Octupolar order in d -orbital Mott insulators

Abstract

Motivated by experimental and theoretical interest in realizing multipolar orders in d-orbital materials, we discuss the quantum magnetism of J = 2 ions on the face-centered cubic lattice which can be realized in spin-orbit coupled oxides with 5d 2 transition metal ions. Based on the crystal field environment, we argue for a splitting of the J = 2 multiplet, leading to a low lying non-Kramers doublet which hosts quadrupolar and octupolar moments. We discuss a microscopic mechanism whereby the combined perturbative effects of orbital repulsion and antiferromagnetic Heisenberg spin interactions leads to ferro-octupolar coupling between neighboring sites, and stabilizes ferrooctupolar order. This same mechanism is also shown to disfavor quadrupolar ordering. We study spin dynamics in the ferro-octupolar state using a slave-boson approach, uncovering a gapped and dispersive magnetic exciton. For sufficiently strong magnetic exchange, the dispersive exciton can condense, leading to conventional type-I antiferromagnetic order which can preempt octupolar order. Our proposal for ferrooctupolar order, with specific results in the context of a model Hamiltonian, provides a comprehensive understanding of thermodynamics, µSR, X-ray diffraction, and inelastic neutron scattering measurements on a range of cubic 5d 2 double perovskite materials including Ba2ZnOsO6, Ba2CaOsO6, and Ba2MgOsO6. Our proposal for exciton condensation leading to type-I magnetic ordering is argued to be relevant to materials such as Sr2MgOsO6.PACS numbers: 75.25.aj, 75.40.Gb, 75.70.Tj Multipolar symmetry-breaking orders have been extensively discussed in f -orbital based lanthanide and actinide compounds, which host ions where spin-orbit coupling (SOC) is a dominant energy scale [1]. For instance, the "hidden order" state of URu 2 Si 2 has been proposed to host hexadecapolar symmetry breaking [2]. Another well-known example is cubic NpO 2 [3-6], where a large body of experiments have been reconciled in terms of a primary antiferro-triakontadipolar (rank-5 magnetic multipolar) symmetry breaking which drives secondary antiferro-quadrupolar order. In certain pyrochlore magnets, all-in all-out magnetic order has been proposed to lead to "effective octupoles" on tetrahedra [7]. Ongoing experimental [8-10] and theoretical investigations [11][12][13][14] of PrTi 2 Al 20 and PrV 2 Al 20 have also uncovered quadrupolar and ferro-octupolar orders.Recently, unconventional multipolar orders have also been proposed in d-orbital metals to occur as Pomeranchuk instabilities of spin-orbit coupled Fermi surfaces [15]. Specifically, metallic oxides which have d-orbital ions with large SOC, such as LiOsO 3 and Cd 2 Re 2 O 7 , have been proposed as potential candidates to realize this physics [15]. Experiments have indeed discovered an oddparity nematic metal in Cd 2 Re 2 O 7 below T c ∼ 200 K via optical second-harmonic generation [16]. Other proposed materials for hosting multipolar orders include A 2 OsO 4 (with A = K,Rb,Cs) [17].However, to the best of our knowledg...

Multipolar magnetism in d -orbital systems: Crystal field levels, octupolar order, and orbital loop currents

“…On phenomenological grounds, and the above microscopic calculations, 5d 2 oxides are candidates for a lowlying non-Kramers doublet. As shown previously 19 , this doublet may be described using the wavefunctions of the J = 2 manifold in terms of |J z eigenstates written as pseudospin-1/2 states:…”

“…This highlights a non-trivial effect of t 2g -e g mixing, showing that it can be important for nucleating multipolar order in 5d Mott insulators. However, this effect by itself may be too small to account for the spin gap observed in neutron scattering experiments 18,19 on Ba 2 ZnOsO 6 , Ba 2 CaOsO 6 , and Ba 2 MgOsO 6 . We next turn to an additional mechanism, which can cooperate to enhance this splitting, or perhaps even reverse the level ordering which we argue is important in certain other materials.…”

“…Optical second-harmonic generation experiments on Cd 2 Re 2 O 7 have found evidence for such an inversion broken quadrupolar ordered state below T c ∼ 200 K 16 . Other candidates for multipolar orders include proposed quadrupolar order in A 2 OsO 4 (with A = K,Rb,Cs) 17 .In recent work, we have studied d-orbital Mott insulators with large SOC and a d 2 configuration in a local octahedral environment, and proposed these systems as candidates for realizing ferro-octupolar order 18,19 . Previous studies of such d 2 quantum magnets 20-22 have argued that the combination of crystal field and interaction effects, leads to the stabilization of a state with total L = 1 and S = 1, which are locked by SOC into a J = 2 spin.…”

“…In recent work, we have studied d-orbital Mott insulators with large SOC and a d 2 configuration in a local octahedral environment, and proposed these systems as candidates for realizing ferro-octupolar order 18,19 . Previous studies of such d 2 quantum magnets [20][21][22] have argued that the combination of crystal field and interaction effects, leads to the stabilization of a state with total L = 1 and S = 1, which are locked by SOC into a J = 2 spin.…”

“…Previous studies of such d 2 quantum magnets [20][21][22] have argued that the combination of crystal field and interaction effects, leads to the stabilization of a state with total L = 1 and S = 1, which are locked by SOC into a J = 2 spin. Motivated by experiments 18,23-26 on certain cubic double perovskite (DP) Mott insulators, Ba 2 ZnOsO 6 , Ba 2 CaOsO 6 , and Ba 2 MgOsO 6 , which host a 5d 2 configuration on Os, we have instead proposed 19 that their observed nontrivial phenomenology, such as entropy and a spin gap, could be captured by assuming that the five-fold J = 2 multiplet is weakly split, resulting in a ground state non-Kramers doublet carrying quadrupolar and octupolar moments. The lack of any observed crystal distortions in X-ray and neutron diffraction experiments appears to rule out quadrupolar order 18 .…”