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The incoming Imaging X-ray Polarimetry Explorer (IXPE) observations of X-raybinaries provide a new tool to investigate the underlying accretion geometry.Here we report the first measurements of X-ray polarization of theextra-galactic black-hole X-ray binary LMC X$-$3. We find a polarizationfraction of $\sim$ 3 % at a polarization angle of $\sim 135^\circ$ in the $2-8$keV energy band with statistical significance at the 7$\sigma$ level. Thispolarization measurement significantly exceeds the minimum detectablepolarization threshold of 1.2 % for the source, ascertained at a 99 %confidence level within the $2-8$ keV energy band. The simultaneousspectro-polarimetric fitting of NICER, Swift/XRT, and IXPE revealed thepresence of a disc with a temperature of 1 keV and a Comptonized component witha power-law index of 2.4, confirming the soft nature of the source. Thepolarization degree increases with energy from $\sim$3 % in the $2-5$ keV bandto $\sim$8 % in the $5-8$ keV band, while the polarization angle is energyindependent. The observed energy dependence and the sudden jump of polarizationfraction at $\sim$ 5 keV supports the idea of a static slab coronal geometryfor the comptonizing medium of LMC X$-$3. We further observed no change in thepolarization properties with time over the period of the IXPE observations.

Unveiling the X-ray polarimetric properties of LMC X-3 with IXPE, NICER, and Swift/XRT