Magnetization plateaus and enhanced magnetocaloric effect of a spin-1/2 Ising-Heisenberg and Heisenberg double sawtooth ladder with four-spin interaction

TL;DR

The paper addresses magnetization plateaus and the magnetocaloric effect in a spin-1/2 Ising-Heisenberg double sawtooth ladder augmented by a cyclic four-spin Ising interaction. It combines an exact solution for the Ising-Heisenberg ladder via a generalized classical transfer-matrix (with $Z = \text{Tr} \, T^N$ and a $4\times4$ matrix $T$) with numerical Lanczos ED and DMRG studies of the full quantum Heisenberg ladder to map zero-temperature magnetization processes. A key finding is a quadruple point where four ground states coexist (with $\Delta_Q/J_{\parallel}=2.0$, $K_Q/J_{\parallel}\approx0.2929$, $B_Q/J_{\parallel}\approx4.4142$ for the symmetric case) and that enhanced MCE occurs near triple and quadruple points, evidenced by isentropes and the magnetic Grüneisen parameter. The full quantum model exhibits a quantum Luttinger spin-liquid phase absent in the Ising-Heisenberg limit, and the results illuminate how multi-spin couplings shape magnetization plateaus and thermodynamics, offering insight into the fully quantum system from the exactly solvable Ising-Heisenberg case.

Abstract

The ground state, the entropy and the magnetic Grüneisen parameter of the antiferromagnetic spin-1/2 Ising-Heisenberg model on a double sawtooth ladder are rigorously investigated using the classical transfer-matrix technique. The model includes the XXZ interaction between the interstitial Heisenberg dimers, the Ising coupling between nearest-neighbor spins of the legs and rungs, and additional cyclic four-spin Ising term in each square plaquette. For a particular value of the cyclic four-spin exchange we found in the ground-state phase diagram of the Ising Heisenberg ladder a quadruple point, at which four different ground states coexist together. During an adiabatic demagnetization process a fast cooling accompanied with an enhanced magnetocaloric effect can be detected nearby this quadruple point. The ground-state phase diagram of the Ising-Heisenberg ladder is confronted with the zero-temperature magnetization process of the purely quantum Heisenberg ladder, which is calculated by using exact diagonalization (ED) based on the Lanczos algorithm for a finite-size ladder of 24 spins and the density-matrix renormalization group (DMRG) simulations for a finite-size ladder with up to 96 spins. Some indications of existence of intermediate magnetization plateaus in the magnetization process of the full Heisenberg model for a small but non-zero four-spin Ising coupling were found. The DMRG results reveal that the quantum Heisenberg double sawtooth ladder exhibits a quantum Luttinger spin-liquid phase that is absent in the Ising-Heisenberg counterpart model. Except this difference the magnetic behavior of the full Heisenberg model is quite analogous to its simplified Ising-Heisenberg counterpart and hence, one may bring insight into the fully quantum Heisenberg model from rigorous results for the Ising-Heisenberg model.

Figures (11)

• Figure 1: A schematic illustration of the magnetic structure of the frustrated spin-1/2 double sawtooth ladder. The balls denote spin-1/2 particles. Green balls represent Heisenberg spins that are connected with each other with red solid lines. The dark-blue balls show Ising spins. The blue dashed circle in each square plaquette denotes four-spin Ising coupling.
• Figure 2: The spin configurations of the spin-1/2 double sawtooth ladder associated to the possible ground states (\ref{['Eigns']}). Each panel indicates spin arrangement of two successive unit blocks that are repeated throughout the ladder. Tick arrows represent the spin orientations, whereas oval shapes stand for the Heisenberg dimers in quasi-singlet state $|\varphi_2 \rangle$. Notations in the kets denote the orientation of the two spins on each rung such that "up" means both spins of the same rung are up, while "n" indicates that one spin of the rung is up and another one is down, and "s" means that the state of the two spins on the identical rung is quasi-singlet state $|\varphi_2 \rangle$.
• Figure 3: Ground-state phase diagram of the pure Ising double sawtooth ladder in the $\Delta/J_{\parallel}-B/J_{\parallel}$ plane for $\eta/J_{\parallel}=0$ and $J/J_{\parallel}=1$.
• Figure 4: (a) Topological representation of the critical four-spin exchange interaction $K_\text{Q}/J_{\parallel}=\frac{1}{2}[\eta/J_{\parallel}+J/J_{\parallel}-\sqrt{(\eta/J_{\parallel})^2+(J/J_{\parallel})^2}]$ at which four ground states $\vert\text{nsus}\rangle$, $\vert\text{usus}\rangle$, $\vert\text{nunu}\rangle$ and $\vert\text{nuuu}\rangle$ coexist together at a quadruple point with magnetic field position $B_\text{Q}/J_{\parallel}=3+2J/J_{\parallel}-2K_\text{Q}/J_{\parallel}$. (b) The $K_\text{Q}/J_{\parallel}$ as a function of the magnetic field position of the quadruple point $B_\text{Q}/J_{\parallel}$ for $\eta/J_{\parallel}, J/J_{\parallel}\in [0,1]$. The line marked with blue hexagons shows maximum amount of $B_\text{Q}^\text{max}$ and $K_\text{Q}^\text{max}$ for $J/J_{\parallel}=1$ where $\eta/J_{\parallel}$ varies from 0 (red crosses) up to 1 (yellow circles). $K_\text{Q}$ as a function of $B_\text{Q}$ is shown for a few selected values of $\eta/J_{\parallel}$ by lines with different styles. Filled circle on the top of curve plotted in panel (a) shows the coordination of the point $K_\text{Q}^\text{max}/J_{\parallel}=\frac{1}{2}(2-\sqrt{2}|\eta/J_{\parallel}|)\approx 0.2929$, assuming $\eta/J_{\parallel}=J/J_{\parallel}=+1$. This point is geometrically the same one on the ending point of the yellow curve plotted in panel (b) with $B_\text{Q}/J_{\parallel}=4.4142$.
• Figure 5: Ground-state phase diagram of the Ising-Heisenberg double sawtooth ladder in the $\Delta/J_{\parallel}-B/J_{\parallel}$ plane for $\eta/J_{\parallel}=J/J_{\parallel}=1$ and $K=K_\text{Q}\approx 0.2929$, where the quadruple point occurs at $[\Delta_\text{Q}/J_{\parallel}=2.0, B_\text{Q}/J_{\parallel}\approx 4.4142]$. Red circle manifests the quadruple point.