Universit t zu K ln Prof. Dr. John Mydosh 03.10.2008 Hidden - - PowerPoint PPT Presentation

• II. Physikalisches Institut

Zülpicher Str. 77, 50937 Köln

• Prof. Dr. John Mydosh

03.10.2008

Universität zu Köln

Folie: 1

Hidden Order, Novel Phases and Hidden Order, Novel Phases and Unconventional Superconductivity in URu2Si2 URu2Si2

• 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

• f Solids, Dresden, Germany

Kamerlingh Onnes Laboratory, Leiden Kamerlingh Onnes Laboratory, Leiden University, The Netherlands

• II. Physikalisches Institut

Zülpicher Str. 77, 50937 Köln

• Prof. Dr. John Mydosh

03.10.2008

Universität zu Köln

Folie: 2

HO NP and US in URu Si HO, NP and US in URu2Si2

• Main Collaborators:
• H. Amitsuka – Hokkaido University

N H i d M J i NHMFL LANL

• N. Harrison and M. Jaime – NHMFL-LANL
• K. H. Kim – Seoul National University

Haung Ying Kai – Amsterdam/Leiden P Oppeneer – Uppsala University

• P. Oppeneer

Uppsala University

Outline Outline

a) What is Hidden Order (HO) a) What is Hidden Order (HO). b) Sample preparation. ) P ti f HO t t i UR Si c) Properties of HO state in URu2Si2. 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)

F i S f R i ( i )

• Fermi Surface Reconstruction (gapping)
• 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 it f HO O Now quite common usage of HO. Or as some theorists call it “Dark Quantum Matter” or as

• thers call it “Novel Forms of Order” and “Novel

Ph ” A f f th ‘‘D k O d ’’ Phases”. As of a few months ago ‘‘Dark Order’’ A clear from bulk thermodynamic and transport A clear, from bulk thermodynamic and transport measurements, phase transition at T0 where the

• rder parameter (OP) and elementary excitations

(EE) are unknown i e cannot be determined (EE) are unknown, i.e., cannot be determined from microscopic experiments.

Ψ is primary, unknown OP; m is antiferromagnetic, secondary OP

(A) BreaksTRS (B) Invariant

See Bourdarot et l PRL 90(2003)

• al. PRL 90(2003)

for n-experiment. P of I

In URu2Si2 all bulk measurements show a mean In URu2Si2 all bulk measurements show a mean field-like (continuous) phase transition at T0=17.5K, yet neutron and X-ray scattering, NMR, SR t d t i OP d EE µSR, etc. do not give OP and 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 t d b ti fi ld d Rh 5) Destroyed by pressure, magnetic field and Rh- doping

Super clean URu2Si2 crystal via Czochralski tetra-arc furnace, p

2 2

y ,

• 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 →TC

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

URu2Si2

ThCr2Si2 bct - type ( I4/mmm )

U Ru

a = 4.127 (Å) c = 9.570 (Å)

Si Ru Coexistence of HO with SC

500

T T M Palstra et al (1985)

300 400

Ω cm )

I // a

T ~ 17 5 K

T.T.M. Palstra et al.(1985)

• W. Schlabitz et al.(1986)

M.B. Maple et al.(1986)

100 200

ρ (µΩ

I // c

T

• ~ 17.5 K

T

c ~ 1.2 K

100 1 10 100 1000

T (K)

Magnetic susceptibility g p y

10 12

)

URu2Si2

6 8

emu / mol)

µz

eff ~ 2.2 µB

4 6

χ (10 -3 e H // c

T

• 2

100 200 300 400

H // a

100 200 300 400

T (K)

Specific heat vs. magnetic Bragg peak intensity magnetic Bragg-peak intensity

URu2Si2 J/K2mol)

400 500

Smag ~ 0.2 R ln 2 T

c

C5f / T (mJ

200 300

mag

µord ~ 0.01 - 0.04 µB T

• C

100

) y (arb.unit)

1

Q = (1,0,0) Intensity Mason Fåk Honma ξc ~ 100 Å ξa ~ 300 Å T (K)

5 10 15 20 25

Type-I AF

Pseudo-gap in URu2Si2 measured through optical conductivity Pseudo-gap in URu2Si2 measured through optical conductivity,

• D. A. Bonn et al. PRL (1988).

Zone-center and (1.4 00) gaps in URu2Si2 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).

2.16 10-3 0.02 tesla) 0.016 0.018 m tesla) 2.13 10-3 6T 12T B (µ

B/U-atom

0.012 0.014 0 1T B (µ

B/U-atom

2.1 10-3 13 14 1 16 1 18 19 20 21 1T M/B 0.008 0.01 20 40 60 80 100 0.1T 1.0 T 6.0 T 12 T M/B 13 14 15 16 17 18 19 20 21 T(K) 20 40 60 80 100 T(K)

c-axis ab-plane c axis ab plane

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 URu2Si2 -- 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).

I HO t t 0 02 h l /U i HFL t t 0 15 h l /U In HO-state 0.02 holes/U; in HFL-state 0.15 holes/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).

