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On the basis of ab-initio calculations we have investigated the electronic and magnetic properties of Cr_1-xBa_xP alloy, our calculations suggest that as we dope BaP with Cr atoms and move towards Cr_1-xBa_xP where x=0, 0.125, 0.25, 0.50, and 0.75 all alloy are HM-FM. Interestingly Cr_0.25Ba_0.75P is a HM-AFM otherwise "˜fully compensated ferrimagnet', this alloy should be of special interest for applications since it creates no external stray field and thus exhibit minimal energy losses. In addition, the robustness of half-metallicity with respect to the variation of lattice constants of Cr_1-xBa_xP is also discussed; moreover ferrimagnetism co-exists with the half-metallicity, resulting in the desired fully compensated half-metallic ferrimagnetism, for a wide range of lattice constants. Furthermore we found that this new HMFCF is stable according to its small formation energy