I agree with Pickingup and Guni. Here's the pronunciation of 자기. http://www.forvo.com/word/%EC%9E%90%EA%B8%B0/

"자기" literally means "oneself". If you love someone deeply, you will think he is important as much as you. So "자기" is used to call one's lover.

Jagiya '자기야~' is a sweet word to call your lover like 'honey~'