Multiple Magnetization Plateaus and the Magnetic Structures in $S=1/2$ Heisenberg Model on the Checkerboard Lattice

Abstract

We study the ground state of $S=1/2$ Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group (DMRG) method with the sine-square deformation. We obtain magnetization plateaus at $M/M_{\mathrm{sat}}=$0, 1/4, 3/8, 1/2, and 3/4 where $M_{\mathrm{sat}}$ is the saturated magnetization. The obtained 3/4 plateau state is consistent with the exact result, and the 1/2 plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the 1/3 plateau of the kagome lattice. Different four-spin loop structures are obtained in the 1/4 and 3/8 plateaus but no corresponding states exist in the kagome lattice. The 3/8 plateau has a unique magnetic structure of three types of four-spin local quantum states in a $4\sqrt{2}\times 2\sqrt{2}$ magnetic unit cell with a 16-fold degeneracy.

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Cited by in corpus (12)

• Quantum Skyrmion Lattices in Heisenberg Ferromagnets
• Magnetic phase diagrams and magnetization plateaus of the spin-1/2 antiferromagnetic Heisenberg model on square-kagome lattice with three nonequivalent exchange interactions
• Enhancement of magnetization plateaus in low dimensional spin systems
• Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice
• Magnetization plateau and supersolid phases in the spin-1/2 antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice
• Sine-square deformed mean-field theory
• Translation constraints on quantum phases with twisted boundary conditions
• Strong ferromagnetic fluctuations in a doped checkerboard lattice
• Magnetization jump in one dimensional $J-Q_2$ model with anisotropic exchange
• RKKY plateau in zero- and one-dimensional triangular Kagome lattice models
• Magnetization Plateaus in the Two-dimensional S = 1/2 Heisenberg Model with a 3$\times$3 Checkerboard Structure
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice