Topological solitons in amorphous magnets

Amorphous magnets of the spin-glass type are characterized by completely disordered spatial distribution of magnetic ions, coupled by exchange interaction in such a way that the directions of the spins are also completely random, and the net magnetization is zero. The spin dynamics of such magnets can be described macroscopically by equations for a time-dependent non-uniform is space three-dimensional rotations of the spins. The non-commutative character of such rotations leads to the non-trivial topological properties of the space of dynamical variables, the rotations angles, and to a complex form of the significantly non-linear equations for them. For the disordered magnets of the type of spin glasses, stable three-dimensional topological solitons are found within this phenomenological approach. These solitons are characterized by internal precessional dynamics of the spins, from the quantum-mechanical viewpoint they can be treated as bound states of large number of linear excitations of this system, magnons.