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Zero-Temperature Configurations of Short Odd-Numbered Classical Spin Chains with Bilinear and Biquadratic Exchange Interactions

The lowest energy configurations of short odd open chains with classical spins are determined for antiferromagnetic bilinear and biquadratic nearest-neighbor exchange interactions. The zero field residual magnetization generates differences with the magnetic behavior of even chains, as the odd chain is like a small magnet for weak magnetic fields. The lowest energy configuration is calculated as a function of the total magnetization M, even for M less than the zero field residual magnetization. Analytic expressions and their proofs are provided for the threshold magnetic field needed to drive the system away from the antiferromagnetic configuration and the spin polar angles in its vicinity, when the biquadratic interaction is relatively weak. They are also given for the saturation magnetic field and the spin polar angles close to it. Finally, an analytic expression along with its proof is given for the maximum magnetization in zero magnetic field for stronger biquadratic interaction, where the lowest energy configuration is highly degenerate.