Hall magnetohydrodynamics (MHD) is investigated through three-dimensional direct numerical simulations. We show that the Hall effect induces a spontaneous chiral symmetry breaking of the turbulent dynamics. The normalized magnetic polarization is introduced to separate the right- ($R$) and left-handed ($L$) fluctuations. A classical $k^{-7/3}$ spectrum is found at small scales for $R$ magnetic fluctuations which corresponds to the electron MHD prediction. A spectrum compatible with $k^{-11/3}$ is obtained at large-scales for the $L$ magnetic fluctuations; we call this regime the ion MHD. These results are explained heuristically by rewriting the Hall MHD equations in a succinct vortex dynamical form. Applications to solar wind turbulence are discussed.

• Received 11 May 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.194501