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Generalized Spin Fluctuation Feedback in Heavy Fermion Superconductors
- 1. Generalized spin fluctuation feedback effect and the tale of two transitionsAdil Amin & Daniel F. Agterberg University of Wisconsin-Milwaukee arXiv:1910.10780 arXiv:1910.10780 Accepted : Physics Review Research
- 2. Experimental Survey UPt3 𝑈1−𝑥 𝑇ℎ 𝑥 𝐵𝑒13 𝑃𝑟𝑂𝑠4 𝑆𝑏12 Hasselbach et al. 1989 Kim et al. 1991 Vollmer et al. 2003 Specific HeatTime Reversal Symmetry Breaking Schemm et al. 2014 Heffner et al 1990 Levenson-Falk et al. 2018
- 3. Low Energy Excitations Spin fluctuations : (Inelastic) Neutron Scattering Aeppli et al. 1988 Antiferromagnetic (AFM) fluctuations Hiess et al. 2002 AFM fluctuations Kaneko 2007 et al. Antiferroquadrapolar (AFQ) fluctuations Q= (1/2,0,0) Q= (1/2,1/2,0) Q= (1,0,0) Neutron Scattering Inelastic Neutron Scattering Inelastic Neutron Scattering UPt3 𝑈1−𝑥 𝑇ℎ 𝑥 𝐵𝑒13 𝑃𝑟𝑂𝑠4 𝑆𝑏12
- 4. Common Mechanism? Multi dimensional irreps (order parameter) UPt3 𝑈1−𝑥 𝑇ℎ 𝑥 𝐵𝑒13 𝑃𝑟𝑂𝑠4 𝑆𝑏12 3D (T irreps) 2D (E irreps) 2D (E irreps) 3D (T irreps) 2D (E irreps) A : (1,0) Nematic TRS B : (1,i) Broken TRS A : Time Reversal Symmetry (TRS) B: Time reversal Symmetry Breaking (TRSB) Hexagonal : 𝐷6ℎ Tetrahedral: 𝑇ℎOctarahedral: 𝑂ℎ 𝑇𝑐𝐴 = 550𝑚𝐾 𝑇𝑐𝐵 = 480𝑚𝐾
- 5. 𝑈𝑃𝑡3 𝛽2> 0 (1,i) 𝛽2 < 0 (1,0) Two transitions ?? AFM → Symmetry Breaking Field : But AFM not long ranged Kioke et. Al 1998
- 6. 3He Add coupling to paramagnetic fluctuations Large fluctuations imply 𝐴1 → 0 and +ve 𝑑 𝑎 = 𝑘 𝑥 + 𝑖𝑘 𝑦 𝒛 𝑑 𝑏 = 𝑘 A phase puzzling : weak coupling → B stable always We want phenomenogical model Resolved by Anderson & Brinkman : Spin fluctuation feedback effect Couple superfluidity + spin fluctuations : Microscopic
- 7. The SFEE cheat code Integrate out the Gaussian spin fluctuations 𝑓𝐵 − 𝑓𝐴= 3𝐾2 2 𝐴1 2 , A : Stable with large fluctuations (𝐴1 → 0) A—B transition : temperature dependence 𝛽 → 1 𝑇2 , 𝐾 → 1 𝑇 [ Brinkman et al. 1973, Kozii 2019] Start in A state (SFFE) : T ↓ : → B state (weak coupling)
- 8. Back to 𝑈𝑃𝑡3 Add a coupling between superconductivity and AFM fluctuations Q1 = 1 2 a*, Q2 = 1 2 (b*-a*), Q3 = − 1 2 b*𝑚1, 𝑚2 and 𝑚3 → New effective free energy 𝛽2 > 0 but ( 𝛽2- 6 4 𝐾2 2 𝐴1 2 ) < 0 → (1,0) : nematic TRS A state A → B TRSB (1,i) as T ↓
- 9. 𝑈1−𝑥 𝑇ℎ 𝑥 𝐵𝑒13 𝑂ℎ: AFM fluctuations : TRSB ( 𝜇SR) 2D Case * → Kerr Inactive : Ruled out by possible Kerr measurement 3D Case Ruled out by coupling See paper A B A B
- 10. 𝑃𝑟𝑂𝑠4 𝑆𝑏12 Aoki et al 2003 𝑇ℎ: AFQ fluctuations : TRSB ( 𝜇SR + Polar Kerr) 2D Case A—B Kerr Inactive 3D Case A B
- 11. Take away • Developed a simple and quick phenomenological approach to generalized SFFE • Provides a unifying description of two transitions in heavy fermion superconductors • 2D 𝐸 𝑔/𝑢 for 𝑃𝑟𝑂𝑠4 𝑆𝑏12 ruled out by polar Kerr • For 𝑈1−𝑥 𝑇ℎ 𝑥 𝐵𝑒13, form SFFE allows only one out of two possible A states • Suggest polar Kerr measurements for 𝑈1−𝑥 𝑇ℎ 𝑥 𝐵𝑒13 → can rule out 2D 𝐸 𝑔/𝑢 rep scenario and constrain 3D (𝑇𝑔/𝑢) situation https://arxiv.org/abs/1910.10780
- 12. Thank you and Questions https://arxiv.org/abs/1910.10780
- 13. Effective theory for A—B transitions • Start out in A state of UP𝑡3 stabilized by SFFE i.e. (1,0) with for and for • Grow B phase continuously out of A , i.e. (1 + 𝜂1𝑅 + 𝜂1𝐼, 0 + 𝜂2𝑅+𝜂2𝐼) • Use time reversal symmetry to classify these effective order parameter Want to break time reversal Character table for 𝐷2 → 𝐴1 → 𝐵1 Now use polar Kerr effect Signal trainable by field → order parameter TRSB & has same symmetry as magnetic field (𝑅 𝑥, 𝑅 𝑦, 𝑅 𝑧) Schemm et . al 2014