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{{Short description|Superconductors whose ferromagnetism is related to their superconductivity
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'''Ferromagnetic superconductors''' are materials that display intrinsic coexistence of [[ferromagnetism]] and [[superconductivity]]. They include UGe<sub>2</sub>,<ref name=Agarwal1>{{cite journal|doi=10.1038/35020500|pages=587–92|issue=6796|volume=406|last1=Saxena|journal=Nature|first1=S. S.|last2=Agarwal|first2=P|last3=Agarwal|first3=P.|last4=Ahilan|first4=K.|last5=Grosche|first5=F. M.|last6=Haselwimmer|first6=R. K. W.|last7=Steiner|first7=M. J.|last8=Pugh|first8=E.|last9=Walker|first9=I. R.|last10=Julian|first10=S. R.|last11=Monthoux|first11=P.|last12=Huxley|first12=A.|last13=Sheikin|first13=I.|last14=Braithwaite|first14=D.|last15=Flouquet|first15=J.|last16=Lonzarich|pmid=10949292|year=2000|first16=G. G.|title=Superconductivity on the border of itinerant-electron ferromagnetism in UGe<sub>2</sub>|bibcode = 2000Natur.406..587S |display-authors=8}}</ref> URhGe,<ref name=Argawal2>{{cite journal|doi=10.1038/35098048|last1=Aoki|pmid=11595943|year=2001|first1=Dai|pages=613|issue=6856|volume=413|last2=Huxley|journal=Nature|first2=Andrew|last3=Ressouche|first3=Eric|last4=Braithwaite|first4=Daniel|last5=Flouquet|first5=Jacques|last6=Brison|first6=Jean-Pascal|last7=Lhotel|first7=Elsa|last8=Paulsen|first8=Carley|title=Coexistence of superconductivity and ferromagnetism in URhGe|bibcode = 2001Natur.413..613A }}</ref> and UCoGe.<ref name=Huang>{{cite journal|doi=10.1103/PhysRevLett.99.067006|last1=Huy|year=2007|volume=99|issue=6|pages=67006|journal=Physical Review Letters|arxiv=0708.1388|first1=N.|last2=Gasparini|first2=A.|last3=De Nijs|first3=D.|last4=Huang|first4=Y.|last5=Klaasse|first5=J.|last6=Gortenmulder|first6=T.|last7=De Visser|first7=A.|last8=Hamann|first8=A.|last9=G�rlach|first9=T.|last10=Löhneysen|first10=H.|title= Superconductivity on the border of weak itinerant ferromagnetism in UCoGe|bibcode=2007PhRvL..99f7006H}}</ref> Evidence of ferromagnetic superconductivity was also reported for ZrZn<sub>2</sub> in 2001, but later reports<ref name=Yelland>{{cite journal|arxiv=cond-mat/0502341|last1=Yelland|journal=Physical Review B|first1=E.|volume=72|issue=21|pages=214523|last2=Hayden|first2=S.|last3=Yates|first3=S.|last4=Pfleiderer|first4=C.|last5=Uhlarz|first5=M.|last6=Vollmer|first6=R.|last7=L�hneysen|first7=H.|last8=Bernhoeft|first8=N.|last9=Smith|first9=R.|last10=Saxena|first10=S.S.|last11=Kimura|first11=N.|year=2005|title= Superconductivity induced by spark erosion in ZrZn2|doi=10.1103/PhysRevB.72.214523|bibcode = 2005PhRvB..72u4523Y }}</ref> question these findings. These materials exhibit superconductivity in proximity to a magnetic quantum critical point.
