The surface tension of quark matter plays a crucial role for the possibility of quark matter nucleation during the formation of compact stellar objects and also for the existence of a mixed phase within hybrid stars .
However , despite its importance , this quantity does not have a well established numerical value .
Some early estimates have predicted that , at zero temperature , the value falls within the wide range \gamma _ { 0 } \approx 10 - 300 { MeV / fm ^ { 2 } } but , very recently , different model applications have reduced these numerical values to fall within the range \gamma _ { 0 } \approx 5 - 30 { MeV / fm ^ { 2 } } which would favor the phase conversion process as well as the appearance of a mixed phase in hybrid stars .
In magnetars one should also account for the presence of very high magnetic fields which may reach up to about eB \approx 3 - 30 m _ { \pi } ^ { 2 } ( B \approx 10 ^ { 19 } -10 ^ { 20 } G ) at the core of the star so that it may also be important to analyze how the presence of a magnetic field affects the surface tension .
With this aim we consider magnetized two flavor quark matter , described by the Nambu–Jona-Lasinio model .
We show that although the surface tension oscillates around its B = 0 value , when 0 < eB \lesssim 10 m _ { \pi } ^ { 2 } , it only reaches values which are still relatively small .
For eB \approx 5 m _ { \pi } ^ { 2 } the B = 0 surface tension value drops by about 30 \% while for eB \gtrsim 10 m _ { \pi } ^ { 2 } it quickly raises with the field intensity so that the phase conversion and the presence of a mixed phase should be suppressed if extremely high fields are present .
We also investigate how thermal effects influence the surface tension for magnetized quark matter .