Question and answer from reddit's ask science.  

"If you cut a magnet in half many many times, will you eventually have an atom that has a north and south pole?

In my physics textbook it says if you cut a magnet, it has two poles. And if you cut it again, it still has two poles, etc. I already knew that part. At what point are you left with just atoms?" - djwm12

"NO, to strictly answer your title, "will you eventually have an atom that has a north and a south pole?" However, your textbook was right to say that breaking a magnet in half into large pieces still gives you two magnets. But you can't take that concept too far, down to a single atom, while still being correct. You can't extrapolate your physics textbook to say that you can keep cutting up a magnet down to a single atom and still maintain polarity. A simple answer is this: you can cut up your magnet down to a few thousand atoms or so and have it still be a magnet, but beyond that and it will just be a chunk of metal. Only read further if you're prepared for a little more advanced answer. I'm giving this answer because there likely many people that will see your post that have the necessary background to understand it.

Before I go further: trying to explain this in one shot, to a level that you can understand without any hiccups, is impossible for me. But I tried. Now you just read and tell me where you get confused. Maybe I can reword this and make it more clear, but believe me when I say this: the idea of cutting up a magnet down to a single atom has hundreds of top magnetic researchers around the world scratching their heads. You have no idea how incredibly complex the answer is to your question! If I were able to do this, I'd be a millionaire. My research group studies this to some extent.

If you take a bar magnet that is 10cm long and cut it in half to 5cm, it will still be a permanent magnet (well, okay, you'll have two permanent magnets). Cut one of those 5cm magnets into 2.5cm and you'll still have a magnet. Continue this a few more times down to a few hundred micrometers, and you still have a magnet. So far, your textbook is correct.

But you can't go much further than that point, and how much further you're able to chop up your magnet depends on special material properties. Unfortunately for you, you don't have a solid background in magnetic materials (yet), and to understand why all the sudden your magnet stops behaving as if it has north and south 'poles' requires quite a bit of background.

First you'd need to understand that magnets contain atoms that each have their own little magnetic moment, or their north and south poles. Sounds like you already understand that. Next, you'd need to understand that in a typical magnet, these atoms align their poles so they point in the same direction. This adds up all of the magnetic energy inside the magnet. Sounds like you already understand that as well.

The next step is to understand that this alignment of magnetic poles only travels so far throughout the magnet. Let's say you have a chunk of magnet that is 1,000,000,000 (billion) atoms across. Well, it turns out that there might only be a block of atoms that are 10,000 across that are actually aligned almost perfectly. We call that volume of atoms a magnetic domain . In the left picture, you can see 9 different domains that each have a group of atoms that are perfectly aligned. But these domains are all pointed in different directions. This is what a chunk of iron would look like if you zoomed in far enough. If you apply an outside magnetic field (H) you'll align allof the domains in your specimen, and then BAM, you now have a strong magnet. Here is a picture . Now if this were pure iron, and you took away the magnetic field, it would go back to that initial state where the domains were random. But let's instead pretend we have a special alloy, Nd2Fe14B for one random example. Now with this special alloy, all of the domains will stay aligned quite well, and we'll have a bar magnet.

What happens when we cut up this bar magnet into smaller and smaller pieces? Well, above I said you can easily cut this up into pieces that are a few hundred micrometers long and still have a tiny magnet. That's true. But eventually we cut up our magnet so small, that we're now about the size of a single domain (a few thousand atoms across). Do we still have a magnet? Yep, that single domain particle of magnetic material is still a magnet. But then what happens when we try to chop that up even further? That's where odd stuff starts to happen.

You see, the atoms can align their magnetic moments due to a very special interaction that takes place on the quantum level. Imagine a force that is holding neighboring atoms to keep their alignment parallel. This force needs to be pretty large, actually, for reasons you probably already understand. If you take two bar magnets and place them parallel to each other so their North poles are next to each other and their South poles are next to each other, you'd find that they'll repel each other. So why in the heck would neighboring atoms do the same thing? That's where this force comes from. It has a fancy name: exchange interaction. It has a very confusing Wikipedia article, so I'm not even going to link it. But let's just say that it's this exchange interaction that binds your neighboring atoms' poles to align in the same direction.

But there is another energy that is in competition- thermal energy, or heat. If you add enough heat to your magnet, it completely stops working. It's called the Curie temperature. Heat basically knocks around your atoms so violently that they can no longer stay parallel to each other. As long as your thermal energy is less than the energy that comes from your exchange interaction, you'll have a magnet. But if the thermal energy becomes greater than the exchange interaction, you'll lose your magnet. The energy from heat is always at work, but the exchange energy doesn't work like that. The smaller you cut up your magnet, the less effective the exchange energy becomes.

Eventually you'll chop up your magnet into such a small volume of atoms, that the exchange energy diminishes to the point where the atom's won't align. It's at this point, the "superparamagnetic limit", where your magnetic moment is dimished for all practical purposes. And that's the answer- no, you can't cut up a magnet down to a single atom. It stops being a permanent magnet a few hundred atoms before it reaches that point, depending on the specific alloy your material is made of." - nd2fe14b