Hc2(a)=12T, Hc2(c)=2.8T, H c1(a,c)≈0.1Hc2(a,c), Hs=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 Hs << Hc2, i.e., virtual critical field that closes smaller of the two gaps.

Proposed Fermi surface for URu2Si2 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 T2 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 URu2Si2: BLUE-PM, RED-AFM via L(S)DA, FPLO/FPLAPW All itinerant 5f electrons FPLO/FPLAPW. All itinerant 5f-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 ??

A

. .

Ζ R Γ X M

. . .

Σ R Γ.

. .

∆

Fermi surface gapping visualized Fermi surface gapping visualized Fermi surface gapping visualized Fermi surface gapping visualized

PM

> > Often speculated, but never microscopically identified

A Σ Ζ R Γ

PM

X M Σ ∆

L i LMAF Large gapping

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 l plane plane

Two entangled FS sheets in PM phase,

LMAF PM

Γ X

g p , break-up in LMAF phase

PM

Μ

EF Degenerate crossing at EF

Fermi surface nesting in z=0 Fermi surface nesting in z=0 plane plane

Γ

LMAF PM

Γ X Μ

Nesting in the LMAF phase 0.6a* 0.4a* is supposed to be close to nesting in HO phase.

FS gapping at “hot spots” FS gapping at “hot spots” tifi d tifi d quantified quantified

LMAF PM Gapping vs. longitudinal U-moment

Γ X

PM pp g g

Μ Μ

EF

Our electronic structure model of URu Si URu2Si2

Explains the following properties:

lattice constant (≤0.5%) magnetic moment 0 39 µ anisotropy of resistivity AFM order under pressure magnetic moment 0.39 µB energy scale ≤7 K AFM order under pressure nesting vector compensated metal Hall effect - number of holes breaking of time-reversal

& body-centering

Hall effect number of holes FS gapping at EF dispersive f-dominated

bands

infrared optical spectra jump ∆ρ in resistivity

ARPES ?? d H/ A ? jump ∆ρ in resistivity deH/vA ?

But Novel Mechanism for HO Transition But…Novel Mechanism for HO Transition

• Substantial static magnetic moments as seen in

g pressure-created (100) Bragg peak cause gapping thereby leading to LMAF transition TN. Thi LMAF i f ll d ib d b BS l l ti

• This LMAF is fully described by BS calculations.
• No Bragg peaks seen in HO phase! Only INS modes!!
• INS (100) mode: dynamical fluctuations which couple
• INS (100)-mode: dynamical-fluctuations which couple

to a small/tiny OP and lead to HO transition T0. Dynamical symmetry breaking!

• KEY here is a collective mode of long-lived (lattice

coherent) longitudinal AF excitations. S h l t h t 2nd d PT

• Such causes large entropy change at 2nd order PT.
• HO Bragg peak seen in magnetic X-ray scattering?

• Neutron scattering under

h drostatic press re hydrostatic pressure

• H. Amitsuka, M. Sato, N.

Metoki, M. Yokoyama, K. K h T S k kib Kuwahara, T. Sakakibara,

• H. Morimoto, S. Kawarazaki,
• Y. Miyako, and JAM

PRL 83 (1999) 5114

29Si NMR under hydrostatic pressure

• K. Matsuda,Y. Kohori, T. Kohara,
• K. Kuwahara, H. Amitsuka

PRL 87(2001)087203 0.3 < P (GPa) < 0.83 ; T < T

• New resonance lines

Bint ≈ ± 910 G evidence of a static AF order Coexistence of previous line the AF order occurs partly in crystal !

• H. Amitsuka et al.,JMMM

310, 214(2007).

P – T phase diagram

LMAF Little change in bulk properties with const. P when crossings into HO(T0)

• r LMAF(TN) phases, e.g. opening of similar gaps: Adiabatic Continuity.

Magnetic properties of URu2Si2 at ambient pressure: HO is non-magnetic at ambient pressure: HO is non magnetic

IB = A µ

d 2 = A v µAF 2

IB A µord A v µAF v ≈ ≈ 1 % µord

2

µAF

2

≈ (0.25 µB)2 (0.02 µB)2 Volume fraction of AF order: µAF ( µB) Hidden order : ≈ 99% Hidden order : ≈ 99% Best crystals today HO ≈ 99 9% or 1000 ppm AF Best crystals today HO 99.9% or 1000 ppm AF Conclusion: LM-AFM is extrinsic, crystal strain effect See M Yokoyama et al PRB 72 214419(2005) See M. Yokoyama et al. PRB 72, 214419(2005).

Crystalline strain model (c/a) and LMAF based upon uniaxial stress (σ) of neutron scattering and elastic constants l i analysis.

• M. Yokoyama et al. PRB 72, 214419 (2005).

η = δ(c/a) which has a distribution N(η) that is shifted as a function of strain or c/a ratio. Above ηC inhomogeneous LMAFM starts to appear leading to LR-AFM.

HO excitations via INS as fct. of pressure – pioneering p p g

• measurements. H. Amitsuka et al. JPSJ 69(supl.A), 5(2000).

Inconclusive, both excitations seem to disappear with pressure as LMAF is entered

Phase diagram T vs P based upon resistivity and calorimetric experiments under pressure experiments under pressure.

