  Multiple transition phenomena in divalent Eu compound EuAl$_4$ with the
tetragonal structure were investigated via the single-crystal time-of-flight
neutron Laue technique. At 30.0 K below a charge-density-wave (CDW) transition
temperature of $T_{\rm CDW}$ = 140 K, superlattice peaks emerge near nuclear
Bragg peaks described by an ordering vector $q_{\rm CDW}$=(0 0 ${\delta}_c$)
with ${\delta}_c{\sim}$0.19. In contrast, magnetic peaks appear at $q_2 =
({\delta}_2 {\delta}_2 0)$ with ${\delta}_2$ = 0.085 in a magnetic-ordered
phase at 13.5 K below $T_{\rm N1}$ = 15.4 K. By further cooling to below
$T_{\rm N3}$ = 12.2 K, the magnetic ordering vector changes into $q_1 =
({\delta}_1 0 0)$ with ${\delta}_1$ = 0.17 at 11.5 K and slightly shifts to
${\delta}_1$ = 0.194 at 4.3 K. No distinct change in the magnetic Bragg peak
was detected at $T_{\rm N2}$=13.2 K and $T_{\rm N4}$=10.0 K. The structural
modulation below $T_{\rm CDW}$ with $q_{\rm CDW}$ is characterized by the
absence of the superlattice peak in the (0 0 $l$) axis. As a similar CDW
transition was observed in SrAl$_4$, the structural modulation with $q_{\rm
CDW}$ could be mainly ascribed to the displacement of Al ions within the
tetragonal $ab$-plane. Complex magnetic transitions are in stark contrast to a
simple collinear magnetic structure in isovalent EuGa$_4$. This could stem from
different electronic structures with the CDW transition between two compounds.
