Magnetotransport properties of nearly-free electrons in two-dimensional hexagonal metals and application to the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>A</mml:mi><mml:msub><mml:mi>X</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:math>phases

We propose a general, yet simple model for describing the weak field magnetotransport properties of nearly-free electrons in two-dimensional hexagonal metals. We modify this model so as to apply it to the magnetotransport properties of the ${M}_{n+1}A{X}_{n}$ phases, a particular class of nanolamellar carbides and nitrides. We argue that the values of the in-plane Hall coefficient and the in-plane parabolic magnetoresistance are due to the specific shape of the Fermi surface of almost two-dimensional hole and electron bands. If the contribution of the electron pockets to in-plane resistivity is often (but not always) predicted to be a minor one, in contrast, both holes and electrons should substantially contribute to the overall value of the in-plane Hall coefficient. The relevance of our model is supported by elementary considerations and a set of experimental data obtained from single crystals of ${\mathrm{V}}_{2}\mathrm{AlC}$ and $\mathrm{C}{\mathrm{r}}_{2}\mathrm{AlC}$. In particular, we obtain a high ratio between the in-plane $({\ensuremath{\rho}}_{ab})$ and parallel to the $c$ axis $({\ensuremath{\rho}}_{c})$ resistivities.

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