}}
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{{Use American English|date=January 2019}}'''Ferromagnetic superconductors''' are materials that display intrinsic coexistence of [[ferromagnetism]] and [[superconductivity]]. They include UGe<sub>2</sub>,<ref name="Agarwal1">{{cite journal|doi=10.1038/35020500|pages=587–92|issue=6796|volume=406|last1=Saxena|journal=Nature|first1=S. S.|last2=Agarwal|first2=P|last3=Agarwal|first3=P.|last4=Ahilan|first4=K.|last5=Grosche|first5=F. M.|last6=Haselwimmer|first6=R. K. W.|last7=Steiner|first7=M. J.|last8=Pugh|first8=E.|last9=Walker|first9=I. R.|last10=Julian|first10=S. R.|last11=Monthoux|first11=P.|last12=Huxley|first12=A.|last13=Sheikin|first13=I.|last14=Braithwaite|first14=D.|last15=Flouquet|first15=J.|last16=Lonzarich|pmid=10949292|year=2000|first16=G. G.|title=Superconductivity on the border of itinerant-electron ferromagnetism in UGe<sub>2</sub>|bibcode = 2000Natur.406..587S |s2cid=983431|display-authors=8}}</ref> URhGe,<ref name="Argawal2">{{cite journal|doi=10.1038/35098048|last1=Aoki|pmid=11595943|year=2001|first1=Dai|pages=613–6|issue=6856|volume=413|last2=Huxley|journal=Nature|first2=Andrew|last3=Ressouche|first3=Eric|last4=Braithwaite|first4=Daniel|last5=Flouquet|first5=Jacques|last6=Brison|first6=Jean-Pascal|last7=Lhotel|first7=Elsa|last8=Paulsen|first8=Carley|title=Coexistence of superconductivity and ferromagnetism in URhGe|bibcode = 2001Natur.413..613A |s2cid=4415338}}</ref> and UCoGe.<ref name="Huang">{{cite journal|doi=10.1103/PhysRevLett.99.067006|last1=Huy|year=2007|volume=99|issue=6|pages=67006|journal=Physical Review Letters|arxiv=0708.1388|first1=N.|last2=Gasparini|first2=A.|last3=De Nijs|first3=D.|last4=Huang|first4=Y.|last5=Klaasse|first5=J.|last6=Gortenmulder|first6=T.|last7=De Visser|first7=A.|last8=Hamann|first8=A.|last9=Görlach|first9=T.|last10=Löhneysen|first10=H.|title= Superconductivity on the border of weak itinerant ferromagnetism in UCoGe|bibcode=2007PhRvL..99f7006H|pmid=17930860|s2cid=10155231}}</ref> Evidence of ferromagnetic superconductivity was also reported for ZrZn<sub>2</sub> in 2001, but later reports<ref name="Yelland">{{cite journal|arxiv=cond-mat/0502341|last1=Yelland|journal=Physical Review B|first1=E.|volume=72|issue=21|pages=214523|last2=Hayden|first2=S.|last3=Yates|first3=S.|last4=Pfleiderer|first4=C.|last5=Uhlarz|first5=M.|last6=Vollmer|first6=R.|last7=Löhneysen|first7=H.|last8=Bernhoeft|first8=N.|last9=Smith|first9=R.|last10=Saxena|first10=S.S.|last11=Kimura|first11=N.|year=2005|title= Superconductivity induced by spark erosion in ZrZn2|doi=10.1103/PhysRevB.72.214523|bibcode = 2005PhRvB..72u4523Y |s2cid=119485503}}</ref> question these findings. These materials exhibit superconductivity in proximity to a magnetic quantum critical point.


