  Conventional hadron interpolating fields, which utilise gauge-covariant
Gaussian smearing, are ineffective in isolating ground state nucleons in a
uniform background magnetic field. There is evidence that residual Landau mode
physics remains at the quark level, even when QCD interactions are present. In
this work, quark-level projection operators are constructed from the $SU(3)
\times U(1)$ eigenmodes of the two-dimensional lattice Laplacian operator
associated with Landau modes. These quark-level modes are formed from a
periodic finite lattice where both the background field and strong interactions
are present. Using these eigenmodes, quark-propagator projection operators
provides the enhanced hadronic energy-eigenstate isolation necessary for
calculation of nucleon energy shifts in a magnetic field. The magnetic
polarisability of both the proton and neutron is calculated using this method
on the $32^3 \times 64$ dynamical QCD lattices provided by the PACS-CS
Collaboration. A chiral effective-field theory analysis is used to connect the
lattice QCD results to the physical regime, obtaining magnetic polarisabilities
of $\beta^p = 2.79(22)({}^{+13}_{-18}) \times 10^{-4}$ fm$^3$ and $\beta^n =
2.06(26)({}^{+15}_{-20}) \times 10^{-4}$ fm$^3$, where the numbers in
parantheses describe statistical and systematic uncertainties.
