Diamagnetic Levitation

(Molecular Magnetism and Levitation)
Seeing is believing:

A little frog (alive !) and a water ball levitate inside a Ø32mm vertical bore of a Bitter solenoid in a magnetic field of about 16 Tesla at the Nijmegen High Field Magnet Laboratory.

The image of a high-temperature superconductor levitating above a magnet in fog of liquid nitrogen can hardly surprise anyone these days – it has become common knowledge that superconductors are ideal diamagnetics and magnetic field must expel them. On the other hand, the enclosed photographs of water and a frog hovering inside a magnet (not on board a spacecraft) are somewhat counterintuitive and will probably take many people (even physicists) by surprise. This is the first observation of magnetic levitation of living organisms as well as the first images of diamagnetics levitated in a normal, room-temperature environment (if we disregard the tale about Flying Coffin of Mohammed as such evidence, of course). In fact, it is possible to levitate magnetically every material and every living creature on the earth due to the always present molecular magnetism. The molecular magnetism is very weak (millions times weaker than ferromagnetism) and usually remains unnoticed in everyday life, thereby producing the wrong impression that materials around us are mainly nonmagnetic. But they are all magnetic. It is just that magnetic fields required to levitate all these "nonmagnetic" materials have to be approximately 100 times larger than for the case of, say, superconductors.

Whether an object will or will not levitate in a magnetic field B is defined by the balance between the magnetic force F = M∇B and gravity mg = ρV g where ρ is the material density, V is the volume and g = 9.8m/s². The magnetic moment M = (χ/ µ₀)VB so that F = (χ/µ₀)BV∇B = (χ/2µ₀)V∇B². Therefore, the vertical field gradient ∇B² required for levitation has to be larger than 2µ₀ρg/χ. Molecular susceptibilities χ are typically 10^-5 for diamagnetics and 10^-3 for paramagnetic materials and, since ρ is most often a few g/cm³, their magnetic levitation requires field gradients ~1000 and 10 T²/m, respectively. Taking l = 10cm as a typical size of high-field magnets and ∇B² ~ B²/l as an estimate, we find that fields of the order of 1 and 10T are sufficient to cause levitation of para- and diamagnetics. This result should not come as a surprise because, as we know, magnetic fields of less than 0.1T can levitate a superconductor (χ= -1) and, from the formulas above, the magnetic force increases as B².

If the above is too complicated for you, read the Simple explanation

The water and the frog are but two examples of magnetic levitation. We have observed plenty of other materials floating in magnetic field - from simple metals (Bi and Sb), liquids (propanol, acetone and liquid nitrogen) and various polymers to everyday things such as various plants and living creatures (frogs, fish and a mouse). We hope that our photographs will help many – particularly, non-physicists – to appreciate the importance of magnetism in the world around us. For instance, it is not always necessary to organize a space mission to study the effects of microgravity– some experiments, e.g. plants or crystal growth, can be performed inside a magnet instead. Importantly, the ability to levitate does not depend on the amount of material involved, V, and high-field magnets can be made to accommodate large objects, animals or even man. In the case of living organisms, no adverse effects of strong static magnetic fields are known – after all, our frog levitated in fields comparable to those used in commercial in-vivo imaging systems (currently up to 10T). The small frog looked comfortable inside the magnet and, afterwards, happily joined its fellow frogs in a biology department.

There is one important aspect in which the diamagnetic levitation differs from any other known way of levitating or floating things. In the case of diamagnetic levitation, the gravitational force is compensated on the level of individual atoms and molecules. This is, in fact, as close as we can - probably ever - approach the science-fiction antigravity machine.

Why frogs?

However common in biology research, frogs are rare customers in physics laboratories and one may wonder why the Dutch boffins levitated frogs rather than "something scientific", ... like a mumbo-jumbo, for instance. We apologise to those who believe that "the real physics" should involve only obscure substances and be always dull.

Diamagnetic levitation was first demonstrated as long ago as in 1939 when small beads of graphite and bismuth were levitated in an electromagnet (for historic details, read Physics Today (pdf, 689 kB)). It took scientists another 50 years to rediscover levitation when physicists from Grenoble lifted several organic materials by the diamagnetic force. They were not aware of the earlier experiment. Although Grenoble's research was published in Nature, a few scientists noticed it.

When we, in our turn, rediscovered levitation being unaware of the previous experiments, we were amazed to find out that 90% of our colleagues did not believe that we were not joking that water can levitate. It became obvious to us that it was important to make scientists (as well as non-scientists) aware of the phenomenon. We levitated a live frog and other not-very-scientific objects because of their obvious appeal to a broader audience and in the hope that researchers from various disciplines, not only physicists, would never ever forget this often neglected force and the opportunities it offers.

In addition, the frog picture will probably help students studying magnetism to get less easily bored.

Why does the frog fly?

(this explanation is written in response to numerous inquiries from children who have not studied physics yet ... or even do not want to study it at all)

As you might well know, all matter in the universe consists of small particles called atoms and each atom contains electrons that circle around a nucleus. This is how the world is made.
If one places an atom (or a large piece of a matter containing billions and billions of atoms) in a magnetic field, electrons doing their circles inside do not like this very much. They alter their motion in such a way as to oppose this external influence.
Incidentally, this is the most general principle of Nature: whenever one tries to change something settled and quiet, the reaction is always negative (you can easily check out that this principle also applies to the interaction between you and your parents). So, according to this principle, the disturbed electrons create their own magnetic field and as a result the atoms behave as little magnetic needles pointing in the direction opposite to the applied field*.

As you probably saw many times when playing with magnets, magnets push each other away if you try to bring together their like poles, for example, two north or two south poles. Similarly, the north pole of the external field will try to push away the “north poles” of magnetized atoms.
Our magnet creates a very large magnetic field (about 100 to 1000 times larger than school or household magnets).
In this field, all the atoms inside the frog act as very small magnets creating a field of about 2 Gauss (although very small, such a field can still be detected by a compass). One may say that the frog is now built up of these tiny magnets all of which are repelled by the large magnet. The force, which is directed upwards, appears to be strong enough to compensate the force of gravity (directed downwards) that also acts on every single atom of the frog. So, the frog’s atoms do not feel any force at all and the frog floats as if it were in a spacecraft.

*) There are a few materials (such as iron) whose atoms are a bit crazy and love to be in a magnetic field. Their magnetic “needles” are oriented in the same direction. But those are exceptions from the general rule.

This original work carried out by Nijmegen's researchers was first featured in Physics World, April 1997, p. 28.
The most complete account is given in:

• "Everyone's Magnetism (pdf, 689 kB)" by A.Geim, Physics Today, Sep.1998, page 36-39 and
• "Of Flying Frogs and Levitrons (pdf, 229 kB)" by M.V.Berry and A.K.Geim, European Journal of Physics, v. 18, p. 307-313 (1997).

Further reading:

• "Magnetic Levitation"
• E.H. Brandt, Science 243, 349 (1989) and Physics World, September 1997
• Good popular book on magnetism: "Driving Force" by James Livingston.
• If you like to learn more about (micro-) gravity and how its absence can effect living organisms, please visit the Dutch Experiment Support Center: one of the websites related to the European Space Agency.