The nature of the superconducting state in ferromagnetic superconductors is currently under debate. Early investigations<ref name=Karchev>[http://arxiv.org/abs/cond-mat/9911489 Coexistence of superconductivity and ferromagnetism in ferromagnetic metals]</ref> studied the coexistence of conventional ''s''-wave superconductivity with itinerant ferromagnetism. However, the scenario of spin-triplet pairing soon gained the upper hand.<ref name=Machida>{{cite journal|last1=MacHida|arxiv=cond-mat/0008245|journal=Physical Review Letters|first1=Kazushige|volume=86|last2=Ohmi|issue=5|first2=Tetsuo|pages=850 |title=Theory of Ferromagnetic Superconductivity|year=2001|pmid=11177956|doi=10.1103/PhysRevLett.86.850|bibcode=2001PhRvL..86..850M}}</ref><ref name=Walker>{{cite journal|arxiv=cond-mat/0206487|last1=Samokhin|journal=Physical Review B|first1=K.|volume=66|issue=17|pages=174501|last2=Walker|first2=M. |title=Order parameter symmetry in ferromagnetic superconductors|year=2002|doi=10.1103/PhysRevB.66.174501|bibcode = 2002PhRvB..66q4501S }}</ref> A mean-field model for coexistence of spin-triplet pairing and ferromagnetism was developed in 2005,<ref name=Nevidomskyy>{{cite journal|last1=Nevidomskyy|arxiv=cond-mat/0412247|journal=Physical Review Letters|first1=Andriy|volume=94|issue=9|pages=97003|year=2005 |title=Coexistence of ferromagnetism and superconductivity near quantum phase transition: The Heisenberg- to Ising-type crossover|doi=10.1103/PhysRevLett.94.097003|bibcode=2005PhRvL..94i7003N}}</ref><ref name=Lindner>{{cite journal|arxiv=0707.2875|last1=Linder|journal=Physical Review B|first1=J.|volume=76|issue=5|pages=54511|last2=Sudb�|first2=A. |title=Quantum transport in noncentrosymmetric superconductors and thermodynamics of ferromagnetic superconductors|year=2007|doi=10.1103/PhysRevB.76.054511|bibcode = 2007PhRvB..76e4511L }}</ref>
The nature of the superconducting state in ferromagnetic superconductors is currently under debate. Early investigations<ref name="Karchev">{{cite arXiv|last1=Karchev|first1=N. I.|last2=Blagoev|first2=K. B.|last3=Bedell|first3=K. S.|last4=Littlewood|first4=P. B.|date=1999-11-30|title=Coexistence of superconductivity and ferromagnetism in ferromagnetic metals|eprint=cond-mat/9911489}}</ref> studied the coexistence of conventional ''s''-wave superconductivity with itinerant ferromagnetism. However, the scenario of spin-[[Triplet state|triplet]] pairing soon gained the upper hand.<ref name=Machida>{{cite journal|last1=MacHida|arxiv=cond-mat/0008245|journal=Physical Review Letters|first1=Kazushige|volume=86|last2=Ohmi|issue=5|first2=Tetsuo|pages=850–3 |title=Theory of Ferromagnetic Superconductivity|year=2001|pmid=11177956|doi=10.1103/PhysRevLett.86.850|bibcode=2001PhRvL..86..850M|s2cid=22804232}}</ref><ref name=Walker>{{cite journal|arxiv=cond-mat/0206487|last1=Samokhin|journal=Physical Review B|first1=K.|volume=66|issue=17|pages=174501|last2=Walker|first2=M. |title=Order parameter symmetry in ferromagnetic superconductors|year=2002|doi=10.1103/PhysRevB.66.174501|bibcode = 2002PhRvB..66q4501S |s2cid=119355166}}</ref> A mean-field model for coexistence of spin-triplet pairing and ferromagnetism was developed in 2005.<ref name=Nevidomskyy>{{cite journal|last1=Nevidomskyy|arxiv=cond-mat/0412247|journal=Physical Review Letters|first1=Andriy|volume=94|issue=9|pages=97003|year=2005 |title=Coexistence of ferromagnetism and superconductivity near quantum phase transition: The Heisenberg- to Ising-type crossover|doi=10.1103/PhysRevLett.94.097003|bibcode=2005PhRvL..94i7003N|pmid=15783990|s2cid=31327399}}</ref><ref name=Lindner>{{cite journal|arxiv=0707.2875|last1=Linder|journal=Physical Review B|first1=J.|volume=76|issue=5|pages=54511|last2=Sudbø|first2=A. |title=Quantum transport in noncentrosymmetric superconductors and thermodynamics of ferromagnetic superconductors|year=2007|doi=10.1103/PhysRevB.76.054511|bibcode = 2007PhRvB..76e4511L |s2cid=119313463}}</ref>


