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We perform a systematic study on the local and global spin polarization of$\Lambda$ and $\overline{\Lambda}$ hyperons in relativistic heavy-ioncollisions at beam energy scan energies via the (3+1)-dimensional CLVischydrodynamics model with AMPT and SMASH initial conditions. Following thequantum kinetic theory, we decompose the polarization vector as the partsinduced by thermal vorticity, shear tensor and the spin Hall effect (SHE). Wefind that the polarization induced by SHE and the total polarization stronglydepends on the initial conditions. At $7.7$GeV, SHE gives a sizeablecontribution and even flips the sign of the local polarization along the beamdirection for AMPT initial condition, which is not observed for SMASH initialcondition. Meanwhile, the local polarization along the out-of-plane directioninduced by SHE with AMPT initial condition does not always increase withdecreasing collision energies. Next, we find that the polarization along thebeam direction is sensitive to the baryon diffusion coefficient, but the localpolarization along the out-of-plane direction is not. Our results for theglobal polarization of $\Lambda$ and $\overline{\Lambda}$ agree well with theSTAR data. Interestingly, the global polarization of $\overline{\Lambda}$ isnot always larger than that of $\Lambda$ due to various competing effects. Ourfindings are helpful for understanding the polarization phenomenon and thedetailed structure of quark-gluon plasma in relativistic heavy-ion collisions.

Local and global polarization of $\Lambda$ hyperons across RHIC-BES energies: the roles of spin hall effect, initial condition and baryon diffusion