  We show that ions at the low densities and high magnetic fields relevant to
the outer crust of magnetars form a novel crystalline phase where ions are
strongly coupled along the magnetic field and loosely coupled in the transverse
direction. The underlying cause is the anisotropic screening of the Coulomb
force by electrons in the presence of a strongly quantizing magnetic field
which leads to Friedel oscillations in the ion-ion potential. In particular,
the Friedel oscillations are much longer-ranged in the direction of the
magnetic field than is the case in the absence of magnetic fields, a factor
that has been neglected in previous studies. These "Friedel crystals" have very
anisotropic elastic moduli, with potentially interesting implications for the
Quasi-periodic Oscillations seen in the X-ray flux of magnetars during their
giant flares. We find the minimum energy configuration of ions taking into
account these anisotropic effects and find that, depending on the density,
temperature and magnetic field strength, different lattice structures (fcc, hcp
or bcc oriented in different ways in relation to the magnetic field) are
favored.
