Mesoscopic conductance fluctuations and spin glasses

Transcription

1 GdR Meso 2010 G Thibaut CAPRON Track of a potential energy landscape evolving on geological time scales B Mesoscopic conductance fluctuations and spin glasses

2 Team project Quantum coherence group : C. Bäuerle, L. Lévy, T. Meunier, L. Saminadayar (Institut Néel - CNRS Grenoble) Collaborations : Theory : David Carpentier, Edmond Orignac Andreï Fedorenko (Post-doc) Guillaume Paulin (PhD) (ENS Lyon) Implantation of magnetic impurities : Christophe Peaucelle, Angela Perrat-Mabillon (IPN Lyon) The polygone scientifique in Grenoble ANR MesoGlass

3 Outline Introduction to spin glass physics Spin glass signatures on the resistivity Universal conductance fluctuations in spin glasses Towards a measurement of the order parameter Conclusion and prospects

4 Outline Introduction to spin glass physics Spin glass signatures on the resistivity Universal conductance fluctuations in spin glasses Towards a measurement of the order parameter Conclusion and prospects

5 Physics of glasses No long-range order Phase transition at Tg Stained glasses Metastable slow relaxation Amorphous Glassy concepts are used for : Human dynamics Complex networks Jamming A major challenge : real transition? ground state?

6 What is a spin glass? Magnetic glass Metallic matrix (Cu,Ag,Au) l Spatial disorder RKKY interaction ~ cos(k F l) => changing sign Magnetic impurities (Mn,Fe, ) Antiferro (J<0) Frustration Below T g spin configuration is randomly frozen => slow relaxation without long-range order A model glass, extensively studied Tg Canella and Mydosh 1972

7 A peculiar phase space T>Tg : free spins An order parameter T<Tg : frozen spins q lim t S i (0). S i ( t) Ferro Spin glass T > Tc F M=0 T < Tc F M 0 Manyvalley phase space M M system trapped

8 Mean-field theory T Tg q αβ represents the distance between states α and β 1 = α qαβ S i. S i N i the spin overlap β Parisi 1983 P(q) When cycling, q can take numerous values q

9 Droplet model When T decreases, Γ is growing There is a unique ground state Γ (and the symmetric ) Γ Γ Fisher and Huse 1988 is an off-equilibrium droplet q can take only 2 values P(q) Γ is in the ground state -q Γ q Γ q

10 A new probe Universal conductance fluctuations (UCF) : P(r,r ) = Ψ a + Ψ b ² = Ψ a ² + Ψ b ² + 2 Ψ a Ψ b cos(φ a -φ b ) Interferences Geometrical dephasing (sample-to-sample UCF) Magnetic dephasing (field UCF) r B L < L φ (b) (a) r Benoit et al Macroscopic measurements Microscopic sensitivity of UCF χ 1 = χ 2 C v1 = C v2 Configuration 1 Configuration 2

11 Ag sample V+ V- L ~L Φ Experimental setup Implantation Mn c=500 ppm (Tg 500 mk) R/R ~ 10-4 for the UCF Low-noise detection 0.4 nv/sqrt(hz) Magnetic field up to 8 T

12 Outline Introduction to spin glass physics Spin glass signatures on the resistivity Universal conductance fluctuations in spin glasses Towards a measurement of the order parameter Conclusion and prospects

13 Calibration on Ag resistivity Ag 0 ppm Quasi-1d wire L = 2 µm w = 50 nm t = 40 nm V+ V- Calibrate the electron-electron interaction Alt shuler Aronov 1981

14 An estimate of Tg AgMn 700 ppm R SG A ( T ) = 2 ln ( T / T K 1 α S ) Vavilov Glazman PRB 2003 T g T T g 0.7 K T K =40 mk Tm Tg Deviation below Tm

15 Magnetic irreversibilities Deviations in ρ between FC and ZFC FC ZFC Tg Nagata et al.1979 Tg consistent with the previous estimate Sharp criterion to measure Tg directly in a mesoscopic wire

16 Outline Introduction to spin glass physics Spin glass signatures on the resistivity Universal conductance fluctuations in spin glasses Towards a measurement of the order parameter Conclusion and prospects

17 UCF magnetofingerprints Ag 0 ppm L=1µm;w=100nm;t=40nm z R ~ 3 mω (R=6Ω) Reproducible Aperiodic

18 UCF in spin glasses UCF amplitude increasing with the field Two field regimes: 0 4 T ; 4 8 T

19 Field effect Vavilov Glazman PRB 2003 L Φ enhanced as we field-freeze the magnetic scattering

20 Freezing the UCF Allows to extract N(T) the number of free spins? Confirm the hierarchical phase space? Low-Field High-Field Tg A factor 3

21 Outline Introduction to spin glass physics Spin glass signatures on the resistivity Universal conductance fluctuations in spin glasses Towards a measurement of the order parameter Conclusion and prospects

22 Studying the correlations Configuration 1 Configuration 2 Frozen disorder i C = 1 i Correlation coefficient : Configuration 1 C (1) (2) =< δ G ( B ). δ G ( ) ( 1,2) B > Configuration 2 i Disorder changed (T, B, ) i 0 < C < 1 C 12 is linked to q 12

23 Ag 0 ppm T=15 K for 15 h AgMn 400 ppm (SG) (T g 400mK) T=15K ( 20 Tg) for 15 mn C = 0.95 C 0.2 Sensitive to magnetic configuration

24 T Modifying the magnetic order? Decorrelation at T>T g B δg (n) δg (n+1) t We measure C (n,n+1) Spin-glass phase diagram? H Para (q=0) Spinglass (q=1) T Tg? C decreases with increasing T

25 Conclusion and prospects UCF are a new and sensitive tool for probing spin glass ordering Magnetic irreversibilities in ρ Spin glass freezing of the UCF Correlations yield a direct measurement of q (and P(q)?) C 12 q 12 D. Carpentier and E. Orignac PRL 2008 G. Paulin and D. Carpentier arxiv: A. Fedorenko and D. Carpentier EPL