Crystal spacing predicts magnetic states in complex alloys better than electron count

In materials chemistry, identifying common parameters that can organize magnetic ground states across complex intermetallic compounds remains a central challenge. Researchers have long used chemically tunable parameters to control magnetic properties. One is valence-electron concentration, commonly discussed as the electron-per-atom (e/a) ratio. The e/a ratio has been widely used to classify magnetic ground states in metallic systems such as Heusler alloys and approximant crystals.

In gold (Au)-based Tsai-type approximant crystals, the e/a ratio has been found to control magnetic ground states, including long-range antiferromagnetic (AFM) and ferromagnetic (FM) orders, as well as the spin-glass state. Tsai-type compounds are generally described as structures built from clusters with multiple shells, in which the moment-bearing rare-earth element occupies an icosahedral site. The predictive power of e/a, however, is limited across different alloy families and constituent elements. Given the potential of quasicrystal-based intermetallics as platforms for exploring emerging magnetic phenomena, researchers need reliable, experimentally accessible parameters to identify and guide the development of their magnetic properties.

To address this gap, a research team led by Assistant Professor Farid Labib of the Research Institute for Science and Technology at Tokyo University of Science (TUS), Japan, and Associate Professor Kazuhiro Nawa of the Institute of Multidisciplinary Research for Advanced Materials at Tohoku University, Japan, along with Professor Ryuji Tamura of TUS, investigated whether the lattice parameter could serve as a unified structural parameter for magnetic ground state selection in Tsai-type icosahedral compounds.

"Quasicrystals are among the most unusual materials discovered to date and are expected to exhibit novel magnetic states and quantum phenomena not found in ordinary crystals," Labib said. "Until now, there has been no unified guideline for systematically exploring these novel phenomena in quasicrystals and their approximant crystals." Their study will be published in the Journal of the American Chemical Society on Sept. 30, 2026.

Lattice size tracks electron concentration

After synthesizing a family of Au–(Al/Ga)-based 1/1 approximant crystals containing the rare-earth elements terbium (Tb), dysprosium (Dy) and holmium (Ho), the researchers systematically investigated their structural and magnetic properties. They found a nearly monotonic inverse correlation between e/a and the lattice parameter.

Further experiments in non-Heisenberg Tsai-type compounds containing Tb, Dy and Ho revealed characteristic whirling AFM and FM orders associated with strong uniaxial magnetic anisotropy. The crystal electric field generates strong magnetic anisotropy that favors specific orientations of the magnetic moments.

Magnetic phases follow structural thresholds

Based on these results, the researchers found that magnetic ground states could be organized with high accuracy according to the lattice parameter, whereas the conventional e/a classification showed systematic shifts depending on the rare-earth element and alloy composition. The compounds exhibited a whirling AFM state at lattice parameters above approximately 14.72 Å, a whirling FM state between 14.62 and 14.72 Å, and a spin-glass state below approximately 14.62 Å. The well-defined thresholds separating the magnetic states establish the lattice parameter as a unified, experimentally accessible structural descriptor for predicting magnetic ground states and guiding the development of new materials.

"The unified magnetic phase diagram constructed in this study can serve as a practical roadmap for systematic exploration of new magnetic quasicrystals and approximant crystals exhibiting novel magnetic orders and quantum phenomena," Nawa said. "It can also provide a guideline for designing new magnetic materials with targeted magnetic ground states, opening new opportunities for discovering unconventional magnetism in quasiperiodic and complex intermetallic systems."

Overall, the study establishes the lattice parameter as a unified structural descriptor for magnetic ground state selection in Tsai-type compounds, providing a practical framework for exploring and designing materials with novel magnetic properties. The findings indicate that structural length scales, alongside electron concentration, should be explicitly considered when studying conduction-electron-mediated magnetic interactions in complex alloys.