When superconductors were first being pioneered, one of the most exciting applications imagined was to the electromagnet. An electromagnet with no internal resistance promised much larger magnetic fields and required less current. However, typical superconductors expel magnetic fields (the Meissner Effect) and retreat to a normal resistive state when applied with a magnetic field of sufficient strength. And thus, this is much of what makes ferromagnetic superconductors so interesting and appealing: the merger of these traditionally rival phenomena.
The BCS theory fails to explain superconductivity in such atypical materials, but theorists have a rough idea of the mechanism responsible. In traditional Type I superconductors, electrons with opposite spins form Cooper pairs with no net momentum or spin. Recall, this is also known as s-wave singlet superconductivity. This new, ferromagnetic superconductivity- known as triplet superconductivity- occurs when electrons with like spins join to form a Cooper pair with a net one unit of spin. A magnetic field destroys singlet superconductivity by the orbital effect or the paramagnetic effect. The orbital effect is a manifestation of the Lorentz force- since the electrons have opposite momenta, the Lorentz force acts in opposite directions, pulling the pair apart. The paramagnetic effect occurs when the applied field attempts to align the spin of both electrons along the magnetic field. However, the paramagnetic effect does not destroy triplet superconductivity because the pair already have their spins aligned. This means that only the orbital effect can destroy triplet superconductivity.
Ferromagnetism occurs from an alignment of atomic spin. Localized magnetism arises from the spin of atoms due to incomplete filling of inner electron shells- this occurs in rare earth metals such as gadolinium and actinides such as neptunium. The second type of magnetism arises from the alignment of the spin of the itinerant conduction electrons. This is what occurs in the recently discovered ferromagnetic superconductors UGe2 and URhGe2.
Ferromagnetic? Antiferromagnetic? Superconductive? Or all three?
Early experiments trying to mate these two dissimilar properties- ferromagnetism and superconductivity- demonstrated that doping with a very small amount of rare-earth impurities would completely destroy superconductivity. This is due to interactions between the spins of the electrons and the atomic magnetic moments- this interaction attempts to align Cooper pairs, which as mentioned above, would destroy superconductivity. Therefore, forcing superconductivity and ferromagnetism to coexist is a tricky situation. Progress has been made with materials such as erbium rhodium boride (ErRh4B4), which becomes superconductive at 8.7K. However, when it is cooled to 1K, something interesting happens: an alternating magnetic structure appears, instead of a typical ferromagnetic ordering. That is, local magnetic moments are aligned, but the amplitude of the magnetization varies sinusoidally. This is pictured below.
In this diagram, d is the period of the alternating domain, and xi is the size of the Cooper pairs.
In this intermediary state, the local magnetic moments in a domain interact with those in neighboring domains, affecting their spin an attempting to align their magnetic moments. The energy an atom gains by this alignment far exceeds the energy electrons gain by forming Cooper pairs (since domain walls cost energy), so this process snowballs until the material displays a uniform magnetic field. That is, ferromagnetism eventually wins out and superconductivity is destroyed. In our sample ErRh4B4, this transition occurs at 0.8K- below which the material is no longer superconductive.
However, this is not truly a ferromagnetic superconductor- the sample displayed either property, depending on its temperature, but not both. In the intermediary state, the alternating magnetic domains make the material look like an antiferromagnet on a large scale, even though on the atomic scale it looks ferromagnetic.
And yet all hope is not lost- the future of the marriage between ferromagnetism and superconductivity is bright. Compounds such as UGe2, URhGe, and ZrZn2 have been shown to posses these dissimilar properties simultaneously. However, experiments with such materials are very preliminary, and they are very sensitive to impurities and pressure. As purer materials are developed and laboratory techniques refined, ferromagnetic superconductivity will no doubt be refined, understood, and harnessed (not particularly in that order).
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TJ Barry MMIII