First of all let me begin by saying that if it is intended that Warrior Mages only be able to draw from the Arcana sphere the most basic spells to show their limited means of Arcane advancement (Not being able to devote the hours to study that a character going full Mage can devote) then I completely understand.
However, in another thread (I'll link it here for easy review http://belariath.com/forum/viewtopic.php?f=42&t=23022) I've been putting together a few Warrior Mage class-specific spells to help give them their own sense of identity and lore in the world to match the other Advanced Classes.
In short, my basic idea is to add a new sphere of magic called 'War Magic' that Warrior Mages would have access too as a place to put spells designed specifically for the class to keep the Arcana sphere from becoming crowded with Warrior Mage spell additions while also adding a bit of lore and identity to Warrior Mages as a class. There is a more detailed write up that shows my reasoning in the thread listed above as well as a bit of potential backstory and lore I've put together to go along with it. I am just happy to be sharing ideas and suggestions, so thank you for reading and for any suggestions and thoughts.