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

Abstract

Low-energy degrees of freedom of a spin-1/2 kagomé antiferromagnet in the vicinity of the saturation field are mapped to a hard-hexagon model on a triangular lattice. The latter model is exactly solvable. The presented mapping allows to obtain quantitative description of the magnetothermodynamics of a quantum kagomé antiferromagnet up to exponentially small corrections as well as predict the critical behavior for the transition into a magnon crystal state. Analogous mapping is presented for the sawtooth chain, which is mapped onto a model of classical hard dimers on a chain.PACS numbers: 75.50. Ee, 75.45.+j, 75.10.Jm, 75.30.Sg 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. 10,11,12,13 Above H c in the fully polarized phase, these models have a flat branch of magnons with energy (H − H c ). Such dispersionless excitations correspond in real space to localized spin flips, which do not interact with each other unless touched. Upon decreasing magnetic field through H c , the energy of a single excitation becomes negative and magnons condense into a closepacked crystal structure. The present work is devoted to theoretical investigation of the low-temperature thermodynamics of magnon crystals. Specifically, we consider spin-1/2 Heisenberg models on a kagomé lattice and a sawtooth (or ∆) chain, see Fig. 1. While the former lattice is one of the best known examples of geometric frustration, which is realized, e.g., in SrCr 9p Ga 12−9p O 19 , 18 the latter spin model is applicable to magnetic delafossite YCuO 2.5 . 19 We show that the thermodynamic potential in the vicinity of H c for the two quantum models can be calculated exactly up to corrections, which are exponentially small at low temperatures.We consider nearest-neighbor spin-1/2 Heisenberg models in an external fieldFor a kagomé lattice all nearest-neighbor bonds have the same strength J ij ≡ 1. The spectrum of single-magnon excitations in the fully polarized phase iswhere γ k = 1 6 δ e ik·δ is a sum over nearest-neighbor sites on a triangular Bravais lattice. At the saturation field H c = 3 the energy of excitations from the lowest dispersionless branch vanishes. The sawtooth chain exhibits a similar behavior for the special ratio of the two coupling constants J 2 = 1 2 J 1 . In the following we always assume the above choice of the parameters with J 1 ≡ 1. Above H c = 2 the sawtooth chain antiferromag...

Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet

“…A similar jump is known to occur in several cases. 11,[47][48][49] Regarding the existence or the absence of the degeneracy, this behavior is different from the magnetization jump observed in square-kagome-lattice and Cairo-pentagon-lattice antiferromagnets, and so on. [50][51][52][53] Although this behavior occurs irrespective of the value of S, the skip of m at the jump gradually decreases as S is increased.…”

Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field

“…[11]) and perform exact-diagonalization calculations [12] to obtain thermodynamic quantities. Then we compare these findings with the results of the exact-diagonalization study of the corresponding effective model (2) of N = 12 sites. For concreteness, we fix the set of parameters as follows: J 2 = 5 and J 1 = 1.1, J X = 0.9.…”

“…We begin with testing the accuracy of the effectivemodel description (2). To this end, we consider the full initial model (1) on a finite bilayer lattice of N = 24 sites (see Fig.…”

“…On the other hand, there are a few theoretical papers considering the ground-state and low-temperature properties of a Heisenberg antiferromagnet on a frustrated bilayer honeycomb lattice [9][10][11], in which classical spin [9] or quantum spin-1 2 [10,11] models in nonzero [9,11] or zero [10] magnetic field were discussed using various complementary approaches. In particular, in our recent work [11] it has been shown that the localized-magnon picture [1][2][3], which emerges for the ideal frustration case, yields a simple effective description of the low-temperature thermodynamics in a moderate and strong magnetic field. Since in this regime only the two states on each vertical bond J 2 , |u = | ↑↑ and |d = 1 √ 2 (| ↑↓ − | ↓↑ ) (localized magnon), dominate thermodynamic properties, it is not astonishing that the effective model is an antiferromagnetic honeycomb-lattice Ising model in a uniform magnetic field with the Hamiltonian operators are defined as follows: T z = 1 2 (|u u| − |d d|), T + = |u d|, and T − = |d u|.…”

“…We are interested in the regime when J 2 is the strongest bond and a deviation of J X from J 1 is small, or, more precisely, J 2 > 3J with J = (J 1 + J X )/2 and |J 1 − J X |/J 2 ≪ 1. If J 1 = J X one faces the so-called ideal frustration case characterized by a flat-one magnon band [1][2][3], otherwise the system is slightly away from the ideal frustration region in the parameter space.…”