  We investigate the effects of Dzyaloshinsky-Moriya (DM) interactions on the
frustrated $J_1$-$J_2$ kagome-Heisenberg model using the pseudo-fermion
functional-renormalization-group (PFFRG) technique. In order to treat the
off-diagonal nature of DM interactions, we develop an extended PFFRG scheme. We
benchmark this approach in parameter regimes that have previously been studied
with other methods and find good agreement of the magnetic phase diagram.
Particularly, finite DM interactions are found to stabilize all types of
non-collinear magnetic orders of the $J_1$-$J_2$ Heisenberg model
($\mathbf{q}=0$, $\sqrt{3}\times\sqrt{3}$, and cuboc orders) and shrink the
extents of magnetically disordered phases. We discuss our results in the light
of the mineral {\it herbertsmithite} which has been experimentally predicted to
host a quantum spin liquid at low temperatures. Our PFFRG data indicates that
this material lies in close proximity to a quantum critical point. In parts of
the experimentally relevant parameter regime for {\it herbertsmithite}, the
spin-correlation profile is found to be in good qualitative agreement with
recent inelastic-neutron-scattering data.

Strongly Correlated Electrons