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Co2Cr1-xFexAl full Heusler alloy thin films (x≥0.4) have been epitaxially grown on GaAs(001) substrates under the optimized condition. Structural analysis reveals the detailed growth mechanism of the films and confirms that the films form the perfectly ordered L21 structure. A magnetization measurement also shows the films possess very strong uniaxial crystalline anisotropy due to the epitaxial growth. By using these films as bottom electrodes of magnetic tunnel junctions, the maximum tunnel magnetoresistance ratio of 8.8% is observed after post-annealing with Al-O insulating barriers for x=1.