  The recent discovery of magnetic ordering in two-dimension has lead to
colossal efforts to find atomically thin materials that order at high
temperatures. However, due to fundamental spin fluctuation in reduced
dimension, the room-temperature ferromagnetism remains elusive. Here, we report
a dramatic manipulation of magnetic ordering up to room temperature in the
monolayer CrBr$_3$, within the first-principles Heisenberg XXZ model. The
exchange and anisotropic magnetic interactions are externally modulated by a
gate-induced charge carrier doping that triggers a nontrivial phase diagram.
High-temperature ferromagnetism is associated with a substantial increase in
both effective ferromagnetic exchange and overall magnetic anisotropy under
experimentally attainable hole doping. In contrast, electron doping quickly
switches the magnetic easy axis. The gate-tuneable room temperature
ferromagnetism in CrBr$_3$ presents new possibilities in electrically
controlled spintronic and magnetoelectric devices based on atomically thin
crystals.
