Multipolar orders in spin–orbit-coupled 5d Mott insulators A2BReO6

Multipolar orders have been studied mainly in lanthanide and actinide compounds, in which localized f electrons have unquenched orbital angular momenta [1–3]. Recently, 4d and 5d electron systems with moderate spin–orbit interactions (SOIs) have become the focus of research as novel platforms for the multipole physics. A $t_{2g}$ manifold of a d electron in an octahedral crystal field possesses an effective angular momentum ($L_{eff}$) of 1, which is entangled with a spin angular momentum by SOIs to give an electronic state characterized by the total angular momentum J. For octahedrally coordinated transition metal ions with $d^1$ electron counts, the combination of a high symmetry crystal field and strong SOIs stabilizes a J = 3/2 quartet as ground states. The multipolar degrees of freedom of J = 3/2 state is expected to give rise to orders of quadrupole and octupole moments [4,5]. Compared to the f electron systems, the spatially extended nature of d orbitals enhances direct interactions between multipoles to stabilize unique multipolar orders in 4d/5d electron systems.
We searched for a model system that shows multipolar order of d electrons and found a promising candidate hosting a quadrupolar order, Ba$_2$MgReO$_6$, in which the Re$^{6+}$ ions with 5$d^1$ electronic configuration form an FCC lattice. Detailed physical properties measurements using high quality single crystals of Ba$_2$MgReO$_6$ revealed a spin-orbit-entangled J = 3/2 state and two phase transitions: a quadrupolar order at $T_q$ = 33 K and a magnetic order at $T_m$ = 18 K [6]. Then we performed synchrotron X-ray diffraction measurements to determine the order pattern of quadrupoles. The very small deformation of ReO$_6$ observed below $T_q$ demonstrates that the quadrupolar order is composed of antiferroically arranged $Q_{x2–y2}$ and ferroically arranged Q$_{3z2–r2}$ moments, as shown in Fig. 1 [7].
We also investigated the physical properties of related double perovskites containing Re$^{6+}$. For example, Ba$_2$CdReO$_6$ shows similar successive phase transitions even in the presence of an additional cubic-to-tetragonal structural transition at a high temperature [8], while tetragonally distorted Sr$_2$MgReO$_6$ shows an only magnetic transition to a layered antiferromagnetic order possibly accompanied by an octupolar order [9]. The observed phases can be mapped on a theoretical phase diagram for spin–orbit-coupled J = 3/2 electrons [4]. A$_2$BRe$^{6+}$O$_6$ double perovskites provide an excellent platform to study multipolar ground states of spin–orbit-coupled 5d electrons.