  We use symmetry analysis and first principles calculations to show that the
linear magnetoelectric effect can originate from the response of orbital
magnetic moments to the polar distortions induced by an applied electric field.
Using LiFePO4 as a model compound we show that spin-orbit coupling partially
lifts the quenching of the 3d orbitals and causes small orbital magnetic
moments ($\mu_{(L)}\approx 0.3 \mu_B$) parallel to the spins of the Fe$^{2+}$
ions. An applied electric field $\mathbf{E}$ modifies the size of these orbital
magnetic moments inducing a net magnetization linear in $\mathbf{E}$.
