Competing magnetic instabilities and self-doping effects in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>KFe</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>As</mml:mi> <mml:mn>2</mml:mn> </mml:ms

By applying density functional theory calculations, we study the electronic and magnetic properties of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>KFe</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mi>As</a:mi> <a:mn>2</a:mn> </a:msub> </a:mrow> </a:math> , which exhibits two superconducting domes under pressure. We find there are competing magnetic instabilities from itinerant electrons in both superconducting phases. The lower <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>T</b:mi> <b:mi>c</b:mi> </b:msub> </b:math> of the first superconducting phase at ambient pressure can be attributed to the competing instabilities at <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mo>(</c:mo> <c:mi>π</c:mi> <c:mo>,</c:mo> <c:mn>0</c:mn> <c:mo>,</c:mo> <c:mi>π</c:mi> <c:mo>)</c:mo> </c:mrow> </c:math> , which favor the double stripe type or plaquette antiferromagnetic order. The second superconducting phase is further suppressed by the competing ferromagnetic and stripe antiferromagnetic instabilities at higher pressure. In addition, we find that applying pressure acts as self-doping, leading to variations in instabilities from the itinerant electrons. Our results imply that the instability of the Pauli susceptibility from itinerant electrons is a possible quantity that describes the various characters of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msub> <d:mi>KFe</d:mi> <d:mn>2</d:mn> </d:msub> <d:msub> <d:mi>As</d:mi> <d:mn>2</d:mn> </d:msub> </d:mrow> </d:math> under pressure and have important implications for understanding the pressure manipulation of superconductivity in iron-based superconductors.