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It is well known that Zigzag graphene nanoribbons[1] are antiferromagnetic semiconductors and the Zigzag BN nanoribbons[2] are nonmagnetic semiconductors.Very recently,the hybridized BNC single sheets are synthesized successfully [3].The tendency to form a separated carbon and BN phase domain inspires many interests on the electronic and magnetic properties of the hybridized Zigzag BNC nanoribbons [4,5].