Charge-Density-Wave Order and Multiple Magnetic Transitions in Divalent Europium Compound EuAl$_4$

Abstract: 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.