There are many ways.
Are you using any Partner Function?? If you have HR module implemented, then department group mail id can be created. You can assign that mail id to that department manager & that person can be mentioned as Person Responsible. So that, system will send the mail to all people in that department.
Else, using partner function, you can mention the department responsible in notification by having HR module, through development, all persons mail id can be read using the department assigned in HR master data.
Else, from user master data, you can make this to happen.
So, please discuss with your HR/Basis/ABAP consultants on this.