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The spin Hall effect (SHE) is a generation of spin polarization for movingspin carriers in materials under an external electric field and has beenobserved in semiconductors, metals, and insulators at or below roomtemperature. Recent theoretical analyses show that spin Hall current can beinduced by the baryon chemical potential gradient which plays the role of theanalogous electric field and which becomes sizable in the fireballs created inheavy-ion collisions at beam energy of ${\cal O}(10)$~GeV. In this letter, westudy this important mechanism for spin polarization generation that has notbeen systematically explored before and predict the signature of the SHE inthose collisions using a (3+1)~D viscous hydrodynamic model MUSIC with AMPTinitial condition. We propose to use the second Fourier coefficients of the netspin polarization of Lambda hyperon as sensitive probes to search for the SHE.Those SHE observables show a qualitative difference in both the sign and beamenergy dependence for the situations with and without the SHE. Futureexperimental observation of these distinct qualitative features would providestrong evidence for the existence of the SHE in the hot and dense QCD matter attrillions of degrees.

Signatures of the spin Hall effect in hot and dense QCD matter