A microscopic self-consistent triaxial relativistic Hartree-Bogoliubov theory in continuum (TRHBc), which simultaneously takes into account the triaxiality and pairing correlations as well as continuum effects, is established and applied to explore the novel halo phenomenon in aluminum isotopes. The experimental proton drip line and the available data of neutron separation energies and charge radii are reproduced well without any free parameters. The neutron-richest odd-odd aluminum isotope observed so far, ${}^{42}\mathrm{Al}$, is predicted to be triaxially deformed with $\beta =0.35$ and $\gamma ={42}^{\circ }$. Its one-neutron separation energy is predicted to be 0.68 MeV, in agreement with the AME2020, and the neutron rms radius is 3.94 fm, remarkably larger than the empirical value. The density distribution of the valance neutron, which extends much farther in space than the core, suggests a possible neutron halo in ${}^{42}\mathrm{Al}$. The dominant components responsible for the spatial extension of the halo are revealed by the single-neutron orbitals around the Fermi energy. A novel phenomenon, the exchange of the intermediate and short axes between the triaxial core with $\beta =0.38$ and $\gamma ={50}^{\circ }$ and the triaxial halo with $\beta =0.79$ and $\gamma =-{23}^{\circ }$ is found. Future experiments to explore the halo phenomenon and the novel shape decoupling in ${}^{42}\mathrm{Al}$ are highly demanded.

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• Binding energy & masses
• Charge distributions
• Energy levels
• Neutron skin thickness
• Nuclear many-body theory
• Nuclear radii
• Nuclear shapes and moments
• Nuclear structure & decays
• Nucleon distribution
• 150 ≤ A ≤ 189
• Nuclear binding