August 10, 2005
Resonant x-ray diffraction performed at the $\rm L_{II}$ and $\rm L_{III}$ absorption edges of Ru has been used to investigate the magnetic and orbital ordering in Ca$_2$RuO$_4$ single crystals. A large resonant enhancement due to electric dipole $2p\to 4d$ transitions is observed at the wave-vector characteristic of antiferromagnetic ordering. Besides the previously known antiferromagnetic phase transition at $\rm T_{N}=110$ K, an additional phase transition, between two paramagnetic phases, is observed around 260 K. Based on the polarization and azimuthal angle dependence of the diffraction signal, this transition can be attributed to orbital ordering of the Ru $t_{2g}$ electrons. The propagation vector of the orbital order is inconsistent with some theoretical predictions for the orbital state of Ca$_2$RuO$_4$.
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July 2, 2018
We review the magnetic and orbital ordered states in \cro{} by performing Resonant Elastic X-ray Scattering (REXS) at the Ru L$_{2,3}$-edges. In principle, the point symmetry at Ru sites does not constrain the direction of the magnetic moment below $T_N$. However early measurements reported the ordered moment entirely along the $\vec{b}$ orthorhombic axis. Taking advantage of the large resonant enhancement of the magnetic scattering close to the Ru L$_2$ and L$_3$ absorption ...
August 31, 2001
The key role of the orbital degree of freedom to understand the magnetic properties of layered ruthenates is here discussed. In the G-type antiferromagnetic phase of Ca$_2$RuO$_4$, recent X-ray experiments reported the presence of 0.5 hole per site in the $d_{xy}$ orbital, while the $d_{\rm yz}$ and $d_{zx}$ orbitals contain 1.5 holes. This unexpected $t_{2g}$ hole distribution is explained by a novel state with orbital ordering (OO), stabilized by a combination of Coulomb in...
August 18, 2018
We employ an optical pump-probe technique to study coherent phonon oscillations in Ca$_2$RuO$_4$. We find that oscillation-amplitude of an $A_g$ symmetric phonon mode is strongly suppressed at 260 K, a putative transition point of orbital ordering. The oscillation also shows a gradual but huge change in its $phase$, such that the oscillation even flips over with a 180$^{\circ}$ change across the temperature. Density functional theory calculations indicate that the $A_g$ phono...
September 12, 2018
For the past decades, the low-temperature phase of Ca$_3$Ru$_2$O$_7$ below the 48K first-order phase transition remains a puzzle with controversial suggestions involving metallic ferroelectric, orbital or magnetic ordering. Through analysis of experimental lattice structure, density functional theory calculation, and effective model analysis, we propose that the 48K phase transition is a bond formation transition promoted by the magnetism mediated orbital re-polarization. Mos...
July 13, 2000
The phase diagram of Ca$_{2-x}$Sr$_x$RuO$_4$ has been studied by neutron diffraction on powder and single-crystalline samples. The experiments reveal antiferromagnetic order and structural distortions characterized by tilts and rotations of the RuO$_6$-octahedra. There is strong evidence that the structural details of the isovalent samples tune the magnetic as well as the electronic behavior. In particular we observe for low Sr-concentration a metal insulator transition assoc...
July 30, 2020
The crystalline and magnetic structures of Ca$_2$Ru$_{1-x}$Fe$_x$O$_4$ (x=0.02, 0.05, 0.08 and 0.12) have been studied using neutron and X-ray diffraction. The Fe-doping reduces the Ru-O bond length in both apical and planar directions. The smaller Ru(Fe)O$_6$ octahedron leads to its reduced distortion. The $Pbca$ space group is maintained in all the Fe-dopings, so is the octahedral flattening. Warming has a similar effect on the lattice to that of the Fe-doping in releasing ...
June 3, 2020
Including the orbital off-diagonal spin and charge condensates in the self consistent determination of magnetic order within a realistic three-orbital model for the $4d^4$ compound $\rm Ca_2 Ru O_4$, reveals a host of novel features including strong and anisotropic spin-orbit coupling (SOC) renormalization, coupling of strong orbital magnetic moments to orbital fields, and a magnetic reorientation transition. Highlighting the rich interplay between orbital geometry and overla...
May 10, 2013
We have studied relationship between local lattice disorder, Ru 4$d$ spin-orbit interaction, and global spin/orbital orders of Ca$_{2-x}$Sr$_x$RuO$_4$ in the Sr-rich and Ca-rich regions of its phase diagram by using unrestricted Hartree-Fock calculation on a $8\times8$ RuO$_4$ lattice model. The calculations show that the local elongation of RuO$_6$ octahedron in an antiferromagnetic insulator Ca$_2$RuO$_4$ induces local orbital change with making the Mott gap narrower. On th...
August 1, 2019
The quadruple perovskite CaMn$_7$O$_{12}$ is a topical multiferroic, in which the hierarchy of electronic correlations driving structural distortions, modulated magnetism, and orbital order is not well known and may vary with temperature. x-ray resonant elastic scattering (XRES) provides a momentum-resolved tool to study these phenomena, even in very small single crystals, with valuable information encoded in its polarization- and energy-dependence. We present an application ...
February 4, 2004
We present first-principles studies on the orbital states of the layered perovskites Ca$_{2-x}$Sr$_x$RuO$_4$. The crossover from antiferromagnetic (AF) Mott insulator for $x < 0.2$ to nearly ferromagnetic (FM) metal at $x=0.5$ is characterized by the systematic change of the $xy$ orbital occupation. For the AF side ($x < 0.2$), we present firm evidence for the $xy$ ferro-orbital ordering. It is found that the degeneracy of $t_{2g}$ (or $e_g$) states is lifted robustly due to ...