Motivated by the recent reports of high-$T_c$ superconductivity in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ under pressure, we analyzed theoretically the magnetic excitations in the normal and the superconducting state in this compound, which can be measured by inelastic neutron scattering or resonant inelastic x-ray scattering. We show that the bilayer structure of the spin response allows us to elucidate the role of the interlayer interaction and the nature of the Cooper pairing in a very efficient way. In particular, we demonstrate the key difference between the potential $s_{\pm }$- and $d$-wave gaps, proposed recently, by comparing the corresponding response in the even and odd channels of the spin susceptibility. We show that the mostly interlayer driven bonding-antibonding $s_{\pm }$ Cooper pairing produces a single large spin resonance peak in the odd channel only near the $X$ point, whereas spin resonances in both the odd and the even channel are predicted for the $d$-wave scenario.

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• Multiband superconductivity
• Spin fluctuations
• d-wave
• s-wave
• Nickelates
• Unconventional superconductors
• Random phase approximation