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Register a new userDiffraction by multipoles in a 5d2 rhenium double perovskite
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A recent polarized neutron diffraction experiment on the 5d2 rhenium double perovskite Ba2YReO6 held at a low temperature uncovered weak magnetic diffraction peaks. Data analysis inferred a significantly reduced Re dipole moment, and long-range order compatible with an antiferromagnet, non-collinear motif. To interpret the experimental findings, we present a model wavefunction for Re ions derived from the crystal field potential, Coulomb interaction, and spin-orbit coupling that fully respects the symmetry of the low-temperature ordered state. It is used to calculate in analytic form all multipole moments visible in neutron and resonance enhanced x-ray diffraction. A minimal model consistent with available neutron diffraction data predicts significant multipolar moments up to the hexadecapole, and, in particular, a dominant charge-like quadrupole moment. Calculated diffraction patterns embrace single crystal x-ray diffraction at the Re L-edge, and renewed neutron diffraction, to probe the presumed underlying multipolar order.
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A theoretical investigation of a plausible construct for electronic structure in iridate perovskites demonstrates the existence of magnetic multipoles hitherto not identified. The strange multipoles, which are parity-even, time-odd and even rank tensors, are absent from the so-called jeff = 1/2 model. We prove that the strange multipoles contribute to magnetic neutron diffraction, and we estimate their contribution to intensities of Bragg spots for Sr2IrO4. The construct encompasses the jeff = 1/2 model, and it is consistent with the known magnetic structure, ordered magnetic moment, and published resonant x-ray Bragg diffraction data. Over and above time-odd quadrupoles and hexadecapoles, whose contribution changes neutron Bragg intensities by an order of magnitude, according to our estimates, are relatively small triakontadipoles recently proposed as the primary magnetic order-parameter of Sr2IrO4.
Structural and magnetic transitions in a double perovskite hosting 5d1 Re ions are discussed on the basis of recently published high-resolution x-ray diffraction patterns [D. Hirai, et al., Phys. Rev. Res. 2, 022063(R) (2020)]. A reported structural transition below room temperature, from cubic to tetragonal symmetry, appears not to be driven by T2g-type quadrupoles, as suggested. A magnetic motif at lower temperature is shown to be composed of two order parameters, associated with propagation vectors k = (0, 0, 1) and k = (0, 0, 0). Findings from our studies, for structural and magnetic properties of Ba2MgReO6, surface in predicted amplitudes for x-ray diffraction at rhenium L2 and L3 absorption edges, and magnetic neutron Bragg diffraction. Specifically, entanglement of anapole and spatial degrees of freedom creates a quadrupole in the neutron scattering amplitude. It would be excluded in an unexpected scenario whereby the rhenium atomic state is a manifold. Also, a chiral signature visible in resonant x-ray diffraction will be one consequence of predicted electronic quadrupole and magnetic dipole orders. A model Re wave function consistent with all current knowledge is a guide to electronic and magnetic multipoles engaged in x-ray and neutron diffraction investigations.
We have carried out inelastic neutron scattering experiments to study magnetic excitations in ordered double perovskite Ca$_2$FeReO$_6$. We found a well-defined magnon mode with a bandwidth of $sim$50meV below the ferri-magnetic ordering temperature ($T_csim$520K), similar to previously studied Ba$_2$FeReO$_6$. The spin excitation is gapless for most temperatures within the magnetically ordered phase. However, a spin gap of $sim$10meV opens up below $sim$150K, which is well below the magnetic ordering temperature but coincides with a previously reported metal-insulator transition and onset of structural distortion. The observed temperature dependence of spin gap provides strong evidence for ordering of Re orbitals at $sim$150~K, in accordance with earlier proposal put forward by Oikawa $it{et.,al}$ based on neutron diffraction [J. Phys. Soc. Jpn., $bf{72}$, 1411 (2003)] as well as recent theoretical work by Lee and Marianetti [Phys. Rev. B, $bf{97}$, 045102 (2018)]. The presence of separate orbital and magnetic ordering in Ca$_2$FeReO$_6$ suggests weak coupling between spin and orbital degrees of freedom and hints towards a sub-dominant role played by spin orbit coupling in describing its magnetism. In addition, we observed only one well-defined magnon band near magnetic zone boundary, which is incompatible with simple ferrimagnetic spin waves arising from Fe and Re local moments, but suggests a strong damping of Re magnon mode.
Cubic double perovskites that host heavy ions with total angular momentum J = 2 can exhibit a singular magnetic state epitomized by a lone octupole and bulk ferro-type magnetism. It exists in the Chen - Balents Hamiltonian with a quadrupole interaction and competing exchange forces between the ions. Our symmetry inspired analysis mirrors the Dzyaloshinskii - Manko theory of latent antiferromagnetic ordering, and a 3-k collinear structure. Experimental tests of the singular state include neutron and x-ray Bragg diffraction.
Soft resonant x-ray Bragg diffraction (SRXD) at the Ho M$_{4,5}$ edges has been used to study Ho $4f$ multipoles in the combined magnetic and orbitally ordered phase of HoB$_2$C$_2$. A full description of the energy dependence for both $sigma$ and $pi$ incident x-rays at two different azimuthal angles, as well as the ratio $I_sigma/I_pi$ as a function of azimuthal angle for a selection of energies, allows a determination of the higher order multipole moments of rank 1 (dipole) to 6 (hexacontatetrapole). The Ho 4f multipole moments have been estimated, indicating a dominant hexadecapole (rank 4) order with an almost negligible influence from either the dipole or the octupole magnetic terms. The analysis incorporates both the intra-atomic magnetic and quadrupolar interactions between the 3d core and 4f valence shells as well as the interference of contributions to the scattering that behave differently under time reversal. Comparison of SRXD, neutron diffraction and non resonant x-ray diffraction shows that the magnetic and quadrupolar order parameter are distinct. The $(0 0 1/2)$ component of the magnetic order exhibits a Brillouin type increase below the orbital ordering temperature T$_Q$, while the quadrupolar order increases more sharply. We conclude the quadrupolar interaction is strong, but quadrupolar order only occurs when the magnetic order gives rise to a quasi doublet ground state, which results in a lock-in of the orbitals at T$_Q$.
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