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We have studied the pressure effect on electronic structures and magnetic orders of ternary iron selenide KFeSe by the first-principles electronic structure calculations. At low pressure, the compound is in the blocked checkerboard antiferromagnetic (AFM) semiconducting phase, as observed by the neutron scatting measurements. Applying pressure induces two phase transitions, first from the blocked checkerboard AFM semiconducting phase to a collinear AFM metallic phase around 12 GPa, and then to a non-magnetic metallic phase around 25 GPa, respectively. Our results help to clarify the recent experimental measurements under pressure.

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