Calculated Electronic Structure Properties of URu 2 Si 2 Calculated Electronic Structure Properties of URu 2 Si 2 and of Ce-115 Materials of Ce-115 Materials and 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 CeCoIn 5 from ARPES and calculations � Electronic structure of URu 2 Si 2 and nature of H.O. 1
Collaboration Collaboration NQR Ce-115´s Uppsala Ce-115 ARPES Nick Curro Saad Elgazzar J.D. Denlinger Ricardo Urbano Jan Rusz Jim Allen Ben-Li Young Michi-To Suzuki Feng Wang S. Lebegue Martin Amft R.S. Singh P.G. Pagliuso K. Rossnagel Long D. Pham V.S. Zapf E.D. Bauer M.B. Maple URu 2 Si 2 J.L. Sarrao John Mydosh Z. Fisk 2 Hvar Conference September 2008
Computational methodology Computational methodology Density-functional theory based computational investigations All electron, full-potential, fully-relativistic electronic structure calculations, mainly FL-APW and FPLO codes. 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 3 Hvar Conference September 2008
The Hidden Order of URu 2 Si 2 The Hidden Order of URu 2 Si 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 T PM the FS is gapped LMAF HO � Now: valid electronic structure model SC � Explains most of known properties of URu 2 Si 2 P � 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. 4 Hvar Conference September 2008
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 Important notion from experiment: “adiabatic continuity” = HO & LMAF very similar T PM BUT not the same OP! LMAF HO SC P 5 Hvar Conference September 2008
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 6 Hvar Conference September 2008
Our new electronic structure model of URu 2 Si 2 Explains the following properties: � anisotropy of resistivity � lattice constant ( � 0.5%) � AFM order under pressure � magnetic moment 0.39 μ B � nesting vector � energy scale � 7 K � breaking of time-reversal � compensated metal & body-centering � Hall effect - number of holes � dispersive f -dominated � FS gapping at E F bands near E F � infrared optical spectra ( � ) de Haas-van Alphen � jump �� in resistivity ? ARPES (new exp. coming) 7 Hvar Conference September 2008
Earlier computed FS for LMAF phase Earlier computed FS for LMAF phase Very large difference with regard to previous result (2000) ! 2 bands � is in the center, Z at top; Yamagami & Hamada, 3 bands. Physica B 284 , 1295 (2000) 8 Hvar Conference September 2008
One key feature of HO: FS gapping FS gapping: Palstra et al, PRB 33 (1986) Behnia et al, PRL 94 (2005) resistivity, C/T Nernst effect Hall effect IR optics … Extraction of k-averaged gap � � ~5 - 11 meV Maple et al, PRL Jeffries et al, 56 , 185 (1986) Jeffries et al, PRL 99 (2007) PRL 99 (2007) 9 Hvar Conference September 2008
LMAF vs vs. PM: A small gapping ?? . PM: A small gapping ?? LMAF . � . A . � . R . . � . . � M X Simple tetragonal BZ of AFM phase LMAF and PM phase bands are very close! 10 Hvar Conference September 2008
Fermi surface gapping visualized surface gapping visualized Fermi >> Often speculated, but never microscopically identified PM � R A � � � M X A large gapping LMAF Rugged, arm-shaped FS sheet disappears completely 11 Hvar Conference September 2008
Fermi surface cross section in z=0 z=0 plane plane Fermi surface cross section in LMAF Two entangled FS sheets in PM phase, PM break-up in LMAF phase � X � E F Degenerate crossing at E F 12 Hvar Conference September 2008
Influence of gapping: Computed resistivity resistivity jump jump Influence of gapping: Computed Computed T=0 resistivity change from gapping: [ � AFM � � PM ]/ � PM ( J || c ) = 620% Anisotropy 4:1 [ � AFM � � PM ]/ � PM ( J || a ) = 160% Experiment at T=17.5K: � � HO / � PM ( J || c ) = 400% �� HO / � PM ( J || a ) = 100% Anisotropy 4:1 Large � 0 + �� 2 -background at 17K subtracted, but no other correction 13 Hvar Conference September 2008
Compensated metal, carrier density Compensated metal, carrier density Somewhat larger exc.-splitting: Carrier density: PM: n h ~ 0.08/ U-atom LMAF: n h ~0.0185/ U-atom Factor of 4! Hall resistivity exp: 0.017 < n h (HO) < 0.021 Kasahara et al. PRL 99 , 116402 (2007) n h � n e PM: n h ~0.1 / U-atom Oh et al. PRL 98 , 016401 (2007) 14 Hvar Conference September 2008
Optical conductivity Optical conductivity Bonn et al, PRL 61 , 1305 (1988) Calculated � ( � ) 35 meV E||a Calculated change in � a below 40 meV Larger effect predicted for E||c 12 meV 15 Hvar Conference September 2008
Fermi surface nesting in z=0 z=0 plane plane Fermi surface nesting in LMAF Nesting in the LMAF phase is supposed PM to be close to nesting in HO phase � X � 0.4a* 0.6a* 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) 16 Hvar Conference September 2008
Continuous variation PM <=> SMAF <=> LMAF Continuous variation PM <=> SMAF <=> LMAF Varied the exchange-splitting to go gradually from PM to SMAF to LMAF LMAF PM � X � Moment: 0 μ B <=> 0.04 μ B <=> 0.16 μ B <=> 0.39 μ B (orbitally dominated) E F Entangled FS sheets break-up already for the smallest moments! The smallest energy is sufficient to cause a topological FS transition! 17 Hvar Conference September 2008
Fermi surface “ “hot spots hot spots” ” Fermi surface FS instability at degenerate crossing points, which we identify as “hot spots” for HO/AFM transition Hot spots for HO /AFM : eight lines ~Z to -Z 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 18 Hvar Conference September 2008
FS gapping at “ “hot spots hot spots” ” quantified quantified FS gapping at LMAF Gapping vs. longitudinal U-moment PM � X � � � ( k )-varies between 0 and 700K on FS Exp.: k -independent average gap � on FS ( � 50-100K) � = � ( J ex ) or � = � ( M z ) � even function of M z 19 Hvar Conference September 2008
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 20 Hvar Conference September 2008
Model for the HO order parameter Model for the HO order parameter 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 T PM < � > not zero in HO LMAF “dynamical symmetry breaking” HO (1) = 0 (1) � 0 M z M z Predictions: P • Large orbital moment � � 0 • spectrum � (E||c) • location & size of gap 21 Hvar Conference September 2008
ARPES & Fermi surface of CeCoIn 5 ARPES & Fermi surface of CeCoIn 5 How does the FS of a Kondo lattice material evolve with temperature below T* -> 0 K ? Small to large ? � Investigate archetypical case CeCoIn 5 � FS studied in detail by dHvA down to mK � Use ARPES at T*/2 � Compare with FS calculations 22 Hvar Conference September 2008
Two-fluid model for CeCoIn 5 Kondo lattice Nakatsuji, Pines & Fisk, PRL 92 (2004) Heavy-electron fluid below T* “Kondo impurity fluid” above T* T*~45 K f =(1– T/T* ) fraction of delocalized heavy electrons, f =0.42 at 26K Localized f -moment, dHvA confirms large FS “half expanded”? single-ion Kondo with f ’s embedded behavior “large FS” “small FS” 23 Hvar Conference September 2008
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