Collaboration Collaboration NQR Ce-115s Uppsala Ce-115 ARPES - - PowerPoint PPT Presentation

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Calculated Electronic Structure Properties of URu Calculated Electronic Structure Properties of URu2

2Si

Si2

2

and and

• f Ce-115 Materials
• f Ce-115 Materials

Peter M. Oppeneer

Department of Physics and Materials Science, Box 530 Uppsala University, S-751 21 Uppsala, Sweden

Calculated NQR of pure and doped Ce-115´s Fermi surface of CeCoIn5 from ARPES and calculations Electronic structure of URu2Si2 and nature of H.O.

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Collaboration Collaboration

Uppsala Saad Elgazzar Jan Rusz Michi-To Suzuki Martin Amft URu2Si2 John Mydosh Ce-115 ARPES J.D. Denlinger Jim Allen Feng Wang R.S. Singh

• K. Rossnagel

V.S. Zapf M.B. Maple NQR Ce-115´s Nick Curro Ricardo Urbano Ben-Li Young

• S. Lebegue

P.G. Pagliuso Long D. Pham E.D. Bauer J.L. Sarrao

• Z. Fisk

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Computational methodology Computational methodology

All electron, full-potential, fully-relativistic electronic structure calculations, mainly FL-APW and FPLO codes. Density-functional theory based computational investigations Exchange-correlation treated on LSDA, GGA, LSDA+U, GGA+U levels

f-electron behavior: f-localized f-itinerant LDA f-core DFT+U LDA,GGA

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The Hidden Order of URu The Hidden Order of URu2

2Si

Si2

2

Over 2 decades of much exp. & theo. research, yet no firm understanding of the underlying physics (talks John Mydosh & Brian Maple)

No valid electronic structure model No clue where, how and by what mechanism

the FS is gapped

Now: valid electronic structure model Explains most of known properties of URu2Si2 Detailed picture of FS “hot spots”, FS gapping

and symmetry-breaking

Proposal for mechanism of the H.O. Prediction of various quantities for future exps.

T P LMAF HO

SC

PM

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Our calculations Our calculations

PM, LMAF, and variation of exchange-interaction J to go continuously PM <=> SMAF <=> LMAF Compute properties & compare to existing exp. data 1. Our codes give precisely same result 2. Explain first PM & LMAF phases 3. Zoom in on the HO state T P LMAF HO

SC

PM Important notion from experiment: “adiabatic continuity” = HO & LMAF very similar BUT not the same OP!

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Theoretical models for the HO Theoretical models for the HO

• Santini & Amoretti (1994) Quadrupolar order*
• Barzykin & Gorkov (1995)

three-spin correlations

• Kasuya (1997)

U dimerization

• Ikeda & Ohashi (1998)

d-spin density wave

• Okuno & Miyake (1998)

CEF & quant. fluctuations*

• Chandra, et al (2002)

Orbital currents

• Dora & Maki (2003)
• unconv. SDW
• Mineev & Zhitomirsky (2005) SDW
• Kiss & Fazekas (2005)

Octupolar order*

• Varma & Zhu (2006)

Helicity order

• ...

*localized f models >> But no microscopic, ab initio model

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Our new electronic structure model of URu2Si2

Explains the following properties:

lattice constant (0.5%) magnetic moment 0.39 μB energy scale 7 K compensated metal Hall effect - number of holes FS gapping at EF infrared optical spectra jump in resistivity anisotropy of resistivity AFM order under pressure nesting vector breaking of time-reversal

& body-centering

dispersive f-dominated

bands near EF () de Haas-van Alphen ? ARPES (new exp. coming)

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Earlier computed FS for LMAF phase Earlier computed FS for LMAF phase

Yamagami & Hamada, Physica B 284, 1295 (2000)

Very large difference with regard to previous result (2000) ! is in the center, Z at top; 3 bands. 2 bands

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One key feature of HO: FS gapping

FS gapping: resistivity, C/T Nernst effect Hall effect IR optics …

Jeffries et al, PRL 99 (2007)

Extraction of k-averaged gap ~5 - 11 meV

Maple et al, PRL 56, 185 (1986) Jeffries et al, PRL 99 (2007) Palstra et al, PRB 33 (1986) Behnia et al, PRL 94 (2005)

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LMAF LMAF vs

• vs. PM: A small gapping ??

