  We investigate the far-from-equilibrium nature of magnetic anisotropy and
exchange interactions between molecular magnets embedded in a tunnel junction.
By mapping to an effective spin model, these magnetic interactions can be
divided into three types: isotropic Heisenberg, anisotropic Ising, and
anisotropic Dzyaloshinski-Moriya contributions, which are attributed to the
background non-equilibrium electronic structures. We further demonstrate that
both the magnetic self and exchange interactions can be controlled either
electrically by gating and tuning voltage bias, or thermally by adjusting
temperature bias. We show that the Heisenberg and Ising interactions scale
linearly, while the Dzyaloshinski-Moriya interaction scales quadratically, with
the molecule-lead coupling strength. The interactions scale linearly with the
effective spin-polarizations of the leads and the molecular coherence. Our
results pave a way for smart control of magnetic exchange interactions at
atomic and molecular levels.
