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 = MB and gravity mg = V g where is the material density, V is the volume and g = 9.8m/s2. The magnetic moment M = (/ ÷0)VB so that F = (/÷0)BVB = (/2÷0)VB2. Therefore, the vertical field gradient B2 required for levitation has to be larger than 2÷0 g/. Molecular susceptibilities are typically 10-5 for diamagnetics and 10-3 for paramagnetic materials and, since 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 (= -1) and, from the formulas above, the magnetic force increases as B2.
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.
