Delta chain with anisotropic ferromagnetic and antiferromagnetic interactions

We consider analytically and numerically an anisotropic $\text{spin}-\frac{1}{2}$ 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.

Figure 1

$▵$-chain model.

Figure 2

Ground state phase diagram of the model (14). Rhombus in the “$S_z=0$” phase denotes the point for which the dependence $C\left(T\right)$ is shown in Fig. 14.

Figure 3

Specific heat and the entropy as function of $T$ for the model (33) with $\gamma =0.001$.

Figure 4

Integrated density of states of the normalized Hamiltonian (37) with $g=0.1$ and $N=16$.

Figure 5

Dependence of the specific heat on the temperature of the normalized Hamiltonian (37) with $g=0.1$ and $N=16,20$.

Figure 6

Dependence of the specific heat on the temperature of the normalized Hamiltonian (37) with $g=0.1$ and $N=6,8$.

Figure 7

Dependence of the entropy on the temperature of the normalized Hamiltonian (37) with $g=0.1$ and $N=16,20$.

Figure 8

Dependence of the magnetic susceptibility on the temperature of the normalized Hamiltonian (37) with $g=0.1$ and $N=16,20$.

Figure 9

Integrated density of states of the normalized Hamiltonian (48) with ${\mathrm{\Delta }}_1=0.05$ and $N=16$.

Figure 10

Dependence of the specific heat on the temperature of the normalized Hamiltonian (48) with ${\mathrm{\Delta }}_1=0.05$ and $N=16,20$.

Figure 11

Dependence of the specific heat on the temperature of the normalized Hamiltonian (37) with $g=0.2$ (${\mathrm{\Delta }}_1=2.5$) and $N=16,20$.

Figure 12

Dependence of the specific heat on the temperature for ${\mathrm{\Delta }}_1=1$ and $N=16,20$.

Figure 13

Dependence of the specific heat on the temperature of the normalized Hamiltonian (48) with ${\mathrm{\Delta }}_1=0.5$ and $N=16,20$.

Figure 14

Dependence of the specific heat on the temperature for the Hamiltonian (14) with ${\mathrm{\Delta }}_1=2.5,\alpha =0.3$, and $N=16,20$.