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We study the asymptotic growth of the entanglement entropy of ground statesof non-interacting (spinless) fermions in $\mathbb R^3$ subject to a non-zero,constant magnetic field perpendicular to a plane. As for the case with nomagnetic field we find, to leading order $L^2\ln(L)$, a logarithmicallyenhanced area law of this entropy for a bounded, piecewise Lipschitz region$L\Lambda\subset \mathbb R^3$ as the scaling parameter $L$ tends to infinity.This is in contrast to the two-dimensional case since particles can now movefreely in the direction of the magnetic field, which causes the extra $\ln(L)$factor. The explicit expression for the coefficient of the leading ordercontains a surface integral similar to the Widom formula in the non-magneticcase. It differs however in the sense that the dependence on the boundary isnot solely on its area but on the "area perpendicular to the direction of themagnetic field". On the way we prove an improved two-term asymptotic expansion(up to an error term of order one) of certain traces of one-dimensionalWiener--Hopf operators with a discontinuous symbol. This is of independentinterest and leads to an improved error term of the order $L^2$ of the relevanttrace for piecewise $\mathsf{C}^{1,\alpha}$ smooth surfaces $\partial \Lambda$.

Entanglement entropy of ground states of the three-dimensional ideal Fermi gas in a magnetic field