Superconducting, charge or spin density wave, and magnetic order in d- and f-electron materials M. Brian Maple University of California, San Diego Conference on Concepts in Electron Correlation, Hvar, Croatia, September, 2008
Competing interactions in d- and f-electron materials • Competing interactions in multinary d- and f-electron compounds can often be readily “tuned” by x, P, H (“knobs”) – Wide variety of correlated electron phenomena – Rich and complex phase diagrams in the hyperspace of T, x, P, H • Traced to various factors; e.g., – Hybridization between localized d- or f-electron states and itinerant electron states – Large unit cells, molecular units, atomic cages, low D, etc. – Coupled charge, spin, orbital, lattice degrees of freedom • Examples – Correlated electron phenomena in filled skutterudites (various talks) – Interplay between superconducting, CDW or SDW, and magnetic order in d- and f-electron materials (this talk) • High pressure and chemical substitution experiments on various materials that address this latter issue – Systems � URu 2-x Re x Si 2 � RTe 3 � High T c superconducting lanthanide iron oxypnictides
Superconductivity, hidden order, and magnetic order in the system URu 2-x Re x Si 2 Coworkers University of California, San Diego N. P. Butch, 1 J. R. Jeffries, 2 T. A. Sayles, 3 B. T. Yukich, D. A. Zocco 1 - U. Maryland 2 - Lawrence Livermore National Laboratory 3 - UCSD Medical School - Radiology More information – this conference Poster: Anomalous mixed-state thermal conductivity in URu 2 Si 2 H. Adachi, M. Sigrist Talk: Calculated electronic structure properties of URu 2 Si 2 and Ce-115 materials Peter Oppeneer
Why URu 2 Si 2 is interesting • Moderately heavy Fermi liquid (m* ~ 25 m e ) • “Hidden order (HO)” phase (T 0 ≈ 17.5 K) – BCS-like feature in C(T) at 17.5 K suggests partial gapping of Fermi surface by CDW or SDW – Small moment antiferromagnetism (SMAFM): μ ≈ 0.03 μ B /U, ||c-axis, (100) modulation – δ S ≈ 0.2ln(2) too large ⇒ “HO” phase – Large moment antiferromagnetism (LMAFM) observed at P c ~ 5 - 15 kbar: μ ~ 0.4 μ B /U – SMAFM phase – small volume fraction of LMAFM phase that coexists with HO phase ⇒ μ av ≈ 0.03 μ B • Superconductivity (SC) (T c ≈ 1.5 K) – Unconventional – Coexists with HO and SMAFM phases ThCr 2 Si 2 structure • Ordered phases can be “tuned” with P, H, x: a = 4.13 Å, c = 9.58 Å – Produces LMAFM and LMFM phases – Non-Fermi liquid (NFL) behavior
URu 2 Si 2 : Early experiments and current issues EARLY EXPERIMENTS • Heavy fermion superconductivity (polycrystalline specimens) Schlabitz, Baumann, Pollit, Rauchschwalbe, Mayer, Alheim, Bredl, ZP (86) • Anisotropy of physical properties (single crystal specimens) Palstra, Menovsky, van den Berg, Dirkmaat, Kes, Nieuwenhuys, Mydosh, PRL (85) • Partial gapping of the FS by CDW or SDW (polycrystalline specimens) Maple, Dalichaouch, Kohara, Rossel, Torikachvili, McElfresh, Thompson, PRL (86) • SMAFM – neutron scattering experiments (single crystal specimens) Broholm, Kjems, Buyers, Matthews, Palstra, Menovsky, Mydosh, PRL (86) FOLLOWED BY AN ENORMOUS AMOUNT OF EXPERIMENTAL AND THEORETICAL WORK
URu 2 Si 2 : Early experiments and current issues CURRENT ISSUES BEING ADDRESSED INCLUDE • Identity of “HO” phase order parameter (OP) • Whether SMAFM is intrinsic or extrinsic • T-P phase diagram for ordered phases of URu 2 Si 2 ; e.g., P c (T) where LMAFM forms • T-x and T-H phase diagrams (for various substituents) • NFL characteristics of properties near HO, AFM and FM QCPs • Nature of the unconventional SC
Low temperature specific heat of URu 2 Si 2 C’(T)/T= γ ’+ β T 2 C(T)/T= γ + β T 2 SCing transition Maple, Dalichaouch, Kohara, Rossel, Torikachvili, McElfresh, Thompson, PRL (86) • Superconductivity below T c ≈ 1.5 K (onset) • BCS-type mean field transition at T o = 17.5 K – δ C ≈ Aexp(- Δ /T); Δ ~ 10 2 K ⇒ SDW or CDW – γ (0)/ γ ’ ≈ 0.6 ⇒ ~ 40 % Fermi surface removed by SDW or CDW – SC & SDW or CDW compete for Fermi surface! • δ S ≈ 0.2ln(2) too large for AFM with small μ ≈ 0.03 μ B ⇒ Hidden order (HO) ?
