Theory of magnetic excitations in the multilayer nickelate superconductor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>La</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>Ni</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>7</mml:mn></mml:msub></mml:mrow></mml:math>
Steffen Bötzel, Frank Lechermann, Jannik Gondolf, Ilya Eremin
Abstract
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 ${s}_{\ifmmode\pm\else\textpm\fi{}}$- 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 ${s}_{\ifmmode\pm\else\textpm\fi{}}$ 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.