  We investigate the effect of an external horizontal magnetic field on the
K\"{u}ppers-Lortz instability (KLI) in rotating Rayleigh-B\'{e}nard convection
of Boussinesq fluids using weakly nonlinear theory along with linear theory. By
KLI, we mean the instability where the two-dimensional roll solutions of the
system occurring at the onset of convection becomes unstable against the
perturbations by rolls oriented at different angle with the previous one as the
rotation rate exceeds a critical value. The governing parameters, namely, the
Prandtl number ($\mathrm{Pr}$), Taylor number ($\mathrm{Ta}$) and Chandrasekhar
number ($\mathrm{Q}$) are varied in the ranges $0.8 \leq \mathrm{Pr} < \infty$,
$0 < \mathrm{Ta} \leq 10^4$ and $0 \leq \mathrm{Q} \leq 10^4$ respectively by
considering the vanishingly small magnetic Prandtl number limit. In the
$\mathrm{Pr}\rightarrow \infty$ limit, magnetic field is found to inhibit the
KLI by enhancing the critical Taylor number ($\mathrm{Ta}_c$) for its onset. On
the other hand, for finite Prandtl number fluids, KLI is favored for lower
$\mathrm{Q}$, and it is inhibited for higher $\mathrm{Q}$. Interestingly, in
the finite Prandtl number range both KLI and small angle instability are
manifested depending on the Prandtl number. No small angle instability is
observed for $\mathrm{Pr} \geq 50$ and the rotation induced KLI is inhibited
predominantly by the magnetic field. While, for $\mathrm{Pr} < 50$, along with
the K\"{u}ppers-Lortz instability, small angle instability is also observed.
However, in this case, KLI is favored for lower $\mathrm{Q}$, while it is
inhibited for higher $\mathrm{Q}$.
