Thermodynamic properties of a tetramer Ising-Heisenberg bond-alternating chain as a model system for $\mathrm{Cu}{\left(3\text{−}\text{Chloropyridine}\right)}_2{\left({\mathrm{N}}_3\right)}_2$

Thermodynamic properties of a tetramer ferro-ferro-antiferro-antiferromagnetic Ising-Heisenberg bond-alternating chain are investigated by the use of an exact mapping transformation technique. Exact results for the magnetization, susceptibility, and specific heat in zero as well as nonzero magnetic fields are presented and discussed in detail. The results obtained from the mapping are compared with the relevant experimental data of $\mathrm{Cu}{\left(3\text{−}\mathrm{Clpy}\right)}_2{\left({\mathrm{N}}_3\right)}_2$, where 3-Clpy indicates 3-Chloropyridine.

Figure 1

A fragment of the CCPA structure. (a) shows full details with the azido $\left({\mathrm{N}}_3\right)$ bridges as well as the bulky 3-Clpy ligands; (b) schematically reproduces the considered magnetic structure only. There are three nonequivalent positions of the ${\mathrm{Cu}}^{2+}$ ions: the Cu1 sites coupled purely by the F interaction (black circles), the Cu2 sites coupled via both F and AF interactions (gray circles), and last the Cu3 sites coupled purely by the AF interaction (light gray circles). The rectangles designate the AF trimers.

Figure 2

The comparison between the on-site magnetization of the Ising-Heisenberg BAC and the corresponding pure Heisenberg BAC obtained by the exact diagonalization method as described in Ref. 26. For details see the text.

Figure 3

The ground-state phase diagram in the $J_F\text{−}B$ plane obtained for several exchange anisotropies $\Delta$ under the assumption of uniform $g$ factors, i.e., $g_1=g_2=g_3=g$.

Figure 4

The total magnetization scaled in $g{\mu }_B$ units as a function of the dimensionless magnetic field $g{\mu }_{B}B∕J_{\mathit{AF}}$ for $J_F∕J_{\mathit{AF}}=0.5$, $\Delta =1.0$, and several dimensionless temperatures $k_{B}T∕J_{\mathit{AF}}$.

Figure 5

Some typical temperature variations of the total magnetization obtained for $J_F∕J_{\mathit{AF}}=0.5$, $\Delta =1.0$, and several magnetic fields.

Figure 6

The thermal dependence of the zero-field susceptibility times temperature data scaled in $N_{\mathrm{A}}{\left(g{\mu }_B\right)}^2∕k_B$ units ($N_{\mathrm{A}}$ is Avogadro’s number) for $\Delta =1.0$ and some typical values of $J_F∕J_{\mathit{AF}}$.

Figure 7

The temperature dependence of the $\chi T$ product as a function of the field strength when $J_F∕J_{\mathit{AF}}=0.5$ and $\Delta =1.0$.

Figure 8

The zero-field specific heat as a function of the temperature for some typical values of $J_F∕J_{\mathit{AF}}$ and $\Delta =1.0$. The specific heat is scaled in multipliers of the universal gas constant $R=8.314\mathrm{J}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$.

Figure 9

The thermal dependence of the specific heat by various magnitudes of the external magnetic field when $J_F∕J_{\mathit{AF}}=0.5$ and $\Delta =1.0$.

Figure 10

The field variation of the ground-state magnetization normalized with respect to its saturation value by assuming the nonuniformity of the $g$ factors. (a) [(b)] shows the situation when $g_2>g_1=g_3$ $[g_3>g_1=g_2]$.

Figure 11

The temperature dependence of the susceptibility when varying the external field strength, and $J_F∕J_{\mathit{AF}}=0.5$, $\Delta =1.0$, $g_1=g_2=2.0$, and $g_3=2.25$. The inset displays the low-temperature susceptibility on an enlarged scale.

Figure 12

The low-temperature magnetization curves measured in pulsed (a) and static (b) magnetic fields together with the corresponding theoretical prediction obtained for this fitting set of parameters: $J_{\mathit{AF}}∕k_B=28.2\mathrm{K}$, $J_F∕J_{\mathit{AF}}=0.4$, $\Delta =1.0$, $g_1=2.10$, $g_2=2.14$, and $g_3=2.19$. The hysteresis observed in the experimental curves near zero and saturation fields is probably caused by the magnetocaloric effect.

Figure 13

The zero-field susceptibility times temperature data and the corresponding theoretical prediction (the fitting parameters are indicated in the figure).

Figure 14

The thermal dependence of the specific heat measured at $B=0.0$, 0.5, and 1.0 T. The corresponding theoretical predictions are also included.