Magnetization plateau as a result of the uniform and gradual electron doping in a coupled spin-electron double-tetrahedral chain

The double-tetrahedral chain in a longitudinal magnetic field, whose nodal lattice sites occupied by the localized Ising spins regularly alternate with triangular plaquettes with the dynamics described by the Hubbard model, is rigorously investigated. It is demonstrated that the uniform change of electron concentration controlled by the chemical potential in a combination with the competition between model parameters and the external magnetic field leads to the formation of one chiral and seven nonchiral phases at the absolute zero temperature. Rational plateaux at one-third and one-half of the saturation magnetization can also be identified in the low-temperature magnetization curves. On the other hand, the gradual electron doping results in 11 different ground-state regions that distinguish from each other by the evolution of the electron distribution during this process. Several doping-dependent magnetization plateaux are observed in the magnetization process as a result of the continuous change of electron content in the model.

Figure 1

A part of the spin-electron double-tetrahedral chain. Full circles denote nodal sites occupied by the localized Ising spins $\sigma =1/2$ and empty circles forming triangular clusters are available to mobile electrons.

Figure 2

Ground-state phase diagrams of the model (2) in the $\mu -H$ plane for the fixed Coulomb term $U/\left|J\right|=3$ and four representative values of the kinetic parameter (a) $t/\left|J\right|=0.4$, (b) $t/\left|J\right|=0.7$, (c) $t/\left|J\right|=0.9$, (d) $t/\left|J\right|=1.3$.

Figure 3

The electron density ${\rho }_e$ per triangular plaquette as a function of the chemical potential $\mu$ and the magnetic field $H$ for the Coulomb term $U/\left|J\right|=3$ and the hopping parameter $t/\left|J\right|=0.9$ at the temperature $k_{\mathrm{B}}T/\left|J\right|=0.015$.

Figure 4

3D views of the magnetization process for the Coulomb term $U/\left|J\right|=3$ and the hopping parameters (a) $t/\left|J\right|=0.7$, (b) $t/\left|J\right|=0.9$, (c) $t/\left|J\right|=1.3$ at the temperature $k_{\mathrm{B}}T/\left|J\right|=0.015$.

Figure 5

Ground-state phase diagrams of the model (2) in the ${\rho }_e-H$ parameter plane for the fixed Coulomb term $U/\left|J\right|=3$ and four representative values of the hopping parameter (a) $t/\left|J\right|=0.4$, (b) $t/\left|J\right|=0.7$, (c) $t/\left|J\right|=0.9$, (d) $t/\left|J\right|=1.3$.

Figure 6

The chemical potential $\mu$ as a function of the electron density ${\rho }_e$ and the magnetic field $H$ for the Coulomb term $U/\left|J\right|=3$, the kinetic parameter $t/\left|J\right|=1.3$, and the temperature $k_{\mathrm{B}}T/\left|J\right|=0.015$.

Figure 7

3D views of the magnetization process for the Coulomb term $U/\left|J\right|=3$ and the hopping parameters (a) $t/\left|J\right|=0.7$, (b) $t/\left|J\right|=0.9$, (c) $t/\left|J\right|=1.3$ at the temperature $k_{\mathrm{B}}T/\left|J\right|=0.015$.