Electronic theory for the normal state spin dynamics in Sr₂RuO₄: anisotropy due to spin-orbit coupling

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Using a three-band Hubbard Hamiltonian we calculate within the random-phase-approximation the spin susceptibility, χ(q,ω), and NMR spin-lattice relaxation rate, 1/T₁, in the normal state of the triplet superconductor Sr₂RuO₄ and obtain quantitative agreement with experimental data. Most importantly, we find that due to spin-orbit coupling the out-of-plane component of the spin susceptibility χzz becomes at low temperatures two times larger than the in-plane one. As a consequence strong incommensurate antiferromagnetic fluctuations of the quasi-one-dimensional xz- and yz-bands point into the z-direction. Our results provide further evidence for the importance of spin fluctuations for triplet superconductivity in Sr₂RuO₄.