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In this work, we study the direct-detection constraints of light dark matterin the next-to minimal supersymmetric standard model (NMSSM) with non-universalHiggs masses (NUHM), especially the correlation between higgsino asymmetry andspin-dependent cross section. Finally, we get the following conclusions: (i)The spin-dependent cross section is proportional to the square of higgsinoasymmetry in dark matter $\tilde{\chi}^0_1$ in the NMSSM-NUHM. (ii) For highlysinglino-dominated dark matter $\tilde{\chi}^0_1$, the relic density can besufficient, but the higgsino asymmetry and spin-dependent cross section isalways small. (iii) With a sizeable higgsino component in the light darkmatter, the higgsino asymmetry and spin-dependent cross section can besizeable, but dark matter relic density is always small, thus it can escape thedirect detections. (iv) Light dark matter in the $h_2$- and $Z$-funnelannihilation channels with sufficient relic density can be covered by futureLUX-ZEPLIN (LZ) 7-ton in spin-dependent detections.

Higgsino Asymmetry and Direct-Detection Constraints of Light Dark Matter in the NMSSM with Non-Universal Higgs Masses