. PM: A small gapping ??

A X M

. . . .

• .
• R

.

. .

• LMAF and PM phase bands are very close!

Simple tetragonal BZ

• f AFM phase

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Fermi Fermi surface gapping visualized surface gapping visualized

A X M

• R
• PM

LMAF A large gapping

Rugged, arm-shaped FS sheet disappears completely

>> Often speculated, but never microscopically identified

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Fermi surface cross section in Fermi surface cross section in z=0 z=0 plane plane

• X
• Two entangled FS sheets in PM phase,

break-up in LMAF phase

LMAF PM EF Degenerate crossing at EF

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Influence of gapping: Computed Influence of gapping: Computed resistivity resistivity jump jump

[AFM PM ]/PM(J || c) = 620% [AFM PM ]/PM(J || a) = 160%

Computed T=0 resistivity change from gapping:

Anisotropy 4:1

Experiment at T=17.5K:

HO /PM (J ||c) = 400% HO /PM (J || a) =100%

Large 0+2-background at 17K subtracted, but no other correction

Anisotropy 4:1

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Compensated metal, carrier density Compensated metal, carrier density

Somewhat larger exc.-splitting:

Carrier density:

PM: nh ~ 0.08/ U-atom LMAF: nh ~0.0185/ U-atom

nh ne

Factor of 4! Hall resistivity exp:

0.017 < nh (HO) < 0.021

Kasahara et al. PRL 99, 116402 (2007) Oh et al. PRL 98, 016401 (2007)

PM: nh ~0.1 / U-atom

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Optical conductivity Optical conductivity

Bonn et al, PRL 61, 1305 (1988) 35 meV 12 meV

E||a

Calculated change in a below 40 meV Larger effect predicted for E||c Calculated ()

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

• X
• Nesting in the LMAF phase is supposed

to be close to nesting in HO phase

LMAF PM

0.6a* 0.4a*

Neutron experiments give nesting at vectors Q=(1±0.4, 0, 0) Wiebe et al. PRB 69, 132418 (2004) Wiebe et al. Nat. Phys. 3, 96 (2007)

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Continuous variation PM <=> SMAF <=> LMAF Continuous variation PM <=> SMAF <=> LMAF

• X
• LMAF

PM

Varied the exchange-splitting to go gradually from PM to SMAF to LMAF

EF

Moment: 0 μB <=> 0.04 μB <=> 0.16 μB <=> 0.39 μB (orbitally dominated)

The smallest energy is sufficient to cause a topological FS transition! Entangled FS sheets break-up already for the smallest moments!

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Fermi surface Fermi surface “ “hot spots hot spots” ”

FS instability at degenerate crossing points, which we identify as “hot spots” for HO/AFM transition The system can remove the FS instability through a spontaneous symmetry breaking! From the calculations: breaking of bc and time-reversal symmetry needed Consistent with experiment for both HO / LMAF Hot spots for HO /AFM : eight lines ~Z to -Z

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

• X
• LMAF

PM Gapping vs. longitudinal U-moment

• = (Jex) or = (Mz)

even function of Mz

(k)-varies between 0 and 700K on FS Exp.: k-independent average gap on FS ( 50-100K)

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Importance of collective AF modes Importance of collective AF modes

INS sees collective long-lived AF mode in HO which freezes to static AF order in LMAF =>> “signature of HO” Response at HO/LMAF nesting vector 1.4a* doesn’t change Villaume et al, PRB 78 (2008) Dynamical AF response also seen with RXMS in HO

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Model for the HO order parameter Model for the HO order parameter

T P LMAF HO PM

Mz

(1) 0

Mz

(1) = 0

Collective long-lived AF mode is a weak actor, on small energy scale (7K) but couples to a huge FS gapping (700K) Mediates changes in macroscopic thermodynamic properties Different OP in HO and LMAF <M>=0 in HO, can not be OP <> not zero in HO “dynamical symmetry breaking” Predictions:

• Large orbital moment
• spectrum (E||c)
• location & size of gap

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ARPES & Fermi surface of CeCoIn ARPES & Fermi surface of CeCoIn5

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How does the FS of a Kondo lattice material evolve with temperature below T* -> 0 K ? Investigate archetypical case CeCoIn5 FS studied in detail by dHvA down to mK Use ARPES at T*/2 Compare with FS calculations Small to large ?

