It's ammonium alum or potassium alum. Sometimes derisively called "hippie deodorant." It is not an antiperspirant. There are all sorts of alternatives that people use as deodorants, including lemon juice, baking soda, and tea oils.
The above is my personal experience, with absolute-zero story exaggeration. Though how long you'll need to apply the salt may vary (and how frequent you'll use it).
I don't have a preference for any brand (it's all the same) but here is what I have now: http://www.thecrystal.com/
You should be able to buy these in any good organic food and health store.
What's the mineral in "the crystal?" It's almost certainly an aluminum salt, but I can't find the active ingredient? The FAQ says "Do Crystal deodorants contain aluminum chlorohydrate or aluminum zirconium? No." That's a bit suspicious, as I think people would really want to know "does it contain aluminum?" and the answer is likely "yes."
BTW, you wrote "Your sweat lessens" with this product, but it does not. The FAQ stresses that it does not reduce sweat. "Crystal is not an antiperspirant. It is a deodorant ... Deodorants are generally considered cosmetic product because they simply control odor."
> I think people would really want to know "does it contain aluminum?" and the answer is likely "yes."
The answer is absolutely yes. They admit that it contains an alum, but don't specify which one. The "it's all natural because it's a salt" angle is BS, because aluminum chlorohydrate is also a salt.
Though it's probably just 1 in a mixture of many salts.
Even if regular deodorant has this listed as an ingredient, it's quantity is questionable, and it's mixed in with other substances that prevent the alum from making full contact on the surface of the skin.
> Your sweat lessens" with this product, but it does not. The FAQ stresses that it does not reduce sweat.
It does a bit. But not to a significant effect. It's probably a secondary effect (clean pores, less sweat ... something like that).
I've got pretty sensitive skin and anti-persperant caused it to crack and even bleed. So I tried the rock salt/crystal kind of deodorant. My local supermarket carries it, should I ever run out, but I've had the same one for seven or eight years now. It works pretty well for me.
I also shave my underarms, which probably helps -- less surface area for bacteria to grow and sweat dries faster. If I'm wearing a tight shirt, I'll sometimes use baby powder in case I sweat, but in general it hasn't been a problem.
I bike to work occasionally, but usually change my shirt and wipe the sweat off with an alcohol wet-wipe. That helps as well.
Also, natural fibers are your friend! I will get stinky if I wear a polyester or rayon shirt all day, but that happens even if I wear normal deodorant.
"I also shave my underarms, which probably helps". Interestingly, the Wikipedia article on this topic claims "Underarm hair wicks the moisture away from the skin and aids in keeping the skin dry enough to prevent or diminish bacterial colonization. The hair is less susceptible to bacterial growth and therefore is ideal for preventing the bacterial odor."
Have you tried a mild skin antiseptic cream? I've used Savlon for this in the past (cetrimide & chlorhexidine gluconate are the active ingredients, in a white vanishing cream base). Doesn't block pores, but is effective at killing most of the bacteria and is soothing if you have aggravated the skin there somehow.
No references, but in my family's experiences, it never works for some and it works great for others, but only as long as you use it. The day you forget, the stink comes right back.