We present a spectropolarimetric study of two weak-line T Tauri stars (wTTSs), TWA 6 and TWA 8A, as part of the MaTYSSE (Magnetic Topologies of Young Stars and the Survival of close-in giant Exoplanets) program. Both stars display significant Zeeman signatures that we have modelled using Zeeman Doppler Imaging (ZDI). The magnetic field of TWA 6 is split equally between poloidal and toroidal components, with the largest fraction of energy in higher-order modes, with a total unsigned flux of 840 G, and a poloidal component tilted $35^{circ}$ from the rotation axis. TWA 8A has a 70 per cent poloidal field, with most of the energy in higher-order modes, with an unsigned flux of 1.4 kG (with a magnetic filling factor of 0.2), and a poloidal field tilted $20^{circ}$ from the rotation axis. Spectral fitting of the very strong field in tb (in individual lines, simultaneously for Stokes $I$ and $V$) yielded a mean magnetic field strength of $6.0pm0.5$ kG. The higher field strengths recovered from spectral fitting suggests that a significant proportion of magnetic energy lies in small-scale fields that are unresolved by ZDI. So far, wTTSs in MaTYSSE appear to show that the poloidal-field axisymmetry correlates with the magnetic field strength. Moreover, it appears that classical T Tauri stars (cTTSs) and wTTSs are mostly poloidal and axisymmetric when mostly convective and cooler than $sim4300$ K, with hotter stars being less axisymmetric and poloidal, regardless of internal structure.
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