Universal low-temperature behavior of frustrated quantum antiferromagnets in the vicinity of the saturation field

Abstract

We study the low-temperature thermodynamic properties of a number of frustrated quantum antiferromagnets which support localized magnon states in the vicinity of the saturation field. For this purpose we use 1) a mapping of the low-energy degrees of freedom of spin systems onto the hard-core object lattice gases and 2) an exact diagonalization of finite spin systems of up to N = 30 sites. The considered spin systems exhibit universal behavior which is determined by a specific hard-core object lattice gas representing the independent localized magnon states. We test the lattice gas description by comparing its predictions with the numerical results for low-lying energy states of finite spin systems. For all frustrated spin systems considered we find a strong variation of the low-temperature specific heat passing the saturation field and a maximum in the isothermal entropy at saturation field resulting in an enhanced magnetocaloric effect. [7,8]). These ground states consist of independent (i.e. isolated) localized magnons in a ferromagnetic environment. The localized magnon states were used to predict a ground-state magnetization jump at the saturation field [4-6], a magnetic field induced spin-Peierls instability [9,10], and a residual ground-state entropy at the saturation field [3,8,[11][12][13]. Moreover, in Refs. [8,12,13] the concept of localized magnons was used for a detailed analysis of the low-temperature magnetothermodynamics in the vicinity of the saturation field for two representative systems, the sawtooth chain (or ∆-chain) and the kagomé lattice. In particular, the authors of these papers mapped the low-energy degrees of freedom of the sawtooth chain (the kagomé lattice) to the hard-dimer gas on a one-dimensional lattice (the hard-hexagon gas on a triangular lattice) and used the results for the classical lattice gases to discuss the properties of the spin systems. They also 1

Universal properties of highly frustrated quantum magnets in strong magnetic fields

“…Note that the thermodynamic quantities of the spin system depend on the temperature T and the magnetic field h essentially only through the combination [20]. To test the hard-object description, we have performed full diagonalization of spin-1/2 isotropic Heisenberg systems (i.e., D =1 in Eq.…”

“…Explicit analytic expressions for thermodynamic quantities can be obtained easily [20]. Note that the thermodynamic quantities per site are independent of the system size N .…”

“…Next, in Sec. 4, we discuss the universal thermodynamic behavior which the considered frustrated quantum antiferromagnets exhibit at low temperatures in the vicinity of the saturation field [20,22]. We distinguish different types of the universal behavior depending on the specific classical lattice-gas model which represents the low-energy degrees of freedom of the spin system.…”

Low-Temperature Properties of the Quantum Heisenberg Antiferromagnet on Some One-Dimensional Lattices Containing Equilateral Triangles

“…We find g N (n) = 2 n C n N (double tetrahedra chain) or g N (n) = 2 n Z(n, N ), where Z(n, N ) stands for the canonical partition function of n hard dimers on a simple chain of N sites (frustrated three-leg ladder). Let us note that the factor 2 n appears in g N (n) due to the chirality of the triangles (compare with the results for the diamond chain and frustrated two-leg ladder [5]). …”

Magnetic Grüneisen parameter and magnetocaloric properties of a coupled spin–electron double-tetrahedral chain

“…Of particular interest is the investigation of the MCE in various one-dimensional (1D) quantum spin systems [4][5][6][7][8][9][10][11][12][13] or hybrid spin-electron models [14][15][16]. The reason is a possibility of obtaining the exact analytical or numerical results as well as a potential use of these models for the explanation of MCE data measured for real magnetic compounds.…”