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Register a new userQuadrupolar Superexchange Interactions, Multipolar Order and Magnetic Phase Transition in UO$_2$
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The origin of non-collinear magnetic order in UO$_{2}$ is studied by an ab initio dynamical-mean-field-theory framework in conjunction with a linear-response approach for evaluating inter-site superexchange interactions between U 5$f^{2}$ shells. The calculated quadrupole-quadruple superexchange interactions are found to unambiguously resolve the frustration of face-centered-cubic U sublattice toward stabilization of the experimentally observed non-collinear 3k-magnetic order. Therefore, the exotic 3k antiferromagnetic order in UO$_{2}$ can be accounted for by a purely electronic exchange mechanism acting in the undistorted cubic lattice structure. The quadrupolar short-range order above magnetic ordering temperature $T_N$ is found to qualitatively differ from the long-range order below $T_N$.
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To explore the formation of noncollinear magnetic configurations in materials with strongly correlated electrons, we derive a noncollinear LSDA+$U$ model involving only one parameter $U$, as opposed to the difference between the Hubbard and Stoner parameters $U-J$. Computing $U$ in the constrained random phase approximation, we investigate noncollinear magnetism of uranium dioxide UO$_2$ and find that the spin-orbit coupling (SOC) stabilizes the 3$textbf{k}$ ordered magnetic ground state. The estimated SOC strength in UO$_2$ is as large as 0.73 eV per uranium atom, making spin and orbital degrees of freedom virtually inseparable. Using a multipolar pseudospin Hamiltonian, we show how octupolar and dipole-dipole exchange coupling help establish the 3$textbf{k}$ magnetic ground state with canted ordering of uranium $f$-orbitals. The cooperative Jahn-Teller effect does not appear to play a significant part in stabilizing the noncollinear 3$textbf{k}$ state, which has the lowest energy even in an undistorted lattice. The choice of parameter $U$ in the LSDA+$U$ model has a notable quantitative effect on the predicted properties of UO$_2$, in particular on the magnetic exchange interaction and, perhaps trivially, on the band gap: The value of $U=3.46$ eV computed fully $ab$ $initio$ delivers the band gap of 2.11~eV in good agreement with experiment, and a balanced account of other pertinent energy scales.
An approach is proposed for evaluating dipolar and multipolar inter-site interactions in strongly correlated materials. This approach is based on the single-site dynamical mean-field theory (DMFT) in conjunction with the atomic approximation for the local self-energy. Starting from the local moment paramagnetic state described by DMFT we derive inter-site interactions by considering the response of the DMFT grand potential to small fluctuations of atomic configurations on two neighboring sites. The present method is validated by applying it to one-band and two-band e$_g$ Hubbard models on the simple-cubic 3$d$ lattice. It is also applied to study the spin-orbital order in the parent cubic structure of ternary chromium fluoride KCrF$_3$. We obtain the onset of a G-type antiferro-orbital order at a significantly lower temperature compared to that in real distorted KCrF$_3$. In contrast, its layered A-type antiferromagnetic order and Neel temperature are rather well reproduced. The calculated full Kugel-Khomskii Hamiltonian contains spin-orbital coupling terms inducing a misalignment in the antiferro-orbital order upon the onset of antiferromagnetism.
Structural phase transition accompanying with quadrupolar ordering in DyB4 with Shastry-Sutherland type geometrical frustration has been studied by X-ray diffraction. Previous study [D. Okuyama et al.: J. Phys. Soc. Jpn. 74 (2005) 2434.] using resonant X-ray scattering revealed short-range ordering of the Ozx-type quadrupolar moments and the c-plane component of the magnetic moments in addition to long-range ordering of the c-axis component of the magnetic moments. The present report focuses on the lattice distortion below the quadrupolar ordering temperature at TN2=12.7 K. The (0 0 l=integer) fundamental lattice reflection splits into four peaks along the h and k directions and the (h=even 0 0) reflection becomes broad along the l direction. This indicates that a structural transition from tetragonal to monoclinic takes place below TN2 together with the ordering of the quadrupolar moments.
CaFe$_2$As$_2$ has been synthesized and found to form in the tetragonal, ThCr$_2$Si$_2$ structure with lattice parameters $a = 3.912(68) AA$ and $c = 11.667(45) AA$. Upon cooling through 170 K, CaFe$_2$As$_2$ undergoes a first order, structural phase transition to a low temperature, orthorhombic phase with a $2 - 3$ K range of hysteresis and coexistence. This transition is clearly evident in microscopic, thermodynamic and transport measurements. CaFe$_2$As$_2$ is the third member of the AFe$_2$As$_2$ (A = Ba, Sr, Ca) family to exhibit such a dramatic phase transition and is a promising candidate for studies of doping induced superconductivity.
The Mott-insulating iron oxychalcogenides exhibit complex magnetic behaviour and we report here a neutron diffraction investigation into the magnetic ordering in La2O2Fe2OS2. This quaternary oxysulfide adopts the anti-Sr2MnO2Sb2-type structure and orders antiferromagnetically below TN = 105 K. We consider both its long-range magnetic structure and its magnetic microstructure, and the onset of magnetic order. It adopts the multi-k vector 2k magnetic structure (k = (0.5 0 0.5) and k = (0 0.5 0.5) and has similarities with related iron oxychalcogenides, illustrating the robust nature of the 2k magnetic structure.
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