- Ferromagnetic superconductor
Ferromagnetic superconductors are materials that display intrinsic coexistence of

ferromagnetism andsuperconductivity . To this date, ferromagnetic superconductivity has been experimentally observed in UGe$\_2$ [*http://www.nature.com/nature/journal/v406/n6796/abs/406587a0.html*] , URhGe [*http://www.nature.com/nature/journal/v413/n6856/abs/413613a0.html*] , and UCoGe [*http://arxiv.org/abs/0708.1388*] . Evidence of ferromagnetic superconductivity was also reported for ZrZn$\_2$ by Pfleiderer et al. in 2001, but later reports [*http://arxiv.org/abs/cond-mat/0502341*] cast shadows of doubt on these findings.The nature of the superconducting state in ferromagnetic superconductors is currently under debate. Early investigations [

*http://arxiv.org/abs/cond-mat/9911489*] studied the coexistence of conventional $s$-wave superconductivity with itinerant ferromagnetism. However, the scenario of spin-triplet pairing soon gained the upper hand [*http://arxiv.org/abs/cond-mat/0008245*] , [*http://arxiv.org/abs/cond-mat/0206487*] . Recently, a mean-field model for coexistence of spin-triplet pairing and ferromagnetism was developed by Nevidomskyy [*http://arxiv.org/abs/cond-mat/0412247*] , and further studied by Linder and Sudbø [*http://arxiv.org/abs/0707.2875*] .It should be mentioned that we are here considering the situation of uniform coexistence of

ferromagnetism andsuperconductivity . Another scenario where there is an interplay between magnetic and superconducting order in the same material is superconductors with spiral or helical magnetic order. Examples of such include ErRh$\_4$B$\_4$ and HoMo$\_6$S$\_8$. In these cases, the superconducting and magnetic order parameters entwine each other in a spatially modulated pattern, which allows for their mutual coexistence, although it is no longer uniform. Even spin-singlet pairing may coexist with ferromagnetism in this manner.**Theory**In conventional superconductors, the electrons constituting the Cooper pair have opposite spin, forming so-called spin-singlet pairs. However, other types of pairings are also permitted by the governing Pauli-principle. In the presence of a magnetic field, spins tend to align themselves with the field, which means that a magnetic field is detrimental for the existence of spin-singlet Cooper pairs. A viable mean-field Hamiltonian for modelling itinerant ferromagnetism coexisting with a non-unitary spin-triplet state may after diagonalization be written as [

*http://arxiv.org/abs/cond-mat/0412247*] , [*http://arxiv.org/abs/0707.2875*] :$H\; =\; H\_0\; +\; sum\_\{mathbf\{k\}sigma\}\; E\_\{mathbf\{k\}sigma\}gamma\_\{mathbf\{k\}sigma\}^dagger\; gamma\_\{mathbf\{k\}sigma\}$,

$H\_0\; =\; frac\{1\}\{2\}\; sum\_\{mathbf\{k\}sigma\}(xi\_\{mathbf\{k\}sigma\}\; -\; E\_\{mathbf\{k\}sigma\}\; -\; Delta\_\{mathbf\{k\}sigma\}^dagger\; b\_\{mathbf\{k\}sigma\})\; +\; INM^2/2$,

$E\_\{mathbf\{k\}sigma\}\; =\; sqrt\{xi\_\{mathbf\{k\}sigma\}^2\; +\; |Delta\_\{mathbf\{k\}sigma\}|^2\}$.

**References**Experimental papers:

Theoretical papers:

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