  We have investigated the non-centrosymmetric tetragonal heavy-fermion
compound CeAuAl3 using muon spin rotation (muSR), neutron diffraction (ND) and
inelastic neutron scattering (INS) measurements. We have also revisited the
magnetic, transport and thermal properties. The magnetic susceptibility reveals
an antiferromagnetic transition at 1.1 K with a possibility of another magnetic
transition near 0.18 K. The heat capacity shows a sharp lambda-type anomaly at
1.1 K in zero-filed, which broadens and moves to higher temperature in applied
magnetic field. Our zero-field muSR and ND measurements confirm the existence
of a long-range magnetic ground state below 1.2 K. Further the ND study reveals
an incommensurate magnetic ordering with a magnetic propagation vector k = (0,
0, 0.52) and a spiral structure of Ce moments coupled ferromagnetically within
the ab-plane. Our INS study reveals the presence of two well-defined crystal
electric field (CEF) excitations at 5.1 meV and 24.6 meV in the paramagnetic
phase of CeAuAl3 which can be explained on the basis of the CEF theory.
Furthermore, low energy quasi-elastic excitations show a Gaussian line shape
below 30 K compared to a Lorentzian line shape above 30 K, indicating a
slowdown of spin fluctuation below 30 K. We have estimated a Kondo temperature
of TK=3.5 K from the quasi-elastic linewidth, which is in good agreement with
that estimated from the heat capacity. This study also indicates the absence of
any CEF-phonon coupling unlike that observed in isostructural CeCuAl3. The CEF
parameters, energy level scheme and their wave functions obtained from the
analysis of INS data explain satisfactorily the single crystal susceptibility
in the presence of two-ion anisotropic exchange interaction in CeAuAl3.
