It is a perennial problem with companies that manufacture products for and sell exclusively through big box stores like Lowes and HD. Harbor Breeze is one, Hampton Bay is another one of my pet peeves. Since the product is taken off their hands right away, they don't seem to want to support their customers and most certainly don't make it easy. I think the idea is that you will simply return the entire product to the store. They are usually not deterred by the fact that the product may be installed in the ceiling and is not easy to return, even if the warranty is still valid. [RANT MODE OFF] Harbor Breeze fans are manufactured by the Litex Company
Hampton Bay fans are manufactured by Chien Luen Industry in Taiwan and marketed in US by the King of Fans company out of Fort Lauderdale, FL.
Neither website has any useful info on it
You may want to give them a call and see if they have a reference number and/or supplier for the spring. Be advised that their customer support will not talk to you unless you have the 12-digit UPC for your product handy. It is normally printed on the box the fan came in; it is also on the store receipt and can still be on a sticker on the fan's cover.
Anyhow, I just wanted to add that if this is just a spring, you may actually be more successful looking for a replacement spring elsewhere. Harbor Freight sells sets of springs in a box, you may be able to find one that's close of cut one to size.
Good luck!