If the employee has not corrected his behaviour in spite of giving him memo twice then now you need to escalate the level of negative discipline. However, do not reach to the last option of termination. Impose penalty on him twice. If he still does not improve his behaviour then you may go ahead and terminate him. However, before termination, it is better to conduct domestic enquiry.
One strikingly odd punishment is to transfer him to unrelated department like security. Do not give him access to mobile or computer. He might become fed up and put in his papers on his own. Therefore, no need to impose further punishment or get into termination. This may seem unconscionable, but sometimes we have to take such tough steps.
Thinking from HRM Point of view: - If employee gets time to browse through the social media then it appears that he has sufficient time at his disposal. Have you monitored his performance targets? What is the level of his performance? Is browsing social media impacting his performance? If yes, then you may terminate on the grounds of poor performance also.
In many IT companies, employees are given complete freedom to access internet. Even though they are free from restraints, employees are so laden with the work that they just do not get time to browse the internet. Therefore, you may check this performance angle also.
Monitoring the work very closely was done in the erstwhile era. Rather than monitoring the activities in which employees spend their time, in today's era, companies monitor their performance. To improve performance, employees are well-motivated. Motivation also comes with career plan. Have you designed proper career plan of the employee?
3rd June 2017 From India, Bangalore