A data storage device is introduced. The data storage device comprises a write head. The write head comprises a heating element and a tip. The write head scans a data storage medium, wherein in an operation mode of the data storage device the tip is in contact with a surface of the data storage medium and heat is applied to the tip by means of the heating element. In order to achieve a good thermal contact between the tip and the data storage medium, the tip comprises a carbon element that is at least partially in contact with the surface in that operation mode. Such a write head can also be applied in the field of scanning probe lithography.