双二次交换自旋$ S=1$铁磁体的非线性动力学和二维孤子
Non-linear dynamics and two-dimensional solitons for spin $ S=1$ ferromagnets with biquadratic exchange
摘要：
考虑双线性和双二次自旋算符交换作用，发展了自旋为$ S=1$的各向同性铁磁体自旋动力学的自洽半经典理论。对于这种非海森堡磁体，给出了一类特殊的自旋振荡和波，其量子自旋期望值$ {\rm {\bf m}}=<{\rm {\bf S}}>$不改变它的方向，但改变它的长度。这样的“奇异”激发不存在于规则的磁铁中，其动力学是用朗道-利夫希茨方程或自旋海森堡哈密顿量来描述的。我们证明了非线性均匀振荡和波的存在，以及具有有限能量的自局域动力学激发（孤子）。讨论了用超快激光脉冲激发这种振荡的可能性。
英文摘要：
We develop a consistent semiclassical theory of spin dynamics for an isotropic ferromagnet with a spin $ S=1$ taking into consideration both bilinear and biquadratic over spin operators exchange interaction. For such non-Heisenberg magnets, a peculiar class of spin oscillations and waves, for which the quantum spin expectation value $ {\rm {\bf m}}=<{\rm {\bf S}}>$ does not change it direction, but changes in length, is presented. Such ``longitudinal'' excitations do not exist in regular magnets, dynamics of which are described in terms of the Landau-Lifshitz equation or by means of the spin Heisenberg Hamiltonian. We demonstrate the presence of non-linear uniform oscillations and waves, as well as self-localized dynamical excitations (solitons) with finite energy. A possibility of excitation of such oscillations by ultrafast laser pulse is discussed.
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