Groan up, Haineko!
Japanese sword in serious style
Soul Cutter is a symbol of power and strength that reflects the heart of its wielder. Any Soul Reaper cannot be without at least one of such swords and Rangiku's personal Soul Cutter, Haineko, is as unique as its master in every possible way - even if our lady likes to call it "selfish, whiny and proud" ;)
Name
Hai means "ashes" and Neko means "cat", which sets a double standard for our definition of Rangiku's sword: cats are adorable and free-spirited while "ashes" provide a gloomy, deadly kind of outlook. Interesting much?
Power
Haineko made its first appearance (while in action) at the start of volume 20 (manga) and episode 60 (anime). Rangiku was forced to release Haineko's true power when attacked by Kira's Wabisuke, which however became a power defect almost instantly: while Wabisuke can increase the weight of everything it touched, Haineko is able to shatter into countless pieces of ashes. In other words, Kira is not able to hurt Rangiku at all during battle due to the nature of their swords - this happens to mirror their relationship in real life, too ;)
Stage
Each Soul Cutter is bestowed two stages of release: Shikai (initial activation) and Bankai (ultimate activation). The gap of power between those stages is enormous, and only a selective few Soul Reapers in history had ever been able to accomplish the second type of release. With the exception of Renji and Ikkaku, no vice captain in Gotei 13 has achieved the state of Bankai yet and Rangiku is one of them. That being said, I haven't yet lost hope of ever seeing a female Bankai and Haineko seems like a decent possibility.