Physical Review B 79(5), 054405 (2009).
We study how a bias voltage changes magnetic exchange interactions. We derive a general expression for magnetic
exchange interactions for systems coupled to reservoirs under a bias potential and apply it to spin valves. We find
that for metallic systems, the interlayer exchange coupling shows a weak oscillatory dependence on the bias potential.
For tunneling systems, we find a quadratic dependence on the bias potential and derive an approximate expression for
this bias dependence for a toy model. We give general conditions for when the interlayer exchange coupling is a quadratic
function of bias potential.
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