Understanding the interplay among different magnetic exchange interactions and its physical consequences, especially in the presence of itinerant electrons and disorder, 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 with potential broad technological applications. In this paper, we report the coexistence of antiferromagnetic order and spin-glass behaviors in the 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 paradigm to study the large family of transition metal chalcogenides whose magnetic order or even dimensionality can be tuned to a large extent, forming a fertile playground to manipulate or switch the spin degrees of freedom thereof.

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