We present Halpha spectropolarimetry observations of a sample of 10 bright T Tauri stars, supplemented with new Herbig Ae/Be star data. A change in the linear polarisation across Halpha is detected in most of the T Tauri (9/10) and Herbig Ae (9/11) objects, which we interpret in terms of a compact source of line photons that is scattered off a rotating accretion disk. We find consistency between the position angle (PA) of the polarisation and those of imaged disk PAs from infrared and millimetre imaging and interferometry studies, probing much larger scales. For the Herbig Ae stars AB Aur, MWC 480 and CQ Tau, we find the polarisation PA to be perpendicular to the imaged disk, which is expected for single scattering. On the other hand, the polarisation PA aligns with the outer disk PA for the T Tauri stars DR Tau and SU Aur and FU Ori, conforming to the case of multiple scattering. This difference can be explained if the inner disks of Herbig Ae stars are optically thin, whilst those around our T Tauri stars and FU Ori are optically thick. Furthermore, we develop a novel technique that combines known inclination angles and our recent Monte Carlo models to constrain the inner rim sizes of SU Aur, GW Ori, AB Aur, and CQ Tau. Finally, we consider the connection of the inner disk structure with the orientation of the magnetic field in the foreground interstellar medium: for FU Ori and DR Tau, we infer an alignment of the stellar axis and the larger magnetic field direction.
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