Title: Observation of an unconventional giant negative exchange bias effect in La$_{0.5}$Sr$_{0.5}$Co$_{0.85}$Nb$_{0.15}$O$_3$

Abstract: We find an unconventional giant negative exchange bias (EB) of $H_{\rm EB}$ = --14.1~kOe at 2~K (cooling field of 50~kOe) in the cluster spin-glass (CSG) La$_{0.5}$Sr$_{0.5}$Co$_{0.85}$Nb$_{0.15}$O$_3$ perovsikte cobaltites. The magnetic memory effect, aging measurements, and nonlineraity in specific heat capacity reveal the glassy magnetic state at low temperatures. Further, the detailed analysis of {\it ac-}magnetic susceptibility confirms the glassy state below $\sim$58~K and the obtained characteristic spin-relaxation time-scale of $\tau_0$ = 8.4$\times$10$^{-10}$~s indicates the presence of CSG. Moreover, the analysis of magnetic training effect using the classical EB relaxation model reveals that the frozen spins relax slowly as compared to the rotatable spins at the interface of antiferromagnetic/ferromagnetic (AFM/FM) regions in CSG. Interestingly, the dependence of EB parameters is found to be unconventional for cooling field $>$50~kOe as the $H\rm_{EB}$ and $M\rm_{EB}$ show decreasing trend instead of expected saturation at higher fields. This unusual nature emerges due to large negative values of intrinsic interface exchange coupling ($J_i$), i.e., --10.24$\pm$0.22~meV and --12.55$\pm$0.49~meV for the measuring fields of $\pm$50~kOe and $\pm$90~kOe, respectively, whereas the number of spins in the FM cluster ($N_{\rm FM}$) are found to be small in the range of 2.4--3.1. These obtained values of $J_i $ and $N_{\rm FM}$ indicate the dominant AFM interactions and the presence of FM clusters in the AFM matrix, respectively, which correlate well with the observed unconventional behavior of giant negative exchange bias in the present sample.