Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices

Abstract

For a class of frustrated spin lattices including e.g. the 1D sawtooth chain, the 2D kagomé and checkerboard, as well as the 3D pyrochlore lattices we construct exact product eigenstates consisting of several independent, localized one-magnon states in a ferromagnetic background. Important geometrical elements of the relevant lattices are triangles being attached to polygons or lines. Then the magnons can be trapped on these polygons/lines. If the concentration of localized magnons is small they can be distributed randomly over the lattice. Increasing the number of localized magnons their distribution over the lattice becomes more and more regular and finally the magnons condensate in a crystal-like state.The physical relevance of these eigenstates emerges in high magnetic fields where they become groundstates of the system. As a result a macroscopic magnetization jump appears in the zero-temperature magnetization curve just below the saturation field. The height of the jump decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.

Exact low-temperature behavior of a kagomé antiferromagnet at high fields

“…10,11,12,13 Below we give a shortened proof for the spin-1/2 kagomé antiferromagnet, which is also valid for the checkerboard and the pyrochlore lattice antiferromagnets. The Heisenberg Hamiltonian (1) is split in a standard way into the Ising partĤ zz , which includes all S z i S z j terms plus the Zeeman energy, and the transverse partĤ ⊥ .…”

“…In the past few years there have been increased attention to the behavior of frustrated magnetic materials at high fields. The interest is stimulated by a search for new fundamental effects such as the magnetization plateaus, 1,2,3,4,5,6,7,8,9 the magnetization jumps, 10,11,12,13 new complicated magnetic phase diagrams, 8,14 and new types of the critical behavior 15 as well as by a possible technological application of frustrated magnets in the adiabatic demagnetization refrigerators due to their unique magnetocaloric properties. 16,17 A zerotemperature behavior of geometrically frustrated antiferromagnets in the vicinity of the saturation field H c has been recently discussed by Schulenburg and coworkers.…”

Antiferromagnetic sawtooth chain with Heisenberg and Ising bonds

“…Then, one can obtain analytic expressions for all thermodynamic quantities of the systems by taking derivatives of equation (9). Thus, equations (3)- (9) exactly solve the problem of thermodynamics of the systems under consideration.…”

“…Anisotropic variants of sawtooth chain have also been investigated revealing additional features [7,8]. Another important feature of the sawtooth chain as well as of some other frustrated spin and Hubbard lattices revealed quite recently is the appearance of localized magnon states (dispersionless excitation bands) [9][10][11][12]. The localized low energy excitations in sawtooth chain which exist due to frustrated geometry, more precisely, due to the triangular plaquette, affect the lowtemperature thermodynamics.…”

Multiple magnetization plateaus and magnetic structures in theS=12Heisenberg model on the checkerboard lattice

“…In contrast, S = 1/2 quantum spins on the checkerboard lattice have stable quantum ground state as in the kagome lattice [16][17][18] and Shastry-Sutherland lattice [12][13][14][15]. Indeed previous studies on the checkerboard lattice indicate that the ground state is a plaquette valence-bond crystal (PVBC) with a large spin singlettriplet gap, ∆ st ≈ 0.6J [19,20] and the 3/4 plateau is realized just before the saturation magnetic field [21] as in the case of the 7/9 plateau in the kagome lattice [22].Although the ideal checkerboard lattice with only one exchange energy J has not been synthesized, similar model substances are present [23,24]. The checkerboard lattice is obtained by replacing the position of anions and cations in the CuO 2 -plane structure.…”