Enhanced magnetocaloric effect in a mixed spin-(1/2, 1) Ising–Heisenberg two-leg ladder with strong–rung interaction

Abstract

The magnetic and magnetocaloric properties of the mixed spin-(1/2,1) Ising–Heisenberg model on a two-leg ladder with dimer-rung alternation are exactly examined under an adiabatic demagnetization process using the transfer-matrix formalism. We notify that the magnetization curve of the model exhibits plateaux as a function of the applied magnetic field and cyclic four-spin Ising interaction at certain rational fractions of the saturation value. We precisely investigate the ability of cooling/heating of the model nearby the critical points at which discontinuous ground-state phase transition occurs. It is evidenced that the model manifests an enhanced magnetocaloric effect in a proximity of the magnetization steps and jumps, accompanying with the plateaux and jumps of correlation function of the dimer spins. We conclude that not only the cooling/heating capability of the model could be pleasantly demonstrated by the applied magnetic field variations, but also a typical cyclic four-spin Ising interaction plays essential role to determine an efficiency of the magnetocaloric effect of the model.

Appendix I

Fig. 10

$\varGamma _B$ as a function of the ratio $B/\alpha J_{\parallel }$ at three different temperatures for the parameter sets (a) $\{g_1=1$, $g_2=1$, $g_3=2\}$, $J/\alpha J_{\parallel }=4$, $K/\alpha J_{\parallel }=0$. b $\{g_1=1$, $g_2=4$, $g_3=2\}$, $J/\alpha J_{\parallel }=2$, $K/\alpha J_{\parallel }=0$. c $\{g_1=1$, $g_2=1$, $g_3=2\}$, $J/\alpha J_{\parallel }=4$, $K/\alpha J_{\parallel }=1$. (d) $\{g_1=1$, $g_2=4$, $g_3=2\}$, $J/\alpha J_{\parallel }=2$, $K/\alpha J_{\parallel }=1$. Other parameters $\alpha$, $\gamma$, $\varDelta$ and $J_{\perp }/\alpha J_{\parallel }$ have been taken as Fig. 2

Qualitatively the field and temperature dependence of $\varGamma _B$ around a metamagnetic transition can be understood looking at the two Heisenberg spins only. Here, we would like to investigate this medium by sketching the corresponding figures that are surely of rich pedagogical values for the paper. We plot in Fig. 10 parameter $\varGamma _B$ versus ratio $B/\alpha J_{\parallel }$ at three different selected temperatures. Four panels of this figure represent $\varGamma _B$ in four different situations. By comparing this figure with Figs. 7 and 8, one finds that the low-magnetic field behavior of the parameters $\varGamma _B$ and $B\varGamma _B$ is quite different. However, both parameters behaves similar to each other in the vicinity of first-order zero-temperature phase transition points.

Fig. 11

The contour plot of the entropy and some isentropy lines in the field-temperature plane with the corresponding Grüneisen parameter as a function the magnetic field for the high amount of the cyclic four-spin Ising interaction $K/\alpha J_{\parallel }=2.5$ under the same conditions considered for the panels Fig. 7a, b, d, e. The reason for choosing value $K/\alpha J_{\parallel }=2.5$ is that as shown in Fig. 4, there is a critical point in the $(B/\alpha J_{\parallel }-K/\alpha J_{\parallel })$ plane with the co-ordinates ($B/\alpha J_{\parallel },\; K/\alpha J_{\parallel })\equiv (0, 2.5)$ at which the ground-state phase boundaries cut each other off and make a fascinating point to consider

To better understand the influence of ratio $K/\alpha J_{\parallel }$ on the thermodynamic mechanism of the model, we illustrate in Fig. 11a and b, the entropy and magnetic Grüneisen parameter in terms of the temperature and the magnetic field for the set $\{g_1=1$, $g_2=1$, $g_3=2\}$ and higher value $K/\alpha J_{\parallel }=2.5$ by assuming fixed $J/\alpha J_{\parallel }=4$ (review Fig. 4a in which critical point $(B/\alpha J_{\parallel },\;K/\alpha J_{\parallel })\equiv (0,\;2.5)$ has been marked). While, in Fig. 11c and d, are plotted the entropy and the Grüneisen parameter as functions of the temperature and the magnetic field for the set $\{g_1=1$, $g_2=4$, $g_3=2\}$ and fixed values $K/\alpha J_{\parallel }=2.5$ and $J/\alpha J_{\parallel }=2$ (according to the marked critical point $(B/\alpha J_{\parallel },\;K/\alpha J_{\parallel })\equiv (0,\;2.5)$ in Fig. 4b).

Consequently, by imaging different values of the cyclic four-spin Ising interaction parameter $K/\alpha J_{\parallel }$, despite the fact that phase transitions will occur at detected critical points $B_c/\alpha J_{\parallel }=\{0,\;3,\;5\}$ for the case $\{g_1=1$, $g_2=1$, $g_3=2\}$, and at $B_c/\alpha J_{\parallel }=\{0,\;1.5.\;2. 5,\; 3.5,\;5\}$ for the set $\{g_1=1$, $g_2=4$, $g_3=2\}$, the entropy and magnetic Grüneisen parameter qualitatively and quantitatively change different from Fig. 7.