  Using the determinant quantum Monte Carlo method, we study the magnetic
susceptibility in the parameter space of the on-site interaction $U$,
temperature $T$, electron filling $\avg{n}$, and the frustration control
parameter $t^{\prime}$ within the Hubbard model on a two-dimensional
checkerboard lattice. It is shown that the system exhibits stable and strong
ferromagnetic fluctuations about the electron filling $\avg{n}\ge1.2$ for
different $t^{\prime}$, and the ferromagnetic susceptibility is strongly
enhanced by the increasing interaction and decreasing tempeture. We also
discuss the sign problem to clarify which parameter region is accessible and
reliable. Our findings not only demonstrate important implications for
modulating magnetism in the checkerboard lattice, but will also provide a
theoretical platform for a flat-band model that demonstrates a variety of
physical properties.
