Fermionic spin excitations in two- and three-dimensional antiferromagnets.

Spin excitations in an ordered Heisenberg magnet are magnons-bosons with spin 1. That may change when frustration and quantum fluctuations suppress the order and restore the spin-rotation symmetry. We show that spin excitations in the S=1/2 Heisenberg antiferromagnet on a kagome lattice are spinons-fermions with spin 1/2. In the ground state the system can be described as a collection of small, heavy pairs of spinons with spin 0. A magnetic excitation of lowest energy amounts to breaking up a pair into two spinons at a cost of 0.06 J.