  Topological quantum pumps are topologically equivalent to the quantum Hall
state: In these systems, the charge pumped during each pumping cycle is
quantized and coincides with the Chern invariant. However, differently from
quantum Hall insulators, quantum pumps can exhibit novel phenomena such as the
fractional quantization of the charge transport, as a consequence of their
distinctive symmetries in parameter space. Here, we report the analogous
fractional quantization of the spin transport in a topological spin pump
realized in a one-dimensional lattice via a periodically modulated Zeeman
field. In the proposed model, which is a spinfull generalization of the
Harper-Hofstadter model, the amount of spin current pumped during well-defined
fractions of the pumping cycle is quantized as fractions of the spin Chern
number. This fractional quantization of spin is topological, and is a direct
consequence of the additional symmetries ensuing from the commensuration of the
periodic field with the underlying lattice.
