  Gravitational-wave signals from binaries that contain spinning black holes in
general include an asymmetry between the $+m$ and $-m$ multipoles that is not
included in most signal models used in LIGO-Virgo-KAGRA (LVK) analysis to date.
This asymmetry manifests itself in out-of-plane recoil of the final black hole
and its inclusion in signal models is necessary both to measure this recoil,
but also to accurately measure the full spin information of each black hole. We
present the first model of the anti-symmetric contribution to the dominant
co-precessing-frame signal multipole throughout inspiral, merger and ringdown.
We model the anti-symmetric contribution in the frequency domain, and take
advantage of the approximations that the anti-symmetric amplitude can be
modelled as a ratio of the (already modelled) symmetric amplitude, and analytic
relationships between the symmetric and anti-symmetric phases during the
inspiral and ringdown. The model is tuned to single-spin numerical-relativity
simulations up to mass-ratio 8 and spin magnitudes of 0.8, and has been
implemented in a recent phenomenological model for use in the fourth LVK
observing run. However, the procedure described here can be easily applied to
other time- or frequency-domain models.
