. Alloy disorder has not been included, magnetic correlations and fluctuations will be important, and finally thermal processes will need to be treated.

In summary, Professor Warren Pickett and his research team successfully applied first principles calculations to investigate the magnetic and electronic behavior of the hole-doped weak antiferromagnetic TiAu. The prevailing itinerant picture of TiAu magnetism was concluded to be inappropriate for the alloy system. An interesting question is whether, and how, this unexpected switch from itinerant to local behavior is related to the underlying weak antiferromanget state, for which TiAu is the poster child.


Mathew, M., Goh, W. F., & Pickett, W. E. (2019). Probing hole-doping of the weak antiferromagnet TiAu with first principles methods. Journal of Physics: Condensed Matter, 31(7), 074005.

Go To Journal of Physics: Condensed Matter

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