  The emergence of effective $S=1/2$ spins at the edges of $S=1$ Haldane spin
chains is one of the simplest examples of fractionalization. Whereas there is
indirect evidence of this phenomenon, direct measurement of the magnetic moment
of an individual edge spin remains to be done. Here we show how scanning tunnel
microscopy electron-spin resonance (ESR-STM) can be used to map the stray field
created by the fractional $S=1/2$ edge spin and we propose efficient methods to
invert the Biot-Savart equation, obtaining the edge magnetization map. This
permits one to determine unambiguously the two outstanding emergent properties
of fractional degrees of freedom, namely, their fractional magnetic moment and
their localization length $\xi$.
