Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices

Abstract

For a class of frustrated spin lattices including e.g. the 1D sawtooth chain,\nthe 2D kagom\\'e and checkerboard, as well as the 3D pyrochlore lattices we\nconstruct exact product eigenstates consisting of several independent,\nlocalized one-magnon states in a ferromagnetic background. Important\ngeometrical elements of the relevant lattices are triangles being attached to\npolygons or lines. Then the magnons can be trapped on these polygons/lines. If\nthe concentration of localized magnons is small they can be distributed\nrandomly over the lattice. Increasing the number of localized magnons their\ndistribution over the lattice becomes more and more regular and finally the\nmagnons condensate in a crystal-like state. The physical relevance of these\neigenstates emerges in high magnetic fields where they become groundstates of\nthe system. As a result a macroscopic magnetization jump appears in the\nzero-temperature magnetization curve just below the saturation field. The\nheight of the jump decreases with increasing spin quantum number and vanishes\nin the classical limit. Thus it is a true macroscopic quantum effect.\n