  Recent studies reveal that four-phonon scattering is generally important in
determining thermal conductivities of solids. However, these studies have been
focused on materials where thermal conductivity $\kappa$ is dominated by
acoustic phonons, and the impact of four phonon scattering, although
significant, is still generally smaller than three-phonon scattering. In this
work, taking AlSb as example, we demonstrated that four-phonon scattering is
even more critical to three-phonon scattering as it diminishes optical phonon
thermal transport, and therefore significantly reduces the thermal
conductivities of materials in which optical branches have long three-phonon
lifetimes. Also, our calculations show that four-phonon scattering can play an
extremely important role in weakening the isotope effect on $\kappa$.
Specifically, four-phonon scattering reduces the room-temperature $\kappa$ of
the isotopically pure and natural-occurring AlSb by 70$\%$ and 50$\%$,
respectively. The reduction for isotopically pure and natural-occurring c-GaN
is about 34$\%$ and 27$\%$, respectively. For isotopically-pure w-GaN, the
reduction is about 13$\%$ at room temperature and 25$\%$ at 400 K. These
results provided important guidance for experimentalists for achieving high
thermal conductivities in III-V compounds for applications in semiconductor
industry.
