Long-range magnetic order appears on a side decorated Heisenberg spin nanoribbon at nonzero temperature,although no spontaneous magnetization exists in a one-or two-dimensional isotropic Heisenberg model at any nonzer...Long-range magnetic order appears on a side decorated Heisenberg spin nanoribbon at nonzero temperature,although no spontaneous magnetization exists in a one-or two-dimensional isotropic Heisenberg model at any nonzero temperature according to the Mermin-Wagner theorem.By use of the spin Green's function method,we calculated the magnetizations of Heisenberg nanoribbons decorated by side spins with single-ion anisotropy and found that the system exhibits a nonzero transition temperature,whether the decorated edge spins of the system link together or separate from each other.When the width of the nanoribbon achieves infinite limit,the transition temperatures of the system tend to the same finite constant eventually whether one edge or both edges are decorated by side spins in the nanoribbon.The results reveal that the magnetism of a low-dimensional spin system is different from that of a threedimensional spin system.When the single-ion anisotropy of edge spins in a Heisenberg spin nanoribbon can be modulated by an electric field experimentally,various useful long-range magnetic orders of the system can be obtained.This work can provide a detailed theoretical basis for designing and fabricating next-generation low-dimensional magnetic random-access memory.展开更多
The spin-1/2 antiferromagnetic and spin-(1/2, 1) ferrimagnetic single-walled nanotubes are described by XXZ Heisenberg model. The sublattice magnetization and the critical temperature of the system are calculated by u...The spin-1/2 antiferromagnetic and spin-(1/2, 1) ferrimagnetic single-walled nanotubes are described by XXZ Heisenberg model. The sublattice magnetization and the critical temperature of the system are calculated by using the double-time spin Green's function method. At zero temperature, with the increase of the exchange interaction in the circumferential direction, a maximum value appears in the sublattice magnetization curves of antiferromagnetic and ferrimagnetic systems. As the diameter of the tube increases, the spin quantum fluctuations and thermal fluctuations are suppressed. In addition, the spin quantum fluctuation of the spin-1/2 antiferromagnetic system is greater than that of the spin-(1/2, 1) ferrimagnetic system. The critical temperature of the system increases firstly and then tends to a constant with the increase of the diameter of tube, and it decreases to zero as the exchange anisotropy of the system disappears.展开更多
文摘Long-range magnetic order appears on a side decorated Heisenberg spin nanoribbon at nonzero temperature,although no spontaneous magnetization exists in a one-or two-dimensional isotropic Heisenberg model at any nonzero temperature according to the Mermin-Wagner theorem.By use of the spin Green's function method,we calculated the magnetizations of Heisenberg nanoribbons decorated by side spins with single-ion anisotropy and found that the system exhibits a nonzero transition temperature,whether the decorated edge spins of the system link together or separate from each other.When the width of the nanoribbon achieves infinite limit,the transition temperatures of the system tend to the same finite constant eventually whether one edge or both edges are decorated by side spins in the nanoribbon.The results reveal that the magnetism of a low-dimensional spin system is different from that of a threedimensional spin system.When the single-ion anisotropy of edge spins in a Heisenberg spin nanoribbon can be modulated by an electric field experimentally,various useful long-range magnetic orders of the system can be obtained.This work can provide a detailed theoretical basis for designing and fabricating next-generation low-dimensional magnetic random-access memory.
基金Supported by the National Nature Science Foundation of China under Grant No.11772090
文摘The spin-1/2 antiferromagnetic and spin-(1/2, 1) ferrimagnetic single-walled nanotubes are described by XXZ Heisenberg model. The sublattice magnetization and the critical temperature of the system are calculated by using the double-time spin Green's function method. At zero temperature, with the increase of the exchange interaction in the circumferential direction, a maximum value appears in the sublattice magnetization curves of antiferromagnetic and ferrimagnetic systems. As the diameter of the tube increases, the spin quantum fluctuations and thermal fluctuations are suppressed. In addition, the spin quantum fluctuation of the spin-1/2 antiferromagnetic system is greater than that of the spin-(1/2, 1) ferrimagnetic system. The critical temperature of the system increases firstly and then tends to a constant with the increase of the diameter of tube, and it decreases to zero as the exchange anisotropy of the system disappears.
