 Research in Magnetism
In everyday life, you know magnets as pieces of iron that pick up nails and pins, and hold pictures onto your refrigerator. Magnetism may seem limited in that it seems to work for iron and very little else, but you may know that it stores data on your PC's hard drive and diskettes, and so it is not useless. You may be less aware that magnets are essential in every power plant generator that makes the electricity you use in your home, and are essential in every electric motor, from the ones that lift elevators to the ones that drive electric toothbrushes. So, what does Physics understand about magnetism? The stable elementary particles out of which everything is made have electric charges: protons (+) and electrons (-). Opposite charges attract each other and try to come together to form neutral objects (reducing their joint electrostatic energy). When a proton and an electron try to come together, quantum mechanics stops them in a ground state in which the electron (crudely speaking) orbits the heavier proton. This is called a Hydrogen atom. In the very early stages of the Big Bang beginning of the universe, and in the nuclear reactions powering stars, protons were crushed together (and about 50% of them converted to neutrons by sending out their charge in positrons) to form nuclei of heavier Elements, and when released from those high pressures, they gathered bunches of electrons to orbit around them (again trying to neutralize the charge), forming the elements of the >Periodic Table<. Whenever a charge moves it creates a magnetic field. Additionally, protons and electrons themselves have internal angular momentum (they are quantum mechanical Spin-½ particles), so it is like their charge is spinning, creating their own internal magnetic dipole moments (like the bar magnet illustrated at the top). The electron's magnetic moment is much larger than the proton's, so in atoms, electronic magnetic moments are much larger than nuclear magnetic moments. The electrons' motion in orbits in atoms also can cause magnetic fields. But there is energy in magnetic fields, so the electrons in an atom usually arrange themselves to partially cancel each others' magnetic fields, reducing the atom's total magnetic moment (and magnetic field energy). Most single atoms are highly chemically reactive: they can reduce their electrostatic energy further by binding to other atoms to form molecules, sharing electrons to "close electron shells". This shell-closing usually reduces molecule magnetic moments to zero as well. When atoms or molecules come together to form liquids and solids, the driving interactions are still between electric charges, seeking to reduce their electrostatic energy to even lower values than achievable as separate molecules. Magnetic liquids are very rare, and not part of our research, so we will consider solids. Even in solids, in the vast majority of cases, (atomic and molecular) ion magnetic moments are zero. A small number of atomic ions, however, can often (not always) reduce their energy in a solid (or molecule, in fact) by closing some shells, but leaving others with non-zero angular momentum unclosed, resulting in ionic magnetic moments. Atoms that can do this fairly frequently are shown in the Magnetic-Ion Periodic Table: 
Iron (Fe, #26) sits in the middle of a group of Transition Metals, while #58-70 are known as Rare Earths, and Uranium and heavier elements are Actinides, which are radioactive. For more details, >click here<.
