II. Physikalisches Institut Folie: 1 Z ü lpicher Str. 77, 50937 K ö ln Universit ä t zu K ö ln Prof. Dr. John Mydosh 03.10.2008
Hidden Order, Novel Phases and Hidden Order, Novel Phases and Unconventional Superconductivity in URu 2 Si 2 URu 2 Si 2 J. A. Mydosh Institute of Physics II University of Institute of Physics II, University of Cologne, Germany Max Planck Institute for Chemical Physics Max Planck Institute for Chemical Physics of Solids, Dresden, Germany Kamerlingh Onnes Laboratory, Leiden Kamerlingh Onnes Laboratory, Leiden University, The Netherlands II. Physikalisches Institut Folie: 2 Z ü lpicher Str. 77, 50937 K ö ln Universit ä t zu K ö ln Prof. Dr. John Mydosh 03.10.2008
HO NP and US in URu Si HO, NP and US in URu 2 Si 2 • Main Collaborators: H. Amitsuka – Hokkaido University N H N. Harrison and M. Jaime – NHMFL-LANL i d M J i NHMFL LANL K. H. Kim – Seoul National University Haung Ying Kai – Amsterdam/Leiden P Oppeneer – Uppsala University P. Oppeneer Uppsala University
Outline Outline a) a) What is Hidden Order (HO) What is Hidden Order (HO). b) Sample preparation. c) ) P Properties of HO state in URu 2 Si 2 . ti f HO t t i UR Si d) Unconventional superconducting state. e) L(S)DA band structure and gapping. f) ) INS-excitations as fct. of pressure and p field. g) Destruction of HO state via pressure, g) p magnetic field and doping. h) Novel high-field phases (NP). ) g ( )
Concepts to emphasize Concepts to emphasize • Hidden Order (HO) • Unconventional Superconductivity • Unconventional Superconductivity • Strain Model (c/a-ratio) • Fermi Surface Reconstruction (gapping) F i S f R i ( i ) • Adiabatic Continuity (with pressure) • Novel Phases (at high magnetic fields and with Rh-doping) p g) Work these into my conclusions Work these into my conclusions
What is “Hidden Order” (HO)? What is Hidden Order (HO)? [See, e.g. N. Shah, P. Chandra, P. Coleman and [See, e.g. N. Shah, P. Chandra, P. Coleman and JAM, PRB 6I, 564(2000).] N Now quite common usage of HO. Or as some it f HO O theorists call it “Dark Quantum Matter” or as others call it “Novel Forms of Order” and “Novel Phases” . As of a few months ago ‘‘Dark Order’’ ” A f f th Ph ‘‘D k O d ’’ A clear from bulk thermodynamic and transport A clear, from bulk thermodynamic and transport measurements, phase transition at T 0 where the order parameter (OP) and elementary excitations (EE) are unknown i e (EE) are unknown, i.e., cannot be determined cannot be determined from microscopic experiments. Ψ is primary, unknown OP; m is antiferromagnetic, secondary OP
(A) BreaksTRS (B) Invariant
See Bourdarot et al. PRL 90(2003) l PRL 90(2003) for n-experiment. P of I
In URu 2 Si 2 all bulk measurements show a mean In URu 2 Si 2 all bulk measurements show a mean field-like (continuous) phase transition at T 0 =17.5K, yet neutron and X-ray scattering, NMR, µ SR, etc. do not give OP and EE. SR t d t i OP d EE Only out of HO state evolves a putative highly Only out of HO-state evolves a putative highly unconventional(d-wave, even parity, spin singlet) multi-gap superconducting ground state at 1.5K. g g g Basic properties of HO-state: 1) Reduction of entropy, non-magnetic. 2) Opening of charge and spin gaps. 3) Scattering rate and/or effective mass decrease 4) Strong coupling to lattice 5) D 5) Destroyed by pressure, magnetic field and Rh- t d b ti fi ld d Rh doping
Super clean URu 2 Si 2 crystal via Czochralski tetra-arc furnace, p y , 2 2 T. D. Matsuda et al. JPSJ 77(2008)Suppl.A, 362. 5 – 8 mm diam., ca. 50 mm length Starting uranium electro-transport purified to reduce impurities in ppm range.
Resistivity measurements on different parts of the crystal. T D Matsuda et al JPSJ 77(2008)Suppl A 362 T. D. Matsuda et al. JPSJ 77(2008)Suppl.A, 362. Near surface has best RRR ! RRR ! HO is robust but superconductivity is position (strain) dependent. Note differences in temperature dependences of resistivity as T → T C
Specific heat at superconducting transition: bulk vs. surface. p p g T. D. Matsuda et al. JPSJ 77(2008)Suppl.A, 362. Too small a piece to calibrate Why different regions of superconductivity ? See strain model below !
