How to protect a certain field in the material master for certain manipulations?

Dear colleagues,

We have the following problem in the SAP authorization system.

We have to protect a certain field in the material master for certain manipulations.

It is the field MARA-EAN11 (European Article Number, EAN).

We should install the following security.

a) If the field is empty, the field can be filled by users with the appropriate rights (authorization object, activity).
b) If the field is filled, no user may change the field content.

How can such a request be solved using SAP on-board tools (PFCG, authorization object, activity)?

We would be very grateful for any information or hint!

Regards,
Markus