2005/09/30 by John Hopkinson, John M. Hopkinson, Hae‐Young Kee +1 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Condensed matter physics #Degenerate energy levels #Equilateral triangle #Frustration #Geometrical frustration #Geometry #Ground state #Heisenberg model #Hexagonal lattice #Lattice (music) #Magnetic and transport properties of perovskites and related materials #Mathematics #Mean field theory #Physics #Physics of Superconductivity and Magnetism #Pyrochlore #Quantum mechanics #Spins #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.74.224441
published as Phys. Rev. B 74, 224441 (2006) · 14 pages, 9 figures. Accepted for publication in Phys. Rev. B. Minor changes
arxiv created 2006/11/13 · openalex publication_date 2006/12/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the classical Heisenberg model on a recently identified three dimensional corner-shared equilateral triangular lattice, a magnetic sublattice to a large class of systems with the symmetry group P213. Since the degree of geometric frustration of the nearest neighbor antiferromagnetic model on this lattice lies on the border between the pyrochlore (not ordered) and hexagonal (ordered) lattices, it is nontrivial to predict its ground state. Using a classical rotor model, we find an ordered ground state with wave vector (\frac2\ensuremathπ3a0,0,0) featuring 120\ifmmode^∘\else\textdegree\fi rotated spins on each triangle. However, a mean field approximation on this lattice fails to find an ordered ground state, finding instead a nontrivially degenerate ground state. As the mean field approach is known to agree with Monte Carlo on the pyrochlore lattice, the reasons for this discrepancy are discussed. We also discuss the possible relevance of our results to MnSi.