Dzyaloshinskii-Moriya interaction and chiral damping effect in symmetric epitaxial Pd/Co/Pd(111) trilayers

We investigate the creep of domain walls (DWs) in the combination of in-plane (IP) and out-of-plane magnetic fields in a series of epitaxial Cu(2 nm)/Pd(0--3 nm)/Co(0.7 nm)/Pd(3 nm) samples. Measured velocity curves, $v({H}_x)$, are fitted with an extended dispersive elasticity model, which considers the dependence of both the elastic energy of the DWs and a velocity prefactor in the creep law on the IP magnetic field. The results of the calculations indicate that strong asymmetry in the $v({H}_x)$ curves in the investigated system is primarily defined by the dependence of the velocity prefactor on the IP magnetic field, which may be related to a chiral damping effect. The effective energy of the Dzyaloshinskii-Moriya interaction (DMI) increases with increasing thickness of the Pd bottom layer from \ensuremath{-}0.16 \ifmmode\pm\else\textpm\fi{} 0.03 to $0.19\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}/{\mathrm{m}}²$. We attribute the complex dependence of the effective DMI energy on the thickness of the Pd bottom layer in the epitaxial Pd/Co/Pd(111) system and the existence of the nonzero DMI in the symmetric Pd(3 nm)/Co(0.7 nm)/Pd(3 nm) samples to unequal strains in the bottom Pd/Co and top Co/Pd interfaces. The elastic strains in the interfaces varying depending on the thickness of the Pd bottom layer strongly influence the magnitude and even the sign of the contributions to the net DMI energy from each interface.