Even when there are magnetic moments in a solid, however, it may not show strong magnetic behavior. In the majority of materials with magnetic moments, at room temperature those moments are pointing in random directions and fluctuating (changing their direction) randomly and rapidly. The bulk magnetic moment (when there is no applied field) is so small it is difficult to measure, and it is randomly fluctuating. Microscopically, there are magnetic fields between magnetic ions, but the total energy in magnetic fields is insignificant relative to thermal vibration energies. This is the Paramagnetic state. In order to generate strong magnetic effects, all the magnetic ions in a material must act together. To do that, there must be some magnetic interaction between the ions so that each ion can react to what the others are doing. The effect of the magnetic field generated by one ion's magnetic moment on another ion's magnetic moment (like what you feel when you hold 2 bar magnets and then try to bring them together), is actually very weak, and it tries to line them up in opposite directions, so that the total magnetic field is minimized (because then the energy in the magnetic field is minimized). Since this "magnetic dipole-dipole" interaction always tries to minimize the total magnetic field, it cannot generate any state with the strong magnetic fields you feel from iron magnets. When magnetic ions are bound in solid materials, however, other magnetic interactions can arise through the sharing of the electrons that causes the binding, either through the electrons in bonds (in insulators) or in the electron "bands" that allow conducting materials to actually conduct electricity. These can only really be understood using quantum mechanics, and in the language of quantum mechanics it turns out that strong magnetic interaction can arise from the "Pauli exclusion principle" requirement that the wavefunction of a collection of electrons must change sign when you exchange the positions of any pair of them. Because of this, it is called the Exchange Interaction. Between nearby ion-moments in a solid, this interaction can be quite strong, and sometimes it can favor pointing the two moments in the same direction, even though this maximizes the energy stored in the magnetic field (the Exchange Interaction reduces the energy by more than that amount, in these cases). In these cases, then, a material will minimize its total energy by pointing all its ion magnetic moments in the same direction, maximizing the magnetic field generated. This is called the Ferromagnetic state, and is the state of everything you recognize as a "magnet" in everyday life. Among the pure elements, only iron (Fe), cobalt (Co), nickel (Ni) and gadolinium (Gd) are ferromagnetic at room temperature. Most of the heavier rare earths (Tb through Tm) are paramagnetic at room temperature but become ferromagnetic when cooled to lower temperature. Ferromagnetism at room temperature is a key property for most consumer (and industrial) applications of magnetism, and that is found primarily in alloys and compounds of Fe, Co and Ni. In other cases, the exchange interaction may favor pairs of moments to point opposite to each other, or even to point at some arbitrary angle to each other. These cases can result in magnetically ordered states in which the moments, while fixed and not random, do not point in any particular direction, on average, so over macroscopic distances, the magnetic field generated by the moments will average to zero, and there will not be strong "bulk" magnetic effects. These are called Antiferromagnetic states, and there are a bunch of them: simple ( ), "longer wavelength collinear" ( ,  , etc.) , and huge numbers of non-collinear orderings, some of which are illustrated in the "Magnetic Ordering" figure. The change from paramagnetic to ferromagnetic or antiferromagnetic (called Magnetic Ordering) in cooling is a Phase Transition like the freezing of water into ice. 
Among the other transition metals as pure elemental metals, titanium (Ti), vanadium (V), molybdenum (Mo), ruthenium (Ru) and copper (Cu) ions do not possess ionic moments to order, when surrounded by their own kind. Manganese can have three different stable crystal structures, two of which have complex antiferromagnetic orderings, while the third is non-magnetic. Chromium has strange "incommensurate spin density wave" ordering where the moments are collinear but their size varies as a long-wavelength sine wave in one direction, and the wavelength is not an integer multiple of the crystal lattice parameter. In fact, the heavier rare earths (Tb-Tm) mentioned above, as they are cooled from room temperature, first enter a variety of long-wavelength antiferromagnetic states, as illustrated in the "heavy lanthanide metals" figure. 
When you start combining the ions that can be magnetic with other elements to make alloys and compounds, huge numbers of magnetic materials result. Only a small fraction of them are ferromagnetic at room temperature, as mentioned above. Far larger numbers are antiferromagnetic, but not necessarily at room temperature. Many materials that are paramagnetic at room temperature order magnetically when cooled, but they may need to be cooled as cold as 4 Kelvin, the temperature at which helium gas condenses to liquid (room temperature is 300 Kelvin). To do such cooling, we place the materials we are studying into cryostats, which are insulated cans (thermos bottles) to hold cryogenic liquids (liquid nitrogen: 77K, liquid helium: 4.2K), or in some cases into specialized refrigerators that work on the same principles as your kitchen fridge, but achieve much lower temperatures (at greater expense). By now you should have asked: if antiferromagnets cause no strong bulk effects, then how can one tell if a material is antiferromagnetic, and how can you tell which of the many possible antiferromagnetic states it takes? The answer is: >neutron diffraction<. Profs. Arrott and Noakes have recently done neutron diffraction experiments at >NIST<. These were studies of Iron-Aluminum alloys normally called not antiferromagnets, but spin glasses. A separate page describing spin glasses and the magnetism of Fe-Al alloys is part of: More to come! dnoakes@vsu.edu
May 2004
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