Search for Light Dark Matter with 259-day data in PandaX-4T

We present a search for light dark matter particles through their interactions with atomic electrons and nucleons, utilizing PandaX-4T data with an effective exposure of 1.04 tonne$\cdot$year for ionization-only data and 1.20 tonne$\cdot$year for paired data. Our analysis focuses on the energy range (efficiency$>$0.01) of approximately 0.33 to 3 keV for nuclear recoils, and from 0.04 to 0.39 keV for electronic recoils. We establish the most stringent constraints on spin-independent dark matter-nucleon interactions within a mass range of 2.5 to 5.0 GeV/$c^2$, spin-dependent neutron-only interactions within 2.0 to 5.3 GeV/$c^2$, and spin-dependent proton-only interactions within 2.0 to 3.8 GeV/$c^2$. Their corresponding limits at 3\,GeV/$c^2$ are $1.1 \times 10^{-43}$, $1.6 \times 10^{-38}$, and $5.6 \times 10^{-37}$\,cm$^2$, respectively. Additionally, our results improve the upper limits on the dark matter-electron scattering cross-section by a factor of 1.5 and 9.3 for heavy and light mediator scenarios respectively within 50 MeV/$c^2$ to 10 GeV/$c^2$, compared with previous best results.