The magnetization of the easy-plane quasi-one-dimensional antiferromagnets CsMnBr3 and RbMnBr3 in the presence of an external magnetic field can be well interpreted by minimizing the classical magnetic energy. However, this type of calculation cannot reproduce the observed anisotropy of the magnetization at high magnetic fields, which therefore is usually attributed to quantum effects. We show that the anisotropy is already present at the classical level, provided thermal fluctuations are taken into account.
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