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Two-fluid model for CeCoIn5 Kondo lattice

Heavy-electron fluid below T* “Kondo impurity fluid” above T*

T*~45 K

Nakatsuji, Pines & Fisk, PRL 92 (2004) dHvA confirms large FS with f ’s embedded

f=(1–T/T*) fraction of delocalized heavy electrons, f=0.42 at 26K

Localized f-moment, single-ion Kondo behavior

“large FS” “small FS” “half expanded”?

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De Haas-van Alphen experiments

Shishido et al., JPSJ 71 (2002)

2-D character FS sheets

Good agreement with f-itinerant LDA calculations

• ’
• ’
• Small 3-D

FS sheets

Elgazzar et al, PRB 69 (2004)

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Calculated dHvA frequencies Ce-115´s

For CeRhIn5 better agreement with f-core calculations, but for CeCoIn5 better with f-valence calculations

CeCoIn5 (deloc. f ) CeRhIn5 (loc. f )

• Exp. F

Elgazzar et al, PRB 69 (2004)

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f f-localized vs

• localized vs.

. f f-itinerant

• itinerant Fermi surface

Fermi surface

c1

• j

c2

(a) f-itinerant (b) f-core

’

• ’
• R

A M

2

• 1

3 1 2

X

• c3

131 133 135

Partially 3Dim. Fermi surface Easy for dHvA, difficult for ARPES Elgazzar et al, PRB 69 (2004) Oppeneer et al, JMMM (2007)

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ARPES Fermi surface maps, T=26 K ARPES Fermi surface maps, T=26 K

Fermi surface maps of CeCoIn5 from 90 eV to 125 eV showing kz-evolution of the FS contours (full BZ period, -> )

• sheet clearly visible, with kz-modulation

>> position of kz in BZ

• R

A M

3 1 2

X

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Comparison with calculated FS contours Comparison with calculated FS contours

Overplot with f-itinerant contours Overplot with f-core contours Exp. contours

At 26K definitely best agreement with f-localized FS

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Effect of Effect of k kz

z-broadening

• broadening

No broadening With kz- broadening >> Even better agreement with f-core

At TT*/2 the FS remains contracted!

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NQR of pure and doped Ce-115 NQR of pure and doped Ce-115’ ’s s

Can we compute ab initio NQR’s for these materials? Effect of Cd and Sn doping on NQR frequencies? Connection to the Ce f-electron behavior?

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Calculated NQR frequencies Calculated NQR frequencies

NQR frequencies measured for CeMIn5

115In: I =9/2, large μN & Q 59Co: I =7/2, large μN & Q

HQ = eVzzQ 4I(2I 1) 3Iz

2 I(I +1)

[ ]

Quadrupolar interaction Hamiltonian: NQR frequency:

(Nuclear quadrupole moment Q, spin I )

Q = 3eVzzQ 2I(2I 1)h

Vzz calculated EFG

M

T = Co, Rh, Ir c a b

M M

In(1) In(2)

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Pure Ce-115 compounds Pure Ce-115 compounds

NQR frequencies very well described New window on the f-behavior via NQR of ligand atom CeCoIn5 weakly localized f ’s (U3 eV), CeIrIn5 somewhat

more localized f ’s (U6 eV), CeRhIn5 localized f ’s (at 4-5 K!)

Physical picture consistent with that from de Haas-van Alphen

• Exps. N. Curro

MHz

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Doped Ce-115 Doped Ce-115’ ’s: Tuning from SC to AFM s: Tuning from SC to AFM

Pham et al, PRL 97 (2006)

Tuning CeCoIn5 to AFM through Cd doping on In

=> Connection between AFM fluctuations and unconv. SC

Measured NQR spectrum

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NQR spectrum of NQR spectrum of Cd-doped Cd-doped CeCoIn CeCoIn5

5

impurity

FS of CeCoIn5 becomes more like CeRhIn5 with Cd doping

doping

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NQR spectrum of NQR spectrum of Sn-doped Sn-doped CeRhIn CeRhIn5

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Gives possibility to estimate Sn distribution over In(1) and (2)

Good calculated NQR spectrum doped CeRhIn5

Rusz et al, PRB 77 (2008)