  To probe the $Wtb$ vertex structure, top-quark and $W$-boson polarisation
observables are measured from $t$-channel single-top-quark events produced in
proton--proton collisions at a centre-of-mass energy of 8 TeV. The dataset
corresponds to an integrated luminosity of 20.2 fb$^{-1}$, recorded with the
ATLAS detector at the LHC. Selected events contain one isolated electron or
muon, large missing transverse momentum and exactly two jets, with one of them
identified as likely to contain a $b$-hadron. Stringent selection requirements
are applied to discriminate $t$-channel single-top-quark events from
background. The polarisation observables are extracted from asymmetries in
angular distributions measured with respect to spin quantisation axes
appropriately chosen for the top quark and the $W$ boson. The asymmetry
measurements are performed at parton level by correcting the observed angular
distributions for detector effects and hadronisation after subtracting the
background contributions. The measured top-quark and $W$-boson polarisation
values are in agreement with the Standard Model predictions. Limits on the
imaginary part of the anomalous coupling $g_{\mathrm{R}}$ are also set from
model-independent measurements.
