Power consumption while using micro SD card with microcontroller
You seem to be closing the FAT when you finish writing, so the SDCard should automatically go into IDLE mode (clocks stopped). Make sure you do a read at the end of your write to ensure you cleared any write/erase. 
I'm not sure what SDCard you are using but here is a typical spec. The IDLE current is about 150 uA.

If you want to get lower than this then you could use a digital pin plus FET switch to turn the Vcc off when you are asleep, and turn it back on before initializing the FAT when you wake up.