• E. Hassinger et al. PRB 77, 115117(2008).

N t t i il it ith A it k ’ T P h di Note strong similarity with Amitsuka’s T – P phase diagram. Nesting vector not yet found !!

Lamor diffraction of single crystal under pressure (TRISP: neutron scattering) determines thermal expansion coefficient neutron scattering) determines thermal expansion coefficient. P.G. Niklowitz, C. Pfleiderer, Th. Keller & JAM, to be published.

∆ d ∆ d i t i l i t i h t t t ∆a and ∆c are measured via triple-axis, resonant spin-echo spectrometer at nuclear Bragg peaks (400) and (008).

Definition of HO (TO) and LMAF (TX) phases via thermal expansion and (elastic) Bragg peak at 6 7 GPA expansion and (elastic) Bragg peak at 6.7 GPA.

• A. Villaume et al., PRB 78, 012504(2008).

N t t t t 12 K f LMAF ( hi 0 4 ) hil th HO i l b Note strong onset at 12 K of LMAF (reaching ≈0.4µB) while the HO is only seen by thermal expansion – nonmagnetic.

INS at 6.7 GPa for Qo = (100) as a function of temperature.

• (

) p

• A. Villaume et al., PRB 78, 012504(2008).

The Qo excitation disappears as does the HO upon entering the LMAF phase, and

• pp

p g p , becomes a Braag peak in LMAF phase !! Thus this excitation is characteristic of HO !

INS at 6.7 GPa for Q1 = (1.4 0 0) as a function of temperature.

1

( ) p

• A. Villaume et al. PRB 78, 125040(2008).

Q it ti i th h t b th HO d LMAF h b t hift t hi h Q1 excitation remains throughout both HO and LMAF phases but shifts to higher energy in the latter. Characteristic of both HO and LMFM ? Shows their close relationship: AC.

Energy integrated (+/-0.5meV) cuts in HO across [H00]. High resolution dispersion in HO compared to 20K fits. J A Janik et al to be published (2008) [Broholm et al PRB J.A. Janik et al., to be published (2008). [Broholm et al. PRB 43, 12809(1991); Wiebe et al. Nat.Phys. 3, 97(2007)]

Increased scattering at higher energies. Above T

• heavily damped incommensurate

paramagnons (SF) which become long-lived f-spin excitations below T0

HO excitations as function of field at Qo=(100) and Q1=(1.4 0 0).

• (

)

1 (

)

• F. Bourdarot et al. PRL 90, 06703(2003).

INS excitation energy at Qo increases with Hext while that at Q1 remains

• constant. HO characteristic ?

U(Ru,Rh)2Si2, Key energy scales & high field investigation

Key energy scales at H=0 T, P=1 at m T HO state in URu2Si2 develops a gap in FS below 17K Rh doping removes HO state to make HF groundstates W~Tcoh~50 K Rh doping removes HO state to make HF groundstates THO=17.5 K

HF

TC≈1.5 K

HF HO

HO+AF

B

C

0K

• M. Jaime et al. PRL (2002)

N H i PRL (2003)

Rh x 0.04 0.0

B 50T High magnetic fields of up to 50 T; Zeeman splitting ∆E=gµBB~50 K

• N. Harrison PRL (2003)
• K. H. Kim et al., PRL (2003)
• K. H. Kim et al., PRL (2004)

High magnetic fields of up to 50 T; Zeeman splitting ∆E=gµBB 50 K Specif ic heat , magnet izat ion, and resist ivit y ( previously st udied). The Hall ef f ect s t hrough pulsed magnet ic f ields

Ongoing new experiments - 2008 g g p (not yet published).

• STM/STS at atomic resolution – S. Davis.
• NMR on Rh doped URu2Si2 – N. Curro.

p

2 2

• ARPES

J Denlinger / J Allen vs Y Chen

• ARPES – J. Denlinger / J. Allen vs Y. Chen

/ Z-X Shen.

Conclusions concerning HO Co c us o s co ce g O

• HO mediates the superconductivity

HO b t t ll d t d b H d Rh

• HO can be totally destroyed by H and Rh-x
• HO can be converted to LMAF by P (adiabatic continuity)
• HO is a gapping/reconstruction of FS (itinerant electrons)

Nesting vector indicated from proper band structure/FS

• Nesting vector indicated from proper band structure/FS
• HO breaks both Time-RS and Translational-RS
• HO exhibits two INS modes:(100)@2meV and (1.400)@5meV of

longitudinal fluctuations/excitations. With P (100) becomes the longitudinal fluctuations/excitations. With P (100) becomes the static elastic Bragg peak creating LMAF

• Fluctuations/dynamics INS modes mediate/generate the HO-OP

which is proportional to the amplitude of the INS mode LMAF b th i d bit l t HO h

• LMAF possesses both spin and orbital moments; HO shows no

total magnetic moment

• Problem of elastic neutron scattering with very fast fluctuations

(seen in RMXD) and orbital moments (seen in RMXD) and orbital moments

• HO is caused by a huge FS gapping mediated by a dynamical

mode

To be continued by Peter Oppeneer on Sunday