Temperature-dependent critical spin-orbit field for orthogonal switching in antiferromagnets

The discovery of current-induced spin-orbit torque (SOT) orthogonal reorientation, also known as orthogonal switching, of metallic Mn$_2$Au and CuMnAs has opened the door for ultrafast writing of an antiferromagnet (AFM). Phenomenological theory predicts that the minimum field necessary for SOT switching -- critical field -- for ultrashort pulses increases inversely proportional to the pulse duration, thereby limiting the use of ultrafast stimulus as driving force for switching. We explore the possibility that by varying the working temperature the critical field reduces enabling orthogonal switching in response to ultrashort pulses. To do so, we extend previous theory to finite temperature and show that the critical field for an orthogonal switching strongly depends on temperature. We determine how the temperature dependence of the critical field varies as a function of the pulse duration. While for long pulses, the temperature dependence of the critical field is determined by the anisotropy field, for ultrashort pulses, it is determined by the characteristic frequency of the AFM. We show that the short and long pulse duration limits for the critical field can be connected by an analytical expression.