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The ground state, the entropy and the magnetic Gr\"uneisen parameter of theantiferromagnetic spin-1/2 Ising-Heisenberg model on a double sawtooth ladderare rigorously investigated using the classical transfer-matrix technique. Themodel includes the XXZ interaction between the interstitial Heisenberg dimers,the Ising coupling between nearest-neighbor spins of the legs and rungs, andadditional cyclic four-spin Ising term in each square plaquette. For aparticular value of the cyclic four-spin exchange we found in the ground-statephase diagram of the Ising Heisenberg ladder a quadruple point, at which fourdifferent ground states coexist together. During an adiabatic demagnetizationprocess a fast cooling accompanied with an enhanced magnetocaloric effect canbe detected nearby this quadruple point. The ground-state phase diagram of theIsing-Heisenberg ladder is confronted with the zero-temperature magnetizationprocess of the purely quantum Heisenberg ladder, which is calculated by usingexact diagonalization (ED) based on the Lanczos algorithm for a finite-sizeladder of 24 spins and the density-matrix renormalization group (DMRG)simulations for a finite-size ladder with up to 96 spins. Some indications ofexistence of intermediate magnetization plateaus in the magnetization processof the full Heisenberg model for a small but non-zero four-spin Ising couplingwere found. The DMRG results reveal that the quantum Heisenberg double sawtoothladder exhibits a quantum Luttinger spin-liquid phase that is absent in theIsing-Heisenberg counterpart model. Except this difference the magneticbehavior of the full Heisenberg model is quite analogous to its simplifiedIsing-Heisenberg counterpart and hence, one may bring insight into the fullyquantum Heisenberg model from rigorous results for the Ising-Heisenberg model.

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