Quantum magnetism on the Cairo pentagonal lattice

Abstract

We present an extensive analytical and numerical study of the antiferromagnetic Heisenberg model on the Cairo pentagonal lattice, the dual of the Shastry-Sutherland lattice with a close realization in the S = 5/2 compound Bi2Fe4O9. We consider a model with two exchange couplings suggested by the symmetry of the lattice, and investigate the nature of the ground state as a function of their ratio x and the spin S. After establishing the classical phase diagram we switch on quantum mechanics in a gradual way that highlights the different role of quantum fluctuations on the two inequivalent sites of the lattice. The most important findings for S = 1/2 include: (i) a surprising interplay between a collinear and a four-sublattice orthogonal phase due to an underlying order-by-disorder mechanism at small x (related to an emergent J1-J2 effective model with J2 ≫ J1), and (ii) a non-magnetic and possibly spin-nematic phase with d-wave symmetry at intermediate x.

Frustration and Dzyaloshinsky-Moriya anisotropy in the kagome francisitesCu3Bi(SeO3)2ORousochatzakis1, Richter2, Zinke3 et al. 2015Phys. Rev. B524682View full textAdd to dashboardCite

“…The ferrimagnetic GS is a collinear state, and the magnitude of the net magnetization is a simple fraction of the saturated magnetization. This kind of ferrimagnetism is often called Lieb-Mattis ferrimagnetism [54][55][56][57][58] . Francisites exhibit a frustration-induced unconventional (non-Lieb-Mattis) ferrimagnetism, where the GS is noncollinear and the net magnetization is not a simple fraction of the saturated magnetization 43,56 .…”

Phase diagram of the13-filled extended Hubbard model on the kagome lattice

“…Among the typical two-dimensional lattices possessing a geometrical frustration, one can mention the triangular, checkerboard 8,12 , Cairo-pentagonal 13,14 , and kagome [15][16][17][18] . The latter is the most frustrated two-dimensional lattice and, as a function of the electron filling, possesses several induced local constraint phases.…”

Ab initioinvestigation of the exchange interactions in Bi2Fe4O9: The Cairo pentagonal lattice compo

“…2 The simple pentagonal lattice studied in Ref. 2 consists of two inequivalent sites with three and four nearest neighbors (see Fig.…”

“…1 in Ref. 2). It has two types of the nonequivalent bonds, which connect the threefold sites with each other (J 33 exchange constant) and the threefold sites with the fourfold ones (J 43 exchange path).…”

“…Such a Cairo pentagonal lattice has the square Bravais lattice and the unit cell containing four fourfold-and two threefold-coordinated sites. The phase diagram of the AFM Heisenberg model was obtained as a function of the ratio x ≡ J 43 /J 33 and spin S. In the classical limit (large S), three magnetic phases have been found: (1) a phase, where the spins on the neighboring sites are orthogonal to each other (x < √ 2), (2) the collinear 1/3-ferrimagnetic phase (x > 2), and (3) an intermediate mixed phase ( √ 2 < x < 2), which is a combination of (1) and (2 frustrations in the system. In the unusual nearly orthogonal magnetic structure at low temperatures, the moments on all the iron atoms lying in the (a,b) plane.…”