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[Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$], a two dimensional misfit metalliccompound, is famous for its rich phases accessed by temperature, $i.e.$ hightemperature spin-state transition, metal-insulator transition (MIT) atintermediate temperature ($\sim$ 100 K) and low temperature spin density wave(SDW). It enters into SDW phase below T$_{MIT}$ which becomes long range at 27K. Information on the independent role of misfit layers (rocksalt/Ca$_2$CoO$_3$\& triangular/CoO$_2$) in these phases is scarce. By combining a set ofcomplementary macroscopic (DC magnetization and resistivity) and microscopic(neutron diffraction and X-ray absorption fine structure spectroscopy)measurements on pure (CCO) and Tb substituted in the rocksalt layer of CCO(CCO1), magnetic correlations in both subsystems of this misfit compound areunraveled. CCO is found to exhibit glassiness, as well as exchange bias (EB)effects, while CCO1 does not exhibit glassiness, albeit it shows weaker EBeffect. By combining local structure investigations from extended X-rayabsorption fine structure (EXAFS) spectroscopy and neutron diffraction resultson CCO, we confirm that the SDW arises in the CoO$_2$ layer. Our results showthat the magnetocrystalline anisotropy associated with the rocksalt layer actsas a source of pinning, which is responsible for EB effect. Ferromagneticclusters in the Ca$_2$CoO$_3$ affects SDW in CoO$_2$ and ultimately glassinessarises.

Magnetic correlations in subsystems of the misfit [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$] cobaltate