Effect of pressure on competing electronic states in URu 2 Si 2 McElfresh, Thompson, Willis, Maple, Kohara, Torikachvili ‘87
Low temperature specific heat of URu 2 Si 2 under pressure R. A. Fisher, S. Kim. Y. Wu, N. E. Phillips, M. W. McElfresh, M. S. Torikachvili, M. B. Maple, 90 NOTE: Rapid suppression of specific heat jump Δ C at T c with P
URu 2 Si 2 : Fermi surface competition • Bilbro & McMillan PRB (76) – Theory – CDW/SDW competes with SCing order to gap a simple FS – HO/SMAFM and SCing phases compete for electrons • n = γ 0 / γ norm – Amount of FS not gapped by CDW/SDW – C(T): n(0) = 0.58, T c0 = 3.9 K T c0 = T c (P) n(P) T 0 (P) 1-n(P) n(P) calculated from T c & T 0 and γ (P=0) C(T) measured under P R. A. Fisher et al., Physica B (90) M. B. Maple et al., PRL (86); J. R. Jeffries, N. P. Butch, B. T. Yukich, M. B. Maple, PRL (07)
URu 2 Si 2 : HO/SMAFM – LMAFM phase transition under P Neutron diffraction: AFM μ 29 Si NMR: phase separation – increases with P AFM volume increases with P (HO volume decreases with P) P c ≈ 15 kbar AFM PM H. Amitsuka et al., PRL (99) K. Matsuda et al., JP:CM (03)
URu 2 Si 2 : HO/SMAFM – LMAFM phase transition under P Thermal expansion α (T,P) Neutron diffraction G. Motoyama et al., PRL (03) F. Boudarot et al., Physica B (03) How is SC affected through HO/SMAFM – LMAFM phase transition near ~5 kbar at low T?
URu 2 Si 2 : Objectives and approach • Objectives — Determine: – Nature of HO/SMAFM phase – Whether SMAFM is intrinsic or extrinsic – T-P phase diagram for ordered phases of URu 2 Si 2 ; e.g., P c (T) where LMAFM forms – Relationship between HO and SCing phases – Non-Fermi liquid characteristics of properties near HO and FM quantum critical points • Approach – Tune ordered phases with P, H, and chemical substitution (Re for Ru) – Prepare single crystals of URu 2-x Re x Si 2 – Perform measurements of ρ (T, H, P, x): � 50 mK ≤ T ≤ 300 K � 0 ≤ H ≤ 9 T � 0 ≤ P ≤ 30 kbar � 0 ≤ x ≤ 0.6
ρ (T,P): HO/SMAFM – LMAFM phase transition under P URu 2 Si 2 single crystal dT 0 ≈ K = 0.23 dP kbar dT 0 ≈ K = 0.10 dP kbar Kink in T o (P) suggests transition from HO/SMAFM to LMAFM phase at ~15 kbar ?
