Nernst effect and Kondo scattering in (CeLa)Cu 2 Si 2

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1 Nernst effect and Kondo scattering in (CeLa)Cu 2 Si 2 Peijie Sun MPI Chemical Physics of Solids, Dresden (IOP-CAS, from April 212) Collaborators: C. Geibel, F. Steglich 1

2 Outline Introduction to magneto-thermoelectric transport of HF systems. Nernst effect as a probe of relaxation time spectra and its relation to thermoelectric power. Experimental results on (CeLa)Cu2Si2 and discussion. Summary. 2

3 Introduction Archetype TEP of Kondo systems Thermopower (µv/k) 1 5 Ce-based Kondo systems La-based nonmagnetic analogue Renormalized DOS frequency Typical Kondo resonance (Ce) n-type quasiparticle, which seems inconsistent with TEP. Gradually adding Ce (or Yb) to a nonmagnetic matrix, the TEP responses following certain rules, independent of the carrier type in the matrix. Open issues: microscopic reason for the different type of TEP(T); why carrier type of the nonmagnetic matrix not important 3

4 TE transport tensor in field z B z y Ex Thermoelectric power (diagonal S xx ) S = E x / T x Origin: p/h asymmetric DOS and τ - T x Nernst coefficient (off diagonal S xy ) z B z - T x y Fast carriers Slow carriers x E y T v= Ey / Bz x = E / B T y z Origin: p/h asymmetric τ, band and scattering anisotropy, vortex dynamics Slow-diffusing carriers are more deflected by magnetic field than fast-diffusing carriers 4

5 Interplay between diagonal and offdiagonal TE component 2 2 π kb T lnσ xx Thermopower: Sxx = 3 e ε F 2 2 π kb T tanθ σ H xy Nernst: Sxy = (Hall angle tan θh = ) 3 e ε σ F Important Assumptions: 1, Relaxation time approximation 2, relaxation time is the only E-dependent term in the Hall angle 3, measurements in low magnetic field xx ST ( ) 2 2 v π kt lnd = + µ H 3 e ε = ε ε F In principle, Nernst measurement can disentangle the different sources of thermopower. 5

6 Compare two sets of Nernst data of gold Nernst coeffi. ν (µv/kt) E-3 1E-4 Fletcher 1971 Behnia 27 1E Au Several orders of magnitude different for gold of presumably different quality! Strong indication of Kondo scattering in Fletcher s results (dirty Au). Much more sensitive to unconventional scattering process than thermopower. 6

7 Resistivity of (CeLa)Cu2Si (CeLa)Cu 2 Si 2 ρ (µω cm) Ce1. Ce.9 Ce.2 LaCu2Si M. Ocko et al, 21 x =.5: crossover from coherent to incoherent conduction Interested: how Nernst signal evolves when coherence set in, where Kondo scattering is suppressed? 7

8 thermopower 2 (LaCe)Cu 2 Si 2 S (µv/k) -2 Ce1. Ce.9 Ce.2 LaCu2Si coherency Also interested: does the very different low temperature (< 1K) thermopower of lattice (Ce1.) and impurity (Ce.2,Ce.9) Kondo system indicate that the former is asymmetric DOS driven, and the latter one is asymmetric-scattering-driven (coherency as the control parameter). 8

9 Nernst coefficients ν (µv/kt) Ce1. Ce.9 Ce.2 LaCu2Si2 (CeLa)Cu 2 Si Nernst of LaCu2Si2 much smaller than Ce-based systems 2. Common feature for Ce compounds: high-t negative peak 9

10 Nernst and thermopower: LaCu2Si2.8 LaCu 2 Si LaCu 2 Si 2 3 ν (µv/kt) ν/µ H 2 1 S (µv/k) -1 Thermopower dominated by DOS. Nernst signal dominated by scattering. S and Nernst coefficient are largely independent

11 25 2 LaCu2Si B 2 2 F LaCu2Si2: approach from ac.ph. scattering µ H (cm 2 /Vs) 1 ρ (µω cm) LaCu 2 Si 2 µ H ~T -1 Canonical resistivity and mobility Electron scattered by acoustic phonons ν (µv/kt) e ε S = xy π θ T k H tan LaCu 2 Si Inputs: τ= τε Acoustic phonon scattering: Bare electron mass 1 11

12 Nernst and thermopower : CeCu2Si2 CeCu 2 Si CeCu 2 Si ν (µv/kt) ν /µ H S (µv/k) Thermopower can be well traced by Nernst signal. Asymmetric scattering rate (rather than f derived heavy band) leads to large S in the whole T range (2K -25K). No clear evidence of heavy-band formation down to 2 K. -2 ρ (µω cm) CeCu 2 Si

13 Ce.9- and Ce.2-compounds ν (µv/kt) Ce Ce.9 La Cu Si S (µv/k) ν (µv/kt) Ce ν/µ H S (mv/k) -5-1 Surprise: Thermopower of Ce.9 and Ce.2 cannot be well reproduced by using Nernst signal? 13

14 Measured thermopower vs. anticipation from scattering term 4 2 (LaCe)Cu 2. Si 2 r τ= τε S (µv/k) -2-4 Ce1. Ce.9 Ce.2 LaCu2Si Agreement worsens as Ce concentration decrease. scattering exponent, r Ce.9 La.91 Cu 2 Si Assuming validity of exponent law leads to extremely large exponent r! 14

15 .1 Hall effect R H (cm 3 /C-Ce).1 1E-3 1E Ce.2 Ce.9 Ce1. LaCu2Si2 R H (normalized by Ce concentration) increases with decreasing Ce concentration. Useful hint for understanding the anomalous Nernst effect, especially in the low Ce concentration side. 15

16 Summary Like thermopower, Nernst coefficient in HFs is largely enhanced over a wide T range. New insight concerning Kondo scattering can be obtained by Nernst measurement. For CeCu2Si2, Kondo scattering seems able to fully account for its thermopower. While for its dilute systems, skew scattering contribution develops to Nernst signal, which can even mask the Kondo scattering contribution. Systematic study on different Kondo systems desired. 16