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Register a new userOrbital currents, anapoles, and magnetic quadrupoles in CuO
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We show that orbital currents in a CuO2 plane, if present, should be described by two independent parity and time-reversal odd order parameters, a toroidal dipole (anapole) and a magnetic quadrupole. Based on this, we derive the resonant X-ray diffraction cross-section for monoclinic CuO at the antiferromagnetic wavevector and show that the two order parameters can be disentangled. From our analysis, we examine a recent claim of detecting anapoles in CuO.
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We describe square lattice spin liquids which break time-reversal symmetry, while preserving translational symmetry. The states are distinguished by the manner in which they transform under mirror symmetries. All the states have non-zero scalar spin chirality, which implies the appearance of spontaneous orbital charge currents in the bulk (even in the insulator); but in some cases, orbital currents are non-zero only in a formulation with three orbitals per unit cell. The states are formulated using both the bosonic and fermionic spinon approaches. We describe states with $mathbb{Z}_2$ and U(1) bulk topological order, and the chiral spin liquid with semionic excitations. The chiral spin liquid has no orbital currents in the one-band formulation, but does have orbital currents in the three-band formulation. We discuss application to the cuprate superconductors, after postulating that the broken time-reversal and mirror symmetries persist into confining phases which may also break other symmetries. In particular, the broken symmetries of the chiral spin liquid could persist into the Neel state.
We submit that the magnetic space-group Cac (#9.41) is consistent with the established magnetic structure of BaFe2Se3, with magnetic dipole moments in a motif that uses two ladders [Caron J M et al 2011 Phys. Rev. B 84 180409(R)]. The corresponding crystal class m1 allows axial and polar dipoles and forbids bulk ferromagnetism. The compound supports magneto-electric multipoles, including a magnetic charge (monopole) and an anapole (magnetic toroidal dipole) visible in the Bragg diffraction of x-rays and neutrons. Our comprehensive simulation of neutron Bragg diffraction by BaFe2Se3 exploits expressions of a general nature that can be of use with other magnetic materials. Electric toroidal moments are also allowed in BaFe2Se3. A discussion of our findings for resonant x-ray Bragg diffraction illustrates the benefit of a common platform for neutron and x-ray diffraction.
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.
The electronic states near the Fermi level of recently discovered superconductor Ba$_2$CuO$_{4-delta}$ consist primarily of the Cu $d_{x^2-y^2}$ and $d_{3z^2-r^2}$ orbitals. We investigate the electronic correlation effect and the orbital polarization of an effective two-orbital Hubbard model mimicking the low-energy physics of Ba$_2$CuO$_{4-delta}$ in the hole-rich regime by utilizing the dynamical mean-field theory with the Lanczos method as the impurity solver. We find that the hole-overdoped Ba$_2$CuO$_{4-delta}$ with $3d^8$ (Cu$^{3+}$) is in the orbital-selective Mott phase (OSMP) at half-filling, and the typical two-orbital feature remains in Ba$_2$CuO$_{4-delta}$ when the electron filling approaches $n_esim 2.5$, which closely approximates to the experimental hole doping for the emergence of the high-$T_c$ superconductivity. We also obtain that the orbital polarization is very stable in the OSMP, and the multiorbital correlation can drive orbital polarization transitions. These results indicate that in hole-overdoped Ba$_2$CuO$_{4-delta}$ the OSMP physics and orbital polarization, local magnetic moment, and spin or orbital fluctuations still exist. We propose that our present results are also applicable to Sr$_2$CuO$_{4-delta}$ and other two-orbital cuprates, demanding an unconventional multiorbital superconducting scenario in hole-overdoped high-$T_c$ cuprates.
KCrF3 represents another prototypical orbital-ordered perovskite, where Cr2+ possesses the same electronic configuration of 3d4 as that of strongly Jahn-Teller distorted Mn3+ in many CMR manganites. The crystal and magnetic structures of KCrF3 compound are investigated by using polarized and unpolarized neutron powder diffraction methods. The results show that the KCrF3 compound crystallizes in tetragonal structure at room temperature and undergoes a monoclinic distortion with the decrease in temperature. The distortion of the crystal structure indicates the presence of cooperative Jahn-Teller distortion which is driven by orbital ordering. With decreasing temperature, four magnetic phase transitions are observed at 79.5, 45.8, 9.5, and 3.2 K, which suggests a rich magnetic phase diagram. Below T_N = 79.5 K, the Cr2+ moment orders in an incommensurate antiferromagnetic arrangement, which can be defined by the magnetic propagation vector (1/2$pm,$$delta,$, 1/2$pm,$$delta,$, 0). The incommensurate-commensurate magnetic transition occurs at 45.8 K and the magnetic propagation vector locks into (1/2, 1/2, 0) with the Cr moment of 3.34(5) $mu_B ,$ aligned ferromagnetically in (220) plane, but antiferromagnetically along [110] direction. Below 9.5 K, the canted antiferromagnetic ordering and weak ferromagnetism arise from the collinear antiferromagnetic structure, while the Dzyaloshinskii-Moriya interaction and tilted character of the single-ion anisotropy might give rise to the complex magnetic behaviors below 9.5 K.
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