科研之友
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摘要
A theoretical method recently developed is used to find all possible equilibrium magnetic states of a finite-size classical one-dimensional planar spin chain with competing nearest-neighbor (nn) and next-nearest-neighbor (nnn) exchange interactions. The energy of a classical planar model with N spins is a function of N absolute orientational angles or equivalently, due to the absence of in-plane anisotropy, of (N - 1) relative orientational angles. The lowest energy stable state (ground state) corresponds to a global minimum of the energy in the (N - 1)-dimensional space, while metastable states correspond to local minima. For a given value of the ratio, gamma, between nnn and nn exchange couplings, all the equilibrium configurations of the model were calculated with great accuracy for N %26lt;= 16, and a stability analysis was subsequently performed. For any value of N, the ground state was found to be %26quot;symmetric%26quot; with respect to the middle of the chain in the relative angles representation. For the chosen value of gamma, the ground state consists of a helix whose chirality is constant in sign along the chain (i.e., all the spins turn clockwise, or all anticlockwise), but whose pitch varies owing to finite-size effects; e.g., for positive chirality we found that the chiral order parameter chi(N) %26gt; 0 increases monotonically with increasing N, approaching the value (chi = 1) pertinent to the ground state in the limit N -%26gt;-%26gt; infinity. For finite but not too small values of N, we found metastable states characterized by one reversal of chirality, either localized just in the middle of the chain [%26quot;antisymmetric%26quot; state, with chiral order parameter chi(N)=0], or shifted away from the middle of the chain, to the right or to the left [pairs of %26quot;ugly%26quot; states, with equal and opposite values of chi(N) not equal 0; the attribute %26quot;ugly%26quot; refers to the absence of a definite symmetry in the relative angles representation]. Concerning the stability of these states with one reversal of chirality, two main results were found. First, the antisymmetric state is metastable for even N and unstable for odd N. Second, an additional pair of %26quot;ugly%26quot; states is found whenever the number of spins in the chain is increased by 1; the states in each additional pair are unstable for even N and metastable for odd N. Analysis of stable and metastable configurations in the framework of a discrete nonlinear mapping approach provides further support for the above results.
- 出版日期2014-10-22
