Energy Structure of a Finite Haldane Chain inY2BaNi0.96Mg0.04O5Studied by High Field Electron Spin Resonance

This Letter presents the fine structure of energy levels for the edge states of a Haldane chain. In order to investigate the edge states, we have performed high field and multifrequency electron spin resonance (ESR) measurements of finite length $S=1$ antiferromagnetic chains in ${\mathrm{Y}}_2{\mathrm{BaNi}}_{0.96}{\mathrm{Mg}}_{0.04}{\mathrm{O}}_5$. Owing to the high spectral resolution by high fields and high frequencies, observed ESR signals can be separated into the contributions of the finite chains with various chain lengths. Our results clearly show that the edge spins actually interact with each other through the quantum spin chain and the interaction depends on the chain length $N$. This $N$ dependence has been obtained experimentally for the first time, and shows that the correlation length $\xi$ in the real system is somewhat larger than that calculated by a simple Heisenberg model.