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We have used a spin-1 Ising model Hamiltonian with dipolar (bilinear, J), quadrupolar (biquadratic, K), and dipolar-quadrupolar (odd, L) interactions in pair approximation to investigate the exchange-bias (EB), coercive field, and asymmetric hysteretic shearing properties peculiar to core/surface (C/S) composite nanoparticles (NPs). Shifted hysteresis loops with an asymmetry and coercivity enhancement are observed only in the presence of the odd interaction term in the Hamiltonian expression and their magnitudes show strong dependence on the value of L. The observed coercivity and EB in C/S NPs originated from nonzero odd coupling energies and their dependence on temperature (T) and particle size (R) are also discussed in relation to experimental findings

Origins of the Exchange-Bias Phenomenology, Coercivity Enhancement, and Asymmetric Hysteretic Shearing in Core-Surface Smart Nanoparticles