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Register a new userFerro-octupolar order and low-energy excitations in d$^2$ double perovskites of Osmium
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Conflicting interpretations of experimental data preclude the understanding of the quantum magnetic state of spin-orbit coupled d$^2$ double perovskites. Whether the ground state is a Janh-Teller-distorted order of quadrupoles or the hitherto elusive octupolar order remains debated. We resolve this uncertainty through direct calculations of all-rank inter-site exchange interactions and inelastic neutron scattering (INS) cross-section for the d$^2$ double perovskite series Ba$_2M$OsO$_6$ ($M$= Ca, Mg, Zn). Using advanced many-body first principles methods we show that the ground state is formed by ferro-ordered octupoles coupled within the ground-stated $E_g$ doublet. Computed ordering temperature of the single second-order phase-transition and gapped excitation spectra are fully consistent with observations. Minuscule distortions of the parent cubic structure are shown to qualitatively modify the structure of magnetic excitations.
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We report time-of-flight neutron spectroscopic and diffraction studies of the 5$d^2$ cubic double pervoskite magnets, Ba$_2$MOsO$_6$ ($M$ = Zn, Mg, Ca). These cubic materials are all described by antiferromagnetically-coupled 5$d^2$ Os$^{6+}$ ions decorating a face-centred cubic (FCC) lattice. They all exhibit thermodynamic anomalies consistent with phase transitions at a temperature $T^*$, and exhibit a gapped magnetic excitation spectrum with spectral weight concentrated at wavevectors typical of type I antiferromagnetic orders. While muon spin resonance experiments show clear evidence for time reversal symmetry breaking, no corresponding magnetic Bragg scattering is observed at low temperatures. These results, consistent with low temperature octupolar or quadrupolar order, are discussed in the context of other 5$d^2$ DP magnets, and theories for $d^2$ ions on a FCC lattice which predict exotic orders driven by multipolar interactions.
In 5$d^2$ Mott insulators with strong spin-orbit coupling, the lowest pseudospin states form a non-Kramers doublet, which carries quadrupolar and octupolar moments. A family of double-perovskites where magnetic ions form a face-centered cubic (FCC) lattice, was suggested to unveil an octupolar order offering a rare example in d-orbital systems. The proposed order requires a ferromagnetic octupolar interaction, since the antiferromagnetic (AFM) Ising model is highly frustrated on the FCC lattice. A microscopic model was recently derived for various lattices: for an edge sharing octahedra geometry, AFM Ising octupolar and bond-dependent quadrupolar interactions were found when only dominant inter- and intra-orbital hopping integrals are taken into account. Here we investigate all possible intra- and inter-orbital exchange processes and report that interference of two intra-orbital exchanges generates a ferromagnetic octupolar interaction. Applying the strong-coupling expansion results together with tight binding parameters obtained by density functional theory, we estimate the exchange interactions for the Osmium double-perovskites, Ba$_2$BOsO$_6$ (B = Mg, Ca). Using classical Monte-Carlo simulations, we show these double-perovskites exhibit type-I AFM quadrupolar order followed by an intriguing partial quadrupole order above the transition temperature. Implications of our theory and a way to generate the octupolar order are discussed.
Motivated by experimental and theoretical interest in realizing multipolar orders in $d$-orbital materials, we discuss the quantum magnetism of $J!=!2$ ions 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 ferro-octupolar order for a face-centered cubic lattice. This same mechanism is also shown to disfavor quadrupolar ordering. We show that studying crystal field levels via Raman scattering in a magnetic field provides a probe of octupolar order. 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 (AFM) 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, $mu$SR, X-ray diffraction, and inelastic neutron scattering measurements on a range of cubic $5d^2$ double perovskite materials including Ba$_2$ZnOsO$_6$, Ba$_2$CaOsO$_6$, and Ba$_2$MgOsO$_6$. Our proposal for exciton condensation leading to type-I AFM order may be relevant to materials such as Sr$_2$MgOsO$_6$.
The nature of the unconventional ordered phase occurring in CeRu2Al10 below T0 = 27 K was investigated by neutron scattering. Powder diffraction patterns show clear superstructure peaks corresponding to forbidden (h + k)-odd reflections of the Cmcm space group. Inelastic neutron scattering experiments further reveal a pronounced magnetic excitation developing in the ordered phase at an energy of 8 meV.
Quantum magnets with spin $J=2$, which arise in spin-orbit coupled Mott insulators, can potentially display multipolar orders. We carry out an exact diagonalization study of a simple octahedral crystal field Hamiltonian for two electrons, incorporating spin-orbit coupling (SOC) and interactions, finding that either explicitly including the $e_g$ orbitals, or going beyond the rotationally invariant Coulomb interaction within the $t_{2g}$ sector, causes a degeneracy breaking of the $J!=!2$ level degeneracy. This can lead to a low-lying non-Kramers doublet carrying quadrupolar and octupolar moments and an excited triplet which supports magnetic dipole moments, bolstering our previous phenomenological proposal for the stabilization of ferro-octupolar order in heavy transition metal oxides. We show that the spontaneous time-reversal symmetry breaking due to ferro-octupolar ordering within the non-Kramers doublet leads to electronic orbital loop currents. The resulting internal magnetic fields can potentially explain the small fields inferred from muon-spin relaxation ($mu$SR) experiments on cubic $5d^2$ osmate double perovskites Ba$_2$ZnOsO$_6$, Ba$_2$CaOsO$_6$, and Ba$_2$MgOsO$_6$, which were previously attributed to weak dipolar magnetism. We make further predictions for oxygen NMR experiments on these materials. We also study the reversed level scheme, where the $J!=!2$ multiplet splits into a low-lying magnetic triplet and excited non-Kramers doublet, presenting single-ion results for the magnetic susceptibility in this case, and pointing out its possible relevance for the rhenate Ba$_2$YReO$_6$. Our work highlights the intimate connection between the physics of heavy transition metal oxides and that of $f$-electron based heavy fermion compounds.
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