Introduction ThCr 2 Si 2 bct - type ( I4/mmm ) URu 2 Si 2 a = 4.127 (Å) U c = 9.570 (Å) Ru Ru Si Coexistence of HO with SC 500 T.T.M. Palstra et al.(1985) T T M Palstra et al (1985) I // a 400 W. Schlabitz et al.(1986) Ω cm ) M.B. Maple et al.(1986) 300 T T ~ 17 5 K o ~ 17.5 K ρ ( µΩ 200 I // c T c ~ 1.2 K 100 100 0 1 10 100 1000 T (K)
Magnetic susceptibility g p y 12 URu 2 Si 2 10 ) emu / mol) 8 eff ~ 2.2 µ B µ z 6 6 χ (10 -3 e H // c 4 T o H // a 2 0 0 0 100 100 200 200 300 300 400 400 T (K)
Specific heat vs. magnetic Bragg-peak intensity magnetic Bragg peak intensity J/K 2 mol) 500 URu 2 Si 2 400 S mag ~ 0.2 R ln 2 mag C 5f / T (mJ 300 200 T c C 100 T o µ ord ~ 0.01 - 0.04 µ B 0 ) y (arb.unit) 1 Q = (1,0,0) Intensity Mason Fåk Honma 0 0 5 10 15 20 25 ξ c ~ 100 Å Type-I AF T (K) ξ a ~ 300 Å
Pseudo-gap in URu 2 Si 2 measured through optical conductivity Pseudo-gap in URu 2 Si 2 measured through optical conductivity, D. A. Bonn et al. PRL (1988).
Zone-center and (1.4 00) gaps in URu 2 Si 2 measured through neutron scattering, C. Broholm et al. PRL (1987) & PRB (1991). Similarity between optics and neutrons suggests magnetic excitations y p gg g are strongly coupled to charge excitations
Magnetization as function of temperature, C. Pfleiderer, JAM and M. Vojta, PRB 74, 104412 (2006). 0.02 2.16 10 -3 0.018 m tesla) tesla) 0.016 B /U-atom B /U-atom 0.014 2.13 10 -3 12T B ( µ B ( µ 0.012 6T 0 1T 0.1T M/B M/B 1T 1.0 T 0.01 6.0 T 12 T 2.1 10 -3 0.008 0 0 20 20 40 40 60 60 80 80 100 100 13 13 14 14 1 15 16 16 1 17 18 18 19 19 20 20 21 21 T(K) T(K) ab-plane ab plane c-axis c axis No qualitative change with P up to 17 kbars in M/B or (dM/dT)B -1 !!
Hall effect as function of temperature in different external p fields, Y.S. Oh et al. PRL 98, 016401(2007).
Unconventional superconductivity in URu 2 Si 2 -- multiband ( (two distinct gaps – see below) -- from HO: Compensated, low g p ) p , carrier density, heavy mass semimetal. Y. Kasahara et al. PRL 99, 116402(2007). In HO-state 0.02 holes/U; in HFL-state 0.15 holes/U. I HO t t 0 02 h l /U i HFL t t 0 15 h l /U In HO-state greatly reduced scattering rate 1/ τ .
Field dependence of κ (H)/T extrapolated T → 0, denoting five characteristic fields for a and c field directions. Y. Kasahara et al, PRL 99, 116402(2007). H c2 (a)=12T, H c2 (c)=2.8T, H c1 (a,c) ≈ 0.1H c2 (a,c) , H s =0.4T representing an initial √ H behavior The dashed/dotted lines show expected WF law from quadratic MR behavior. The dashed/dotted lines show expected WF law from quadratic MR. Plateau behavior indicates FS is partially restored at H s << H c2 , i.e., virtual critical field that closes smaller of the two gaps.
Proposed Fermi surface for URu 2 Si 2 with line nodes in light hole band and point nodes in heavy electron band hole band and point nodes in heavy electron band. Y. Kasahara et al., PRL 99, 116402(2007). Based upon thermal conductivity: κ /T vs T 2 at different magnetic fields extrapolated to residual value as T → 0. Different FS from recent band structure LSDA calculations !! Preview P.O’s talk !
Energy dispersion of URu 2 Si 2 : BLUE-PM, RED-AFM via L(S)DA, FPLO/FPLAPW All itinerant 5 f electrons FPLO/FPLAPW. All itinerant 5 f - electrons. S. Elgazzar, M. Amft, J. Rusz, P.M. Oppeneer & JAM, cond-mat. Note the gapping of the AFM phase near Σ and the Fermi surfaces crossings at M, Z, and near Γ . There is no crossing at X.
A small gapping ?? A small gapping ?? A small gapping ?? A small gapping ?? . Ζ . A . Γ . R R Γ . . Σ . . M ∆ X
Fermi surface gapping visualized Fermi surface gapping visualized Fermi surface gapping visualized Fermi surface gapping visualized > > Often speculated, but never microscopically identified PM PM Ζ R A Γ Σ Σ ∆ M X L Large gapping i LMAF Rugged arm shaped FS sheet disappears completely Rugged, arm-shaped FS sheet disappears completely
Fermi surface cross section in z=0 Fermi surface cross section in z=0 plane plane l LMAF Two entangled FS sheets in PM phase, g p , PM PM break-up in LMAF phase Γ X Μ E F Degenerate crossing at E F
Fermi surface nesting in z=0 Fermi surface nesting in z=0 plane plane LMAF PM Γ Γ X Μ 0.4a* 0.6a* Nesting in the LMAF phase is supposed to be close to nesting in HO phase.
FS gapping at “hot spots” FS gapping at “hot spots” quantified quantified tifi d tifi d LMAF Gapping vs. longitudinal U-moment pp g g PM PM Γ X Μ Μ E F
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