Abstract
Ti substituting Ru in Sr$_2$RuO$_4$ in small concentrations induces incommensurate spin density wave order with a wave vector $\boldsymbol{Q} \simeq (2 \pi /3, 2 \pi /3)$ corresponding to the nesting vector of two out of three Fermi surface sheets. We consider a microscopic model for these two bands and analyze the correlation effects leading to magnetic order through non-magnetic Ti-doping. For this purpose we use a position dependent mean field approximation for the microscopic model and a phenomenological Ginzburg-Landau approach, which both deliver consistent results and allow us to examine the inhomogeneous magnetic order. Spin-orbit coupling additionally leads to spin currents around each impurity, which in combination with the magnetic polarization produce a charge current pattern. This is also discussed within a gauge field theory in both charge and spin channel. This spin-orbit coupling effect causes an interesting modification of the magnetic structure, if currents run through the system. Our findings allow a more detailed analysis of the experimental data for Sr$_{2}$Ru$_{1-x}$Ti$_{x}$O$_{4}$. In particular, we find that the available measurements are consistent with our theoretical predictions.
Highlights
Motivated by the discovery of unconventional superconductivity, Sr2RuO4 has been studied extensively for well over two decades due to its many intriguing properties [1,2,3,4]
Incommensurate (IC) correlations have been experimentally observed at the wave vector Q (2π /3, 2π /3) [10,11,12,13,14,15,16], very consistent with theoretical predictions [17,18,19,20,21]
We find that the dominant magnetic correlation in the pure system is connected with the four IC wave vectors Q (±2π /3, 0) and (0, ±2π /3), which, if strong enough, would lead to a spin density wave state based on these wave vectors
Summary
Motivated by the discovery of unconventional superconductivity, Sr2RuO4 has been studied extensively for well over two decades due to its many intriguing properties [1,2,3,4]. Due to its strongly correlated Fermi-liquid properties in the normal state Sr2RuO4 with its single-layer perovskite structure has been considered a two-dimensional analog of 3He [8,9]. Sr2RuO4 falls barely short of establishing magnetic longrange order originating from the strong IC correlations It was, found that replacing some Ru4+ by nonmagnetic Ti4+ (3d0) induces magnetic order already at rather low Ti concentrations, x > 0.025 in Sr2Ru1−xTixO4 [25]. From the microscopic model of the α-β bands including spin-orbit coupling we develop a mean-field theory for a spatially dependent magnetization of the two involved 4d orbitals and determine the pattern of magnetic order around a single impurity. We will analyze the magnetic structure induced by nonmagnetic impurities based on a microscopic model of the α-β bands including the effects of spin-orbit coupling (Sec. II). These phenomena may allow for interesting probes of the magnetic properties of such a system
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