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We present the first optical polarimetric study of the two transitionalpulsars PSR J1023+0038 and XSS J12270-4859. This work is focused on the searchfor intrinsical linear polarisation (LP) in the optical emission from the twosystems. We carried out multiband optical and NIR photo-polarimetry of the twosystems using the ESO NTT at La Silla (Chile), equipped with the EFOSC2 and theSOFI instruments. XSS J12270-4859 was observed during its radio-pulsar state;we did not detect LP in all bands, with 3 sigma upper limits of, e.g., 1.4% inthe R-band. We built the NIR-optical averaged spectral energy distribution(SED) of the system, that could be well described by an irradiated black bodywith radius $R_{*} = 0.33\pm0.03\,R_{\odot}$ and albedo $\eta=0.32\pm0.05$,without the need of further components (thus excluding the visible presence ofan extended accretion disc and/or of relativistic jets). The case was differentfor PSR J1023+0038, that was in its accretion phase during our campaign. Wemeasured a LP of $1.09\pm0.27\%$ and $0.90\pm 0.17\%$ in the V and R bands,respectively. The phase-resolved polarimetric curve of the source in the R-bandreveals a hint of a sinusoidal modulation at the source 4.75 hr orbital period,peaked at the same orbital phase as the light curve. The measured LP of PSRJ1023+0038 could in principle be interpreted as scattering with free electrons(that can be found in the accretion disc of the system or even in the hotcorona that surrounds the disc itself) or to synchrotron emission from arelativistic particles jet or outflow. However, the NIR-optical SED of thesystem built starting from our dataset did not suggest the presence of a jet.We conclude that the optical LP observed for PSR J1023+0038 is possibly due toThomson scattering with electrons in the disc, as also suggested from thepossible modulation of the R-band LP at the system orbital period.

Different twins in the millisecond pulsar recycling scenario: optical polarimetry of PSR J1023+0038 and XSS J12270-4859