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Exchange bias effect in the ferromagnetic double perovskite compoundY$_2$CoMnO$_6$, which is also a multiferroic, is reported. The exchange bias,observed below 8~K, is explained as arising due to the interface effect betweenthe ferromagnetic and antiferromagnetic clusters created by {\it antisite}disorder in this material. Below 8~K, prominent ferromagnetic hysteresis withmetamagnetic "steps" and significant coercive field, $H_c \approx$ 10~kOe areobserved in this compound which has a $T_c \approx$ 75~K. A model based ongrowth of ferromagnetic domains overcoming the elastic energy of structurallypinned magnetic interfaces, which closely resembles martensitic-liketransitions, is adapted to explain the observed effects. The role of {\itantisite} disorder in creating the domain structure leading to exchange biaseffect is highlighted in the present work.

Antisite Disorder-induced Exchange Bias Effect in Multiferroic Y2CoMnO6