Pressure-tuned exchange bias and coercivity in Ru-doped CaMnO3

The pressure effect on exchange bias (EB) and coercive fields, ${H}_{\mathrm{E}}$ and ${H}_{\mathrm{C}}$, in phase-separated ferromagnetic/antiferromagnetic (FM/AFM) CaMn${}_{1\ensuremath{-}x}$Ru${}_{x}$O${}_{3}$ manganites with 0.06 \ensuremath{\le} $x$ \ensuremath{\le} 0.15 was studied by magnetization measurements performed in the temperature range 10--200 K and under hydrostatic pressure up to 11 kbar. Both ${H}_{\mathrm{E}}$ and ${H}_{\mathrm{C}}$ exhibit intriguing dependence on Ru doping and on applied pressure. It was found that ${H}_{\mathrm{E}}$ is apparent only at $x$ 0.1 and decreases progressively with increasing doping, while ${H}_{\mathrm{C}}$ depends nonmonotonically on Ru content, reaching a maximum at around $x$ \ensuremath{\sim} 0.09. The ${H}_{\mathrm{E}}$ was found to increase strongly under applied pressure within doping range 0.06 \ensuremath{\le} $x$ \ensuremath{\le} 0.1, while ${H}_{\mathrm{C}}$ exhibits irregular behavior, namely, increases with increasing pressure for $x$ $=$ 0.15, changes nonmonotonically for $x$ $=$ 0.1, decreases for $x$ $=$ 0.08, and is almost invariable for $x$ $=$ 0.06. Complex pressure and Ru-doping effects on ${H}_{\mathrm{E}}$ and ${H}_{\mathrm{C}}$ are explained within a model involving size-variable nanoscale FM regions (droplets) embedded in an AFM matrix. The enhancement of EB with increasing pressure is attributed to the reduction in the FM droplet size, evidenced by both pressure dependence of spontaneous FM moment and ${H}_{\mathrm{E}}$ dependence upon cooling field ${H}_{\mathrm{cool}}$. The impact of FM droplet size on the EB was further evidenced by the magnetic field effect, which, in contrast to the pressure effect, leads to a growth of the FM droplets. The intricate ${H}_{\mathrm{C}}$ dependencies on both pressure and Ru content are understandable in a view of the transition from the multidomain state to the single-domain one, induced by droplet size decrease with increasing pressure or with doping lowering. Concisely, owing to the unique mechanism of valence modification, the external pressure appears to be an effective tool for controlling the EB and the coercivity in Ru-doped CaMnO${}_{3}$ perovskites.