Title: Realization of the Axial Next-Nearest-Neighbor Ising model in U$_3$Al$_2$Ge$_3$,
Abstract: Here we report small-angle neutron scattering (SANS) measurements and
theoretical modeling of U$_3$Al$_2$Ge$_3$. Analysis of the SANS data reveals a
phase transition to sinusoidally modulated magnetic order, at
$T_{\mathrm{N}}=63$~K to be second order, and a first order phase transition to
ferromagnetic order at $T_{\mathrm{c}}=48$~K. Within the sinusoidally modulated
magnetic phase ($T_{\mathrm{c}} < T < T_{\mathrm{N}}$), we uncover a dramatic
change, by a factor of three, in the ordering wave-vector as a function of
temperature. These observations all indicate that U$_3$Al$_2$Ge$_3$ is a close
realization of the three-dimensional Axial Next-Nearest-Neighbor Ising model, a
prototypical framework for describing commensurate to incommensurate phase
transitions in frustrated magnets.