  Three-terminal magnetic tunnel junction (MTJ), where non-volatile
magnetization state can be switched via spin orbit torque (SOT), is attracting
massive research interests since it is featured by high speed, low power,
nearly unlimited endurance, etc. The threshold switching current is a key
parameter for MTJ as it determines the energy efficiency. Here, with the
Routh-Hurwitz criterion, we theoretically derive the threshold current for
switching in-plane magnetization in the three-terminal MTJ. Two devices with
field-free switching mode are investigated. The one is the Type-x device
switched by the combination of SOT and spin transfer torque (STT). The other is
the three-terminal MTJ with a canted easy-axis. To the best of our knowledge,
this is the first theoretical work on the threshold switching current for these
two devices. Our developed theoretical method shows clear physical picture,
meanwhile good agreement between theoretical derivation and numerical
simulation is achieved.
