  Understanding the interplay among different magnetic exchange interactions
and its physical consequences, especially in the presence of itinerant
electrons and disorders, remains one of the central themes in condensed matter
physics. In this vein, the coupling between antiferromagnetic and spin glass
orders may lead to large exchange bias, a property of potential broad
technological applications. In this article, we report the coexistence of
antiferromagnetic order and spin glass behaviors in a quasi-one-dimensional
iron telluride TaFe$_{1+x}$Te$_3$ ($x$=0.25). Its antiferromagnetism is
believed to arise from the antiferromagnetic interchain coupling between the
ferromagnetically aligned FeTe chains along the $b$-axis, while the spin glassy
state stems from the disordered Fe interstitials. This dichotomic role of chain
and interstitial sublattices is responsible for the large exchange bias
observed at low temperatures, with the interstitial Fe acting as the
uncompensated moment and its neighboring Fe chain providing the source for its
pinning. This iron-based telluride may thereby represent a new paradigm to
study the large family of transition metal chalcogenides whose magnetic order
or even the dimensionality can be tuned to a large extent, forming a fertile
playground to manipulate or switch the spin degrees of freedom thereof.
