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Register a new userMagnetic response of Sr$_2$RuO$_4$: quasi-local spin fluctuations due to Hunds coupling
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We study the magnetic susceptibility in the normal state of Sr$_2$RuO$_4$ using dynamical mean-field theory including dynamical vertex corrections. Besides the well known incommensurate response, our calculations yield quasi-local spin fluctuations which are broad in momentum and centered around the $Gamma$ point, in agreement with recent inelastic neutron scattering experiments [P. Steffens, et al., Phys. Rev. Lett. 122, 047004 (2019)]. We show that these quasi-local fluctuations are controlled by the Hunds coupling and account for the dominant contribution to the momentum-integrated response. While all orbitals contribute equally to the incommensurate response, the enhanced $Gamma$ point response originates from the planar xy orbital.
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A paradigmatic case of multi-band Mott physics including spin-orbit and Hunds coupling is realised in Ca$_2$RuO$_4$. Progress in understanding the nature of this Mott insulating phase has been impeded by the lack of knowledge about the low-energy electronic structure. Here we provide -- using angle-resolved photoemission electron spectroscopy -- the band structure of the paramagnetic insulating phase of Ca$_2$RuO$_4$ and show how it features several distinct energy scales. Comparison to a simple analysis of atomic multiplets provides a quantitative estimate of the Hunds coupling $J=0.4$ eV. Furthermore, the experimental spectra are in good agreement with electronic structure calculations performed with Dynamical Mean-Field Theory. The crystal field stabilisation of the d$_{xy}$ orbital due to $c$-axis contraction is shown to be important in explaining the nature of the insulating state. It is thus a combination of multiband physics, Coulomb interaction and Hunds coupling that generates the Mott insulating state of Ca$_2$RuO$_4$. These results underscore the importance of Hunds coupling in the ruthenates and related multiband materials.
The Hall coefficient $R_H$ of Sr$_2$RuO$_4$ exhibits a non-monotonic temperature dependence with two sign reversals. We show that this puzzling behavior is the signature of two crossovers which are key to the physics of this material. The increase of $R_H$ and the first sign change upon cooling are associated with a crossover into a regime of coherent quasiparticles with strong orbital differentiation of the inelastic scattering rates. The eventual decrease and the second sign change at lower temperature is driven by the crossover from inelastic to impurity-dominated scattering. This qualitative picture is supported by quantitative calculations of $R_H(T)$ using Boltzmann transport theory in combination with dynamical mean-field theory, taking into account the effect of spin-orbit coupling. Our insights shed new light on the temperature dependence of the Hall coefficient in materials with strong orbital differentiation, as observed in Hunds metals.
We use Ru $L_3$-edge (2838.5 eV) resonant inelastic x-ray scattering (RIXS) to quantify the electronic structure of Ca$_2$RuO$_4$, a layered $4d$-electron compound that exhibits a correlation-driven metal-insulator transition and unconventional antiferromagnetism. We observe a series of Ru intra-ionic transitions whose energies and intensities are well described by model calculations. In particular, we find a $rm{J}=0rightarrow 2$ spin-orbit excitation at 320 meV, as well as Hunds-rule driven $rm{S}=1rightarrow 0$ spin-state transitions at 750 and 1000 meV. The energy of these three features uniquely determines the spin-orbit coupling, tetragonal crystal-field energy, and Hunds rule interaction. The parameters inferred from the RIXS spectra are in excellent agreement with the picture of excitonic magnetism that has been devised to explain the collective modes of the antiferromagnetic state. $L_3$-edge RIXS of Ru compounds and other $4d$-electron materials thus enables direct measurements of interactions parameters that are essential for realistic model calculations.
We analyze the spin anisotropy of the magnetic susceptibility of Sr$_2$RuO$4$ in presence of spin-orbit coupling and anisotropic strain using quasi-two-dimensional tight-binding parametrization fitted to the ARPES results. Similar to the previous observations we find the in-plane polarization of the low ${bf q}$ magnetic fluctuations and the out-of-plane polarization of the incommensurate magnetic fluctuation at the nesting wave vector ${bf Q}_1 = (2/3 pi ,2/3 pi)$ but also nearly isotropic fluctuations near ${bf Q}_2=(pi/6,pi/6)$. Furthermore, one finds that apart from the high-symmetry direction of the tetragonal Brillouin zone the magnetic anisotropy is maximal, i.e. $chi^{xx} eq chi^{yy} eq chi^{zz}$. This is the consequence of the orbital anisotropy of the $xz$ and $yz$ orbitals in the momentum space. We also study how the magnetic anisotropy evolves in the presence of the strain and find strong Ising-like ferromagnetic fluctuations near the Lifshitz transition for the $xy$-band.
We have studied the influence of a magnetic field on the thermodynamic properties of Ca$_{2-x}$Sr$_{x}$RuO$_4$ in the intermediate metallic region with tilt and rotational distortions ($0.2leq x leq 0.5$). We find strong and anisotropic thermal expansion anomalies at low temperatures, which are suppressed and even reversed by a magnetic field. The metamagnetic transition of Ca$_{1.8}$Sr$_{0.2}$RuO$_4$ is accompanied by a large magnetostriction. Furthermore, we observe a strong magnetic-field dependence of $c_p/T$, that can be explained by magnetic fluctuations.
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