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We investigate the evolution of magnetic excitations in Sr$_3$Ru$_2$O$_7$using a three band tight binding model that takes into account the influence ofMn and Ti dopant ions. The effect of dopant ions on the Sr$_3$Ru$_2$O$_7$ bandstructure has been included by taking into account the dopant inducedsuppression of the oxygen octahedral rotation in the tight binding bandstructure and changes in electron occupation. We find that the low energy spinfluctuations are dominated by three wave vectors aroundQ=$((0,0),(\pi/2,\pi/2))$, and $(\pi,0)$ which compete with each other. As theoctahedral rotation is suppressed with increasing doping, the three wavevectors evolve differently. In particular, the undoped compound has dominantwavevectors at Q=$((0,0),(\pi/2,\pi/2))$, but doping Sr$_3$Ru$_2$O$_7$ leads toa significant enhancement in the spin susceptibility at the Q=$(\pi,0)$wavevector bringing the system closer to a magnetic instability. All thefeatures calculated from our model are in agreement with neutron scatteringexperiments. We have also studied the effect of a c-axis Zeeman field on thelow energy spin fluctuations. We find that an increasing magnetic fieldsuppresses the AFM fluctuations and leads to stronger competition between theAFM and FM spin fluctuations. The magnetic field dependence observed in ourcalculations therefore supports the scenario that the observed nematic phase inthe metamagnetic region in Sr$_3$Ru$_2$O$_7$ is intimately related to thepresence of a competing ferromagnetic instability.

Structural and magnetic field effects on spin fluctuations in Sr$_{3}$Ru$_2$O$_7$