  Halo phenomena have long been an important frontier in both experimental and
theoretical nuclear physics. $^{37}$Mg was identified as a halo nucleus in 2014
and remains the heaviest nuclear halo system to date. While the halo phenomenon
in $^{37}$Mg was not predicted before the discovery, its description has been
still challenging afterwards. In this Letter, we report a microscopic and
self-consistent description of the neutron halo in $^{37}$Mg using the deformed
relativistic Hartree-Bogoliubov theory in continuum (DRHBc) that was developed
in 2010. The experimental neutron separation energies and empirical matter
radii of neutron-rich magnesium isotopes as well as the deformed $p$-wave halo
characteristics of $^{37}$Mg are well reproduced without any free parameters.
In particular, the orbital occupied by the halo neutron in $^{37}$Mg,
exhibiting $p$-wave components comparable to those suggested in experiments,
remains consistent across various employed density functionals including PC-F1,
PC-PK1, NL3*, and PK1. The DRHBc theory investigated only even-even magnesium
isotopes in previous works and for that reason missed predicting $^{37}$Mg as a
halo nucleus before 2014. Although the core and the halo of $^{37}$Mg are both
prolate, higher-order shape decoupling on the hexadecapole and
hexacontatetrapole levels is predicted.
