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 $mathbf{E}$.
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