ρ (T,P): HO/SMAFM – LMAFM phase transition under P URu 2 Si 2 single crystal Scattering of electrons by gapped AFM magnons: ρ (T) = ρ o +AT 2 +B(T/ Δ )[1+2(T/ Δ )]exp(- Δ /T) Hessel Anderson ‘80
Superconductivity under pressure – T c (P) URu 2 Si 2 single crystal T c decreases smoothly with P and vanishes in the vicinity of the HO/SMAFM – LMAFM phase transition at ~15 kbar
Superconductivity under pressure – T c (P) & H c2 (T,P) URu 2 Si 2 single crystal Phenomenological fits to H c2 (T) data: H c2 (T) = H c2 (0)[1 - A(T/T c ) 2 ] No changes in T c (P) and H c2 (T,P) curves to ~15 kbar ⇒ no qualitative change in SC due to onset of LMAFM phase, if it were to occur near 5 kbar!
URu 2 Si 2 : T-P phase diagram Amitsuka et al, JMMM (07) Explore behavior of P c (T) by exploiting reduction of T 0 with x in URu 2-x Re x Si 2 Knebel et al, JMMM (07)
URu 2 Si 2 : Re substitution 24 25 26 27 28 Cr Mn Fe Co Ni 42 43 44 45 46 Mo Tc Ru Rh Pd 4d 7 5s 1 74 75 76 77 78 W Re Os Ir Pt 4f 14 5d 5 6s 2 106 107 108 109 110 Sg Bh Hs Mt Ds
URu 2-x Re x Si 2 : T-x phase diagram (polycrystals ) URu 2-x M x Si 2 (M = Re,Tc) ⇒ FM! ρ (T) ≈ ρ (0)[1 + (T/T o ) n ] FM QCP Y. Dalichaouch, M. S. Torikachvili, E. D. Bauer, V. S. Zapf, P.-C. Ho, E. J. Freeman, M. B. Maple, A. L. Giorgi PRB (89) C. Sirvent, M. B. Maple, PRL (05)
URu 2-x Re x Si 2 T-x phase diagram : ρ (T,x) & χ (T,x) Single crystals 100 Oe Peaks in M/H curves coincide with Curie temperatures inferred * curves offset for clarity from M 2 vs H/M “Arrott plots”
URu 2-x Re x Si 2 : T-x phase diagram Single crystals
URu 2-x Re x Si 2 : ρ (T,x) under pressure Single crystals
URu 2 Si 2 : T-P phase diagrams • There appears to be a steep (vertical?) phase boundary at P c ≈ 15 kbar (nearly independent of T - red line in figures) • HO/SMAFM - LMAFM phase boundary or another phase boundary? • Lower phase diagram favored by continuous behavior of T c (P) and H c2 (T,P) Amitsuka et al., JMMM (07) • Upper phase diagram could be favored is rapid diminution of Δ C at T c near 6 kbar signals loss of bulk SC (come back to this later in another context) Knebel et al., JMMM (07)
URu 2 Si 2 : Analysis of ρ (x,T) x ≤ 0.06 (HO/SMAFM): FL + gap x ≥ 0.10 (PM, FM): Power law
URu 2-x Re x Si 2 : Magnon gap Δ and exponent n of ρ (T) Single crystals n Δ: ρ (T)= ρ o +AT 2 +B(T/ Δ )[1+2(T/ Δ )]exp(- Δ /T) Hessel Anderson ‘80 n : ρ = ρ o +AT n
URu 2-x Re x Si 2 : Specific heat Single crystals Single crystals C(T)/T = γ o – c o lnT
URu 2-x Re x Si 2 : T-x phase diagram (single crystals) C(T)/T = γ o – c o lnT) ρ (T) ∝ T n (n ≈ 1 - 1.5)
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