The lightly hole-doped system CeOs1.94Re0.06Al10 has been studied by muon spin relaxation and neutron diffraction measurements. A long-range antiferromagnetic ordering of the Ce-sublattice with substantially reduced value of the magnetic moment 0.18(1) mu_B has been found below T_N = 21 K. Similar to the undoped parent compound, the magnetic ground state of CeOs1.94Re0.06Al10 preserves the anomalous direction of the ordered moments along the c-axis. The obtained result reveals the crucial difference between electron- and hole-doping effects on the magnetic ordering in CeOs2Al10. The former suppresses the anisotropic c-f hybridization and promotes localized Ce moments. On the contrary, the latter increases the hybridization and shifts the system towards delocalized non-magnetic state.
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