We study sufficient conditions for the absence of positive eigenvalues of
magnetic Schr\”odinger operators in $\mathbb{R}^d,\, d\geq 2$. In our main
result we prove the absence of eigenvalues above certain threshold energy which
depends explicitly on the magnetic and electric field. A comparison with the
examples of Miller–Simon shows that our result is sharp as far as the decay of
the magnetic field is concerned. As applications, we describe several
consequences of the main result for two-dimensional Pauli and Dirac operators,
and two and three dimensional Aharonov–Bohm operators.
