Magnetization plateaus of spin-1 one-dimensional Heisenberg antiferromagnets alternating interactions.

One of the recent interesting topics is Spin-1 (S=1) one-dimensiOl Heisenberg antiferromagnets with alternating interactions (1DHMI). It can be us to model the magnetic behavior of many materials, During these years, some bond alternating compounds regarded as S=1 1DHMI were synthesized and the magnetic properties were studied [1-2].The ground state in zero magnetic field of the system is defined as absence of fermion (vacuum). With increasing magnetic field, component SZ =1 of trip becomes lowest energy state, this state is defined as existence of one fermion. For > 0, due to the interaction between the dimer, the transition magnetic field decrease as a increases. To determine this boundary analytically, therefore, we need investigate the stability of the vacuum, We determine the difference of enemy between the vacuum state with no fermion and state with one fermion. When the energy difference between them becomes zero, the magnetic field is determined a function of a in the phase diagram of external magnetic field VS, a. Based on the ideas, we can determine other boundaries of the phase diagram.

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