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Register a new userAntiferromagnetism in RuO$_2$ as $d$-wave Pomeranchuk instability
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We present a computational study of antiferromagnetic transition in RuO$_2$. The rutile structure with the magnetic sublattices coupled by $pi/2$-rotation leads to a spin-polarized band structure in the antiferromagnetic state, which gives rise to a $d$-wave modulation of the Fermi surface in the spin-triplet channel. We argue a finite spin conductivity that changes sign in the $ab$ plane is expected RuO$_2$ because of this band structure. We analyze the origin of the antiferromagnetic instability and link it to presence of a nodal line close to the Fermi level.
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Bulk rutile RuO$_2$ has long been considered a Pauli paramagnet. Here we report that RuO$_2$ exhibits a hitherto undetected lattice distortion below approximately 900 K. The distortion is accompanied by antiferromagnetic order up to at least 300 K with a small room temperature magnetic moment of approximately 0.05 $mu_B$ as evidenced by polarized neutron diffraction. Density functional theory plus $U$ (DFT+$U$) calculations indicate that antiferromagnetism is favored even for small values of the Hubbard $U$ of the order of 1 eV. The antiferromagnetism may be traced to a Fermi surface instability, lifting the band degeneracy imposed by the rutile crystal field. The combination of high Neel temperature and small itinerant moments make RuO$_2$ unique among ruthenate compounds and among oxide materials in general.
Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here we report unbiased Quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same onsite symmetries as the standard Hubbard model on a 2D square lattice. Using QMC, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the Heisenberg-Gross-Neveu theory. The topology of our phase diagram resembles that of layered organic materials which host pressure tuned Mott transition from antiferromagnet to unconventional superconductor at half-filling.
Recently, rutile RuO$_2$ has raised interest for its itinerant antiferromagnetism, crystal Hall effect, and strain-induced superconductivity. Understanding and manipulating these properties demands resolving the electronic structure and the relative roles of the rutile crystal field and $4d$ spin-orbit coupling (SOC). Here, we use O-K and Ru $M_3$ x-ray absorption (XAS) and Ru $M_3$ resonant inelastic x-ray scattering (RIXS) to disentangle the contributions of crystal field, SOC, and electronic correlations in RuO$_2$. The locally orthorhombic site symmetry of the Ru ions introduces significant crystal field contributions beyond the approximate octahedral coordination yielding a crystal field energy scale of $Delta(t_{2g})approx 1$ eV breaking the degeneracy of the $t_{2g}$ orbitals. This splitting exceeds the Ru SOC ($approx160$ meV) suggesting a more subtle role of SOC, primarily through the modification of itinerant (rather than local) $4d$ electronic states, ultimately highlighting the importance of the local symmetry in RuO$_2$. Remarkably, our analysis can be extended to other members of the rutile family, thus advancing the comprehension of the interplay among crystal field symmetry, electron correlations, and SOC in transition metal compounds with the rutile structure.
We studied the magnetic ordering of thin films and bulk crystals of rutile RuO$_2$ using resonant X-ray scattering across the Ru L$_2$ absorption edge. Combining polarization analysis and azimuthal-angle dependence of the magnetic Bragg signal, we have established the presence of G-type antiferromagnetism in RuO$_2$ with T$_N$ $>$ 300 K. In addition to revealing a spin-ordered ground state in the simplest ruthenium oxide compound, the persistence of magnetic order even in nanometer-thick films lays the ground for potential applications of RuO$_2$ in antiferromagnetic spintronics.
We derive renormalization group equations which allow us to treat order parameter fluctuations near quantum phase transitions in cases where an expansion in powers of the order parameter is not possible. As a prototypical application, we analyze the nematic transition driven by a d-wave Pomeranchuk instability in a two-dimensional electron system. We find that order parameter fluctuations suppress the first order character of the nematic transition obtained at low temperatures in mean-field theory, so that a continuous transition leading to quantum criticality can emerge.
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