Off-stoichiometry effect on magnetic damping in thin films of Heusler alloy Co2MnSi

We investigated the effect of off-stoichiometry on the Gilbert magnetic damping constant (\ensuremath{\alpha}) of Heusler alloy $\mathrm{C}{\mathrm{o}}_{2}\mathrm{MnSi}$ (CMS) thin films by employing time-resolved magneto-optical Kerr effect (TR-MOKE) measurements along with first-principles calculations based on the linear-response theory for magnetic damping. Because of the contribution of extrinsic damping arising from two-magnon scattering, the effective \ensuremath{\alpha} (${\ensuremath{\alpha}}_{\mathrm{eff}}$) extracted from the TR-MOKE responses showed dependences on the in-plane magnetic-field angle (${\ensuremath{\theta}}_{\mathrm{H}}$) and the field strength ($H$). Then, we obtained the smallest ${\ensuremath{\alpha}}_{\mathrm{eff}}$ (${\ensuremath{\alpha}}_{0}$) for each sample under the most reduced contribution from two-magnon scattering realized through varying ${\ensuremath{\theta}}_{\mathrm{H}}$ and $H$ values, which is the closest value to \ensuremath{\alpha}. The thus obtained ${\ensuremath{\alpha}}_{0}$ values of epitaxially grown off-stoichiometric $\mathrm{C}{\mathrm{o}}_{2}\mathrm{M}{\mathrm{n}}_{\ensuremath{\beta}}\mathrm{S}{\mathrm{i}}_{\ensuremath{\gamma}}$ ($\ensuremath{\gamma}=0.82$) films with various (Mn + Si) compositions, $(\ensuremath{\beta}+\ensuremath{\gamma})$, decreased with increasing $(\ensuremath{\beta}+\ensuremath{\gamma})$ from ${\ensuremath{\alpha}}_{0}=0.0057$ for (Mn + Si)-deficient $(\ensuremath{\beta}+\ensuremath{\gamma})=1.44$ to ${\ensuremath{\alpha}}_{0}=0.0036$ for $(\ensuremath{\beta}+\ensuremath{\gamma})=1.90$ being close to the stoichiometric one of $(\ensuremath{\beta}+\ensuremath{\gamma})=2.0$ at 300 K. It was also demonstrated that a half-metallic (Mn+Si)-rich CMS film with $\ensuremath{\beta}=1.30$ and $\ensuremath{\gamma}=0.90$ showed a low ${\ensuremath{\alpha}}_{0}$ of 0.0035. The dependence of ${\ensuremath{\alpha}}_{0}$ on $(\ensuremath{\beta}+\ensuremath{\gamma})$ in $\mathrm{C}{\mathrm{o}}_{2}\mathrm{M}{\mathrm{n}}_{\ensuremath{\beta}}\mathrm{S}{\mathrm{i}}_{\ensuremath{\gamma}}$ ($\ensuremath{\gamma}=0.82$) was well explained by the first-principles calculations. Through the systematic investigations of off-stoichiometric CMS with various values of $(\ensuremath{\beta}+\ensuremath{\gamma})$, it was clarified that the total density of states (DOS) at the Fermi level, $D({E}_{\mathrm{F}})$, plays the key role for determining the damping constant of CMS. Furthermore, it was revealed that the reduced minority-spin DOS at ${E}_{\mathrm{F}}$, caused by decreasing harmful $\mathrm{C}{\mathrm{o}}_{\mathrm{Mn}}$ antisites, is essential for reducing the damping constant of CMS. These findings demonstrate that appropriately controlling off-stoichiometry and film composition is thus promising for achieving half-metallicity and a low \ensuremath{\alpha} simultaneously for CMS thin films.