  Temperature- and field- dependent $^1$H-, $^{19}$F-, and $^{79,81}$Br- NMR
measurements together with zero - field $^{79,81}$Br-NQR measurements on
polycrystalline samples of barlowite, Cu$_4$(OH)$_6$FBr are conducted to study
the magnetism and possible structural distortions on a microscopic level. The
temperature dependence of the $^{79,81}$Br- NMR spin-lattice relaxation rates
1/$T_1$ indicate a phase transition at $T_{\rm N}\simeq$15 K which is of
magnetic origin, but with an unusually weak slowing down of fluctuations below
$T_{\rm N}$. Moreover, 1/$T_1T$ scales linear with the bulk susceptibility
which indicates persisting spin fluctuations down to 2 K. Quadupolare resonance
(NQR) studies reveal a pair of zero-field NQR- lines associated with the two
isotopes of Br with the nuclear spins of $I$ = 3/2. Quadrupole coupling
constants of $\nu_Q\simeq$ 28.5~MHz and 24.7~MHz for $^{79}$Br- and $^{81}$Br-
nuclei are determined from Br-NMR and the asymmetry parameter of the electric
field gradient was estimated to $\eta \simeq 0.2$. The Br-NQR lines are
consistent with our findings from Br-NMR and they are relatively broad, even
above $T_{\rm N}$. This broadening and the relative large $\eta $ value
suggests a symmetry reduction at the Br- site reflecting the presence of a
local distortion in the lattice. Our density-functional calculations show that
the displacements of Cu2 atoms located between the kagome planes do not account
for this relatively large $\eta$. On the other hand, full structural
relaxation, including the deformation of kagome planes, leads to a better
agreement with the experiment.
