We consider a spin-[Formula: see text] kagome-like chain with competing ferro- and antiferromagnetic anisotropic exchange interactions. The ground state phase diagram of this model consists of the ferromagnetic and ferrimagnetic phases. We study the ground state and the low-temperature properties on the phase boundary between these phases. The ground state on this phase boundary is macroscopically degenerate and consists of localized magnon states. We calculate the ground state degeneracy and corresponding residual entropy. The spontaneous magnetization has a jump on the phase boundary confirming the first-order type of the phase transition. In the limit of a strong anisotropy, the spectrum of the low-energy excitations has multi-scale structure governing the peculiar features of the specific heat behavior.
We consider analytically and numerically an anisotropic $\text{spin}\ensuremath{-}\frac{1}{2}$ delta chain (sawtooth chain) with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interactions. For certain values of the interactions a lowest one-particle band becomes flat and there is a class of localized-magnon eigenstates which form a ground state with a macroscopic degeneracy. In this case the model depends on a single parameter which can be chosen as the anisotropy of the exchange interactions. When this parameter changes from zero to infinity the model interpolates between the one-dimensional isotropic ferromagnet and the frustrated Ising model on the delta chain. It is shown that the low-temperature thermodynamic properties in these limiting cases are governed by the specific structure of the excitation spectrum. In particular, the specific heat has one or infinite number of low-temperature maxima for the small or the large anisotropy parameter, correspondingly. Qualitative features of such behavior survive when the interaction parameters deviate from the relations providing the local magnon ground state.
Frustrated spin-12model consisting of a linear chain of triangles with ferro (F)- and antiferromagnetic interactions connected by ferromagnetic interactions (triangles chain) is studied. The ground state phase diagram depending on the interaction ratios consists of ferromagnetic, two ferrimagnetic and singlet phases. The magnetic properties in these phases are analyzed both analytically and numerically. We show that in some regions of the singlet phase the magnetization curves have magnetization plateau and magnetization jumps. We study the thermodynamics and its relation to the specific structure of the excitation spectrum of the triangle chain.
We investigate the spin-1/2 Heisenberg model on the delta chain (sawtooth chain) with ferromagnetic nearest-neighbor and antiferromagnetic next-neighbor interactions. For a special ratio between these interactions there is a class of exact ground states formed by localized magnons and the ground state is macroscopically degenerate. The degree of this degeneration is found analytically. It is shown that the residual entropy per spin is
s0=21ln2. An important feature of this model is a sharp decrease of the gaps for excited states with an increase of the number of magnons. These excitations give an essential contribution to the low-temperature thermodynamics. The corresponding thermodynamic quantities are calculated using full exact diagonalization of finite chains up to
N=22. The behavior of the considered model is compared with that of the delta chain with both antiferromagnetic interactions.
Background. Low-dimensional quantum magnets based on geometrically frustrated lattices are of considerable interest last time. As a typical example of such systems is the delta-chain which is a linear chain of triangles with spins on vertices. The delta-chain with AF exchange interactions is well studied and has a number of unusual properties. However, the same model with competing ferro (F)-and antiferromagnetic (AF) interactions is less studied. The purpose of this work is the study of the anisotropic F-AF delta-chain on the critical line separating different ground state phases, the calculation of the ground state degeneracy, residual entropy etc. Materials and methods. The study of this model is both analytically and numerically. It is proposed a method of construction of exact ground state wave functions and accounting of the number of ground ststes states in each spin sector. The analytical results are confirmed by numerical calculations of finite chains. Results. It is shown that the ground state manifold of the F-AF delta-chain on the critical line consists of localized magnons. Together with isolated magnons there are bound magnon complexes which give dominated contribution in ground state manifold in the thermodynamic limit. Conclusions. Spin systems with macroscopically degenerated ground state and with residual entropy demonstrate significant magnetocaloric effect. Taking into account great progress in a synthesis of frustrated magnets, it can be expected that real compounds of the FAF delta-chain type with parameters close to critical ones will be obtained and these compounds will be used for the construction of effective magnetocooling devices.
The anisotropic
XXZ spin-
21 Heisenberg chain is studied using renormalization-group theory. The specific heats and nearest-neighbor spin-spin correlations are calculated throughout the entire temperature and anisotropy ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global description and quantitative results. We obtain, for all anisotropies, the antiferromagnetic spin-liquid spin-wave velocity and the Ising-like ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon crossover. A number of characteristics of purely quantum nature are found: The in-plane interaction
sixsjx+siysjy induces an antiferromagnetic correlation in the out-of-plane
siz component, at higher temperatures in the antiferromagnetic
XXZ chain, dominantly at low temperatures in the ferromagnetic
XXZ chain, and, in-between, at all temperatures in the
XY chain. We find that the converse effect also occurs in the antiferromagnetic
XXZ chain: an antiferromagnetic
sizsjz interaction induces a correlation in the
sixy component. As another purely quantum effect, (i) in the antiferromagnet, the value of the specific heat peak is insensitive to anisotropy and the temperature of the specific heat peak decreases from the isotropic (Heisenberg) with introduction of either type (Ising or
XY) of anisotropy; and (ii) in complete contrast, in the ferromagnet, the value and temperature of the specific heat peak increase with either type of anisotropy.