Thermodynamic properties of tetrameric bond-alternating spin chains

Thermodynamic properties of a tetrameric bond-alternating Heisenberg spin chain with ferromagnetic-ferromagnetic-antiferromagnetic-antiferromagnetic exchange interactions are studied using the transfer-matrix renormalization group and compared to experimental measurements. The temperature dependence of the uniform susceptibility exhibits typical ferrimagnetic features. Both the uniform and staggered magnetic susceptibilities diverge in the limit $T\to 0$, indicating that the ground state has both ferromagnetic and antiferromagnetic long-range orders. A double-peak structure appears in the temperature dependence of the specific heat. Our numerical calculation gives a good account for the temperature and field dependence of the susceptibility, the magnetization, and the specific heat for $\mathrm{Cu}{\left(3\text{−}\mathrm{Clpy}\right)}_2{\left({\mathrm{N}}_3\right)}_2$ $(3\text{−}\mathrm{Clpy}=3\text{−}\text{Chloroyridine})$.

Figure 1

Schematic representation of the chain structure of $\mathrm{Cu}{\left(3\text{−}\mathrm{Clpy}\right)}_2{\left({\mathrm{N}}_3\right)}_2$ (CCPA) with interactions described by Hamiltonian (1). The system can be decomposed into two sublattices according to the nature of coupling, i.e., A and B sublattices, respectively.

Figure 2

TMRG results (except for the case $J_F=0$) of the uniform zero-field susceptibility multiplied by temperature for the tetrameric bond-alternating spin model.

Figure 3

The zero-field staggered susceptibilities multiplied by temperature. ${\chi }_s^{\left(1\right)}$ and ${\chi }_s^{\left(2\right)}$ are defined by Eqs. (14, 17), respectively.

Figure 4

TMRG results of the zero-field specific heat at $\mid J_F\mid ∕J_{\mathit{AF}}=0,0.05,0.15,0.5,2.0$ in ascending order along the direction of arrows. The case $\mid J_F\mid ∕J_{\mathit{AF}}=2.0$ is plotted as a dashed line for visual effect. The inset shows the low-temperature part of the specific heat.

Figure 5

The zero-field specific heat coefficient $C∕T$ versus $T$ for $\mid J_F\mid ∕J_{\mathit{AF}}=0,0.05,0.15,0.5,2.0$.

Figure 6

Temperature dependence of the specific heat for $J_F∕J_{\mathit{AF}}=-0.15$ at different external magnetic fields.

Figure 7

Comparison between our numerical results for the magnetic susceptibility multiplied by temperature and the experimental data published in Ref. 7.

Figure 8

Comparison of the measured experimental data of the field dependence of low-temperature longitudinal magnetization[8] to the TMRG results. The parameters used are $J_{\mathit{AF}}∕k_B=29.6\mathrm{K}$, $J_F∕J_{\mathit{AF}}=-0.6$, $g=2.24$. $m_s$ is the saturation magnetization.

Figure 9

TMRG results for the temperature dependence of the specific heat at $H=0,0.5,1.0,1.5$, $2.0\mathrm{T}$ in ascending order along the direction of arrows. The parameters used are the same as for Fig. 8. The inset shows the low-temperature part of $C$.

Figure 10

Comparison of the specific heat of CCPA to the TMRG results. In (a) the triangle (solid), circle (dashed) lines represent the experimental (numerical) data for $H=0$, $0.5\mathrm{T}$, respectively; In (b), (c), (d), the circle and solid lines represent experimental and numerical results, respectively. The parameters used are the same as for Fig. 8.

Figure 11

Comparison of the specific heat of CCPA to TMRG results after subtracting the corresponding zero-field data. Circles and solid lines represent experimental and numerical results, respectively. The parameters are the same as for Fig. 8.

Figure 12

Comparison of the specific heat of CCPA to TMRG results after subtracting the corresponding data at $H=0.5\mathrm{T}$. Circles and solid lines represent experimental and numerical results, respectively. The parameters are the same as for Fig. 8.