  We consider spin relaxation of finite-size spin chains exchanged coupled with
a one dimensional (1D) electron gas at the edge of a Quantum Spin Hall (QSH)
insulator. Spin lifetimes can be enhanced due to two independent mechanisms.
First, the suppression of spin-flip forward scattering inherent in the spin
momentum locking of the QSH edges. Second, the reduction of spin-flip backward
scattering due to destructive interference of the quasiparticle exchange,
modulated by $k_F d$, where $d$ is the inter-spin distance and $k_F$ is the
Fermi wavenumber of the electron gas. We show that the spin lifetime of the
$S=1/2$ ground state of odd-numbered chains of antiferromagnetically (AFM)
coupled $S=1/2$ spins can be increased more than 4 orders of magnitude by
properly tuning the product $k_Fd$ and the spin size $N$, in strong contrast
with the 1D case. Possible physical realizations together with some potential
issues are also discussed.
