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The charge ordered La$_{1/3}$Sr$_{2/3}$FeO$_{3-\delta}$ (LSFO) in bulk andnanocrystalline forms are investigated using ac and dc magnetization,M\"{o}ssbauer, and polarised neutron studies. A complex scenario of short rangecharge and magnetic ordering is realized from the polarised neutron studies innanocrystalline specimen. This short range ordering does not involve any changein spin state and modification in the charge disproportion between Fe$^{3+}$and Fe$^{5+}$ compared to bulk counterpart as evident in the M\"{o}ssbauerresults. The refinement of magnetic diffraction peaks provides magnetic momentsof Fe$^{3+}$ and Fe$^{5+}$ are about 3.15$\mu_B$ and 1.57$\mu_B$ for bulk, and2.7$\mu_B$ and 0.53$\mu_B$ for nanocrystalline specimen, respectively. Thedestabilization of charge ordering leads to magnetic phase separation, givingrise to the robust exchange bias (EB) effect. Strikingly, EB field at 5 Kattains a value as high as 4.4 kOe for average size $\sim$ 70 nm, which is zerofor the bulk counterpart. A strong frequency dependence of ac susceptibilityreveals cluster-glass like transition around $\sim$ 65 K, below which EBappears. Overall results propose that finite size effect directs the complexglassy magnetic behavior driven by unconventional short range charge andmagnetic ordering, and magnetic phase separation appears in nanocrystallineLSFO.

physical review. b, condensed matter and materials physics

Glassy magnetic phase driven by short range charge and magnetic ordering  in nanocrystalline La$_{1/3}$Sr$_{2/3}$FeO$_{3-\delta}$: Magnetization,  Mossbauer, and polarised neutron studies