We analyze the spin anisotropy of the magnetic susceptibility of Sr2RuO4 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 q magnetic fluctuations and the out-of-plane polarization of the incommensurate magnetic fluctuation at the nesting wave vector Q1 = (2/3π, 2/3π) but also nearly isotropic fluctuations near Q2 = (π/6, π/6). Furthermore, one finds that apart from the high-symmetry direction of the tetragonal Brillouin zone the magnetic anisotropy is maximal, i.e. χ xx = χ yy = χ 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.
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