These models consider uniform coexistence of [[ferromagnetism]] and [[superconductivity]], i.e. the same electrons which are both ferromagnetic and superconducting at the same time. 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<sub>4</sub>B<sub>4</sub> and HoMo<sub>6</sub>S<sub>8</sub>. 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.
These models consider uniform coexistence of ferromagnetism and superconductivity, i.e. the same electrons which are both ferromagnetic and superconducting at the same time. 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<sub>4</sub>B<sub>4</sub> and HoMo<sub>6</sub>S<sub>8</sub>. 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==
==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:<ref name=Nevidomskyy/><ref name=Lindner/>
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<ref name=Nevidomskyy/><ref name=Lindner/>


<math>H = H_0 + \sum_{\mathbf{k}\sigma} E_{\mathbf{k}\sigma}\gamma_{\mathbf{k}\sigma}^\dagger \gamma_{\mathbf{k}\sigma}</math>,
: <math>H = H_0 + \sum_{\mathbf{k}\sigma} E_{\mathbf{k}\sigma} \gamma_{\mathbf{k}\sigma}^\dagger \gamma_{\mathbf{k}\sigma},</math>
⚫
: <math>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,</math>
⚫
: <math>E_{\mathbf{k}\sigma} = \sqrt{\xi_{\mathbf{k}\sigma}^2 + |\Delta_{\mathbf{k}\sigma}|^2}.</math>


==See also==
⚫
<math>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</math>,
* [[Bean's critical state model]]

* [[Twistronics#Ferromagnetism|Ferromagnetic superconducting 2D materials]]
⚫
<math>E_{\mathbf{k}\sigma} = \sqrt{\xi_{\mathbf{k}\sigma}^2 + |\Delta_{\mathbf{k}\sigma}|^2}</math>.
* [[Reentrant superconductivity]]


==References==
==References==
{{reflist|2}}
{{Reflist|2}}


==Further reading==
==Further reading==
*{{cite book |title=Interaction of Superconductivity and Ferromagnetism in YBCO-LCMO |page=1 |url=http://books.google.com/?id=RoxyQ8cNdYYC&pg=PA3 |author=Soltan Soltan |year=2005 |isbn=3-86537-349-6 |publisher=Cuvillier Verlag}}
*{{cite book |title=Interaction of Superconductivity and Ferromagnetism in YBCO-LCMO |page=1 |url=https://books.google.com/books?id=RoxyQ8cNdYYC&pg=PA3 |author=Soltan Soltan |year=2005 |isbn=3-86537-349-6 |publisher=Cuvillier Verlag}}
*{{cite book |title=Recent trends in theory of physical phenomena in high magnetic fields |editor=Israel D. Vagner, Peter Wyder, Tsofar Maniv |isbn=1-4020-1373-6 |publisher=Springer |year=2003 |url=http://books.google.com/?id=yNXrbB2UlvoC&pg=PA18 |page=18 |chapter=The interplay of superconductivity and nuclear magnetism |author=T Herrmannsdörfer & F Pobell}}
*{{cite book |title=Recent trends in theory of physical phenomena in high magnetic fields |editor1=Israel D Vagner |editor2=Peter Wyder |editor-link2=Peter Wyder |editor3=Tsofar Maniv |isbn=1-4020-1373-6 |publisher=Springer |year=2003 |chapter-url=https://books.google.com/books?id=yNXrbB2UlvoC&pg=PA18 |page=18 |chapter=The interplay of superconductivity and nuclear magnetism |author1=T Herrmannsdörfer |author2=F Pobell |name-list-style=amp }}
*{{cite journal |title=Antiferromagnetic spin fluctuation and superconductivity |journal=Rep Prog Phys |volume=66 |issue=8 |pages=1299–1341 |author=T Moriya & K Ueda |year=2003 |doi= 10.1088/0034-4885/66/8/202|bibcode = 2003RPPh...66.1299M |last2=Ueda }}
*{{cite journal |title=Antiferromagnetic spin fluctuation and superconductivity |journal=Rep Prog Phys |volume=66 |issue=8 |pages=1299–1341 |author=T Moriya & K Ueda |year=2003 |doi= 10.1088/0034-4885/66/8/202|bibcode = 2003RPPh...66.1299M |last2=Ueda |s2cid=250884100 }}
*[http://xstructure.inr.ac.ru/x-bin/auththeme3.py?level=1&index1=155433&skip=0 Ferromagnetic superconductors – List of Authority Articles on arxiv.org]
*[http://xstructure.inr.ac.ru/x-bin/auththeme3.py?level=1&index1=155433&skip=0 Ferromagnetic superconductors – List of Authority Articles on arxiv.org]


{{Superconductivity}}
{{magnetic states}}
{{magnetic states}}


[[Category:Superconductivity]]
[[Category:Superconductivity]]
[[Category:Magnetic ordering]]
[[Category:Ferromagnetism]]

Latest revision as of 09:37, 1 March 2024

Ferromagnetic superconductors are materials that display intrinsic coexistence of ferromagnetism and superconductivity. They include UGe2,[1] URhGe,[2] and UCoGe.[3] Evidence of ferromagnetic superconductivity was also reported for ZrZn2 in 2001, but later reports[4] question these findings. These materials exhibit superconductivity in proximity to a magnetic quantum critical point.

The nature of the superconducting state in ferromagnetic superconductors is currently under debate. Early investigations[5] studied the coexistence of conventional s-wave superconductivity with itinerant ferromagnetism. However, the scenario of spin-triplet pairing soon gained the upper hand.[6][7] A mean-field model for coexistence of spin-triplet pairing and ferromagnetism was developed in 2005.[8][9]

These models consider uniform coexistence of ferromagnetism and superconductivity, i.e. the same electrons which are both ferromagnetic and superconducting at the same time. 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 ErRh4B4 and HoMo6S8. 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

[edit]

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[8][9]

See also

[edit]

References

[edit]
  1. ^ Saxena, S. S.; Agarwal, P; Agarwal, P.; Ahilan, K.; Grosche, F. M.; Haselwimmer, R. K. W.; Steiner, M. J.; Pugh, E.; et al. (2000). "Superconductivity on the border of itinerant-electron ferromagnetism in UGe2". Nature. 406 (6796): 587–92. Bibcode:2000Natur.406..587S. doi:10.1038/35020500. PMID 10949292. S2CID 983431.
  2. ^ Aoki, Dai; Huxley, Andrew; Ressouche, Eric; Braithwaite, Daniel; Flouquet, Jacques; Brison, Jean-Pascal; Lhotel, Elsa; Paulsen, Carley (2001). "Coexistence of superconductivity and ferromagnetism in URhGe". Nature. 413 (6856): 613–6. Bibcode:2001Natur.413..613A. doi:10.1038/35098048. PMID 11595943. S2CID 4415338.
  3. ^ Huy, N.; Gasparini, A.; De Nijs, D.; Huang, Y.; Klaasse, J.; Gortenmulder, T.; De Visser, A.; Hamann, A.; Görlach, T.; Löhneysen, H. (2007). "Superconductivity on the border of weak itinerant ferromagnetism in UCoGe". Physical Review Letters. 99 (6): 67006. arXiv:0708.1388. Bibcode:2007PhRvL..99f7006H. doi:10.1103/PhysRevLett.99.067006. PMID 17930860. S2CID 10155231.
  4. ^ Yelland, E.; Hayden, S.; Yates, S.; Pfleiderer, C.; Uhlarz, M.; Vollmer, R.; Löhneysen, H.; Bernhoeft, N.; Smith, R.; Saxena, S.S.; Kimura, N. (2005). "Superconductivity induced by spark erosion in ZrZn2". Physical Review B. 72 (21): 214523. arXiv:cond-mat/0502341. Bibcode:2005PhRvB..72u4523Y. doi:10.1103/PhysRevB.72.214523. S2CID 119485503.
  5. ^ Karchev, N. I.; Blagoev, K. B.; Bedell, K. S.; Littlewood, P. B. (1999-11-30). "Coexistence of superconductivity and ferromagnetism in ferromagnetic metals". arXiv:cond-mat/9911489.
  6. ^ MacHida, Kazushige; Ohmi, Tetsuo (2001). "Theory of Ferromagnetic Superconductivity". Physical Review Letters. 86 (5): 850–3. arXiv:cond-mat/0008245. Bibcode:2001PhRvL..86..850M. doi:10.1103/PhysRevLett.86.850. PMID 11177956. S2CID 22804232.
  7. ^ Samokhin, K.; Walker, M. (2002). "Order parameter symmetry in ferromagnetic superconductors". Physical Review B. 66 (17): 174501. arXiv:cond-mat/0206487. Bibcode:2002PhRvB..66q4501S. doi:10.1103/PhysRevB.66.174501. S2CID 119355166.
  8. ^ a b Nevidomskyy, Andriy (2005). "Coexistence of ferromagnetism and superconductivity near quantum phase transition: The Heisenberg- to Ising-type crossover". Physical Review Letters. 94 (9): 97003. arXiv:cond-mat/0412247. Bibcode:2005PhRvL..94i7003N. doi:10.1103/PhysRevLett.94.097003. PMID 15783990. S2CID 31327399.
  9. ^ a b Linder, J.; Sudbø, A. (2007). "Quantum transport in noncentrosymmetric superconductors and thermodynamics of ferromagnetic superconductors". Physical Review B. 76 (5): 54511. arXiv:0707.2875. Bibcode:2007PhRvB..76e4511L. doi:10.1103/PhysRevB.76.054511. S2CID 119313463.

Further reading

[edit]
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