Probing a Metallic Spin Glass Nanowire via Coherent Electronic Waves Diffusion

Transcription

1 Probing a Metallic Spin Glass Nanowire via Coherent Electronic Waves Diffusion D. Carpentier, (Ecole Normale Supérieure de Lyon) Theory : A. Fedorenko, E. Orignac, G. Paulin (PhD) (Ecole Normale Supérieure de Lyon) Experiments : C. Bäuerle, T. Capron (PhD), L. Lévy, T. Meunier, L. Saminadayar (Quantum Coherence Group, Institut Néel, Grenoble) Support : CNRS, Computing center of ENS-Lyon (PSMN) and ANR MesoGlass

2 Using waves to probe matter Various methods to probe (soft) condensed matter using coherent diffusion of light / acoustic waves : Simple diffusion (radar, seismic detector, doppler velocimetry, etc) Source Detector Multiple diffusion : use of correlation Diffusion (acoustic) / coda wave spectroscopy, etc Detector Source Output : speckle no imaging possible

3 Coherent mult. diffusion : acoustic wave spectroscopy Output : speckle too difficult to analyze / use to probe Idea : analyze change of output when the diffusing medium is modified Source R. Snieder and J. Page, Physics Today (2007) Detector Detector Source ~ Interferometer Intensity modified by small variations of diffusion medium good sensitivity

4 Coherent mult. diffusion : acoustic wave spectroscopy Procedure :. At time T : send a pulse Source 2. Record the transmitted amplitude ψ(t,t) as a function of time 3. Repeat another trace ψ(t2,t) at time T2= T+ΔT 4. etc Correlation between traces : mean relative displacement in the medium g(δt) ψ(t,t) ψ*(t+δt,t) dt exp(- N(t)k 2 <Δr 2 (ΔT)>) AMPLITUDE (arbitrary units) a PROPAGATION TIME t ( µ s) AMPLITUDE (arbitrary units) b R. Snieder and J. Page, Physics Today (2007) PROPAGATION TIME t (s) µ Detector ultrasonic pulse in particulate suspension sismographic wave transmitted near Mount Merapi from R. Snieder and J. Page, Physics Today (2007)

5 What about electronic waves? waves diffusion : necessity to be phase coherent electrons interact with environment (phonons, other electrons, impurities) randomization of its phase looses memory of its phase over coherence length L φ (T ) electronic transport is classical in standard situations (Ohm s law) but quantum at low T (fewer phonons), and small length (few μm) L φ (T ) quantum diffusion classical diffusion, Ohm s Law L L φ (T ) only total flux (current) detected : no angle information, no speckle advantages : charge (sensitive to magnetic flux), spin (use it here).

6 General Idea of this work P. de Vegvar, L. Lévy, and T. Fulton, Phys. Rev. Lett. 66, 2380 (99) D.C. and E. Orignac, Phys. Rev. Lett. 00 (2008) How to measure correlations between different spin configurations? Our proposal : use coherent electronic transport to probe of a spin configuration : correlation of spin configurations correlation of transport properties Quantity analogous to Speckle? Coherent transport regime : transport on distances comparable with the coherence length scale L φ (T ) wires ( L z µm) L z : small L z L φ L x, L y L. Lévy et al. : 000ppm Cu:Mn, (d SS 23Å),L µm, L φ 0.5µm, L y 900Å,Nspins 40 L φ (T ) is limited by inelastic scattering : phonons low temperatures (T~ 00 mk) inelastic magnetic scattering : reduced in spin glass!!! L φ (T ) increases in the Spin Glass phase Transport in a wire : L x,l y L z,l φ

7 Transport probe : Classical Quantum Diffusion Probability to diffuse from r P (r r ) to r path C r r Phase variation along a diffusion path : Average interferences vanish, except if C = C (reversed ring) random in a metal Quantum correction : loop contributions (weak localization : first signs of Anderson Localization of waves) A C 2 = C δφ C =2π L C λ F Classical A C 2 + C=C A C A C O E. Akkermans and G. Montambaux, Mesoscopic Physics of electrons and photons, 2007 Interferences

8 Transport probe : Magnetic field effects E. Akkermans and G. Montambaux, Mesoscopic Physics of electrons and photons, 2007 Application of a magnetic field : dephase path with respect to each other : δφc,c = 2πΦC,C /Φ0 quantum corrections affected with 2 consequences : mk B 2000 conductance -0.2 Conductance, same sample, different spins config. universal conductance fluctuations : fingerprint of disorder configurations weak localization (long wires) -5 O Flux Through the Sample Quantity analogous to Speckle 00

9 Transport probe : Magnetic field effects Application of a magnetic field : dephase path with respect to each other : δφ C,C =2πΦ C,C /Φ 0 E. Akkermans and G. Montambaux, Mesoscopic Physics of electrons and photons, 2007 quantum corrections affected with 2 consequences : universal conductance fluctuations : fingerprint of disorder configurations P (r r ) O path C r r A C 2 = C A C 2 + C=C A C A C conductance Conductance, same sample, different spins config Flux Through the Sample Quantity analogous to Speckle Ergodic Hypothesis : Changing random potential (length of paths) or applying B : similar statistical dephasing averaging over B or V equivalent (δg(b,v )) 2 B = (δg(b,v )) 2 V = c e2 h Crucial for theoretician

10 General Idea of this work (2) D.C. and E. Orignac, Phys. Rev. Lett. 00 (2008) correlation of spin configurations correlation of transport properties Measure traces G(B) in sample, but for 2 spin configurations G B,{S () j },G B,{S (2) j } L x, L y L z L φ Consider average correlation between the two traces : δg B,{S () δg B,{S (2) j } Provides a measure of correlation between the spin configurations? B exp B,E F Temperature, T T T SG T exp 0 {S (n) i } t w {S (n+) i } j } B Conductance, same sample, different spins config Flux Through the Sample time t

11 D Diffusion but 3D Spin Glass! In theory : no Spin Glass phase in d=,2 (Ising SG) Typical number of spins in a section : N 40 putative overlap / equilibration length for a 3D spin glass (t) Evaluation of (t) from field change experiments and recent simulations (Ising SG) : (t w = 000s) 30 50spins N (3D) eq N (3D) eq N (3D) eq Depending on concentration : L x, L y L z L φ Probing a 3D spin glass through D coherent electronic diffusion ( N N eq (3D) (t w ) ) Probing D/3D cross-over through D coherent electronic diffusion J.-P. Bouchaud, V. Dupuis, J. Hammann, and E. Vincent, Phys. Rev. B 65, (200) S. Jimenez, V. Martin-Mayor, and S. Perez-Gaviro, Phys. Rev. B 72, (2005). L. Lévy et al. (99) : 000ppm Cu:Mn, (d SS 23Å), L µm, L φ 0.5µm, L y 900Å, N spins 40

12 Brief history P. de Vegvar, L. Lévy, and T. Fulton, Phys. Rev. Lett. 66, 2380 (99) N. Israeloff, et al., Phys. Rev. Lett. 63, 794 (989). G. Alers, M. Weissman, and N. Israeloff, Phys. Rev. B 46, 507 (992). J. Jaroszynski, et al. Phys. Rev. Lett. 80, 5635 (998) G. Neuttiens, et al., Phys. Rev. B 62, 3905 (2000). Pioneering work of L. Lévy et al.: Coupling between SG freezing and electronic transport 000ppm Cu:Mn Electron s transport is coherent de Vegvar et al. PRL (99) But most focused electronic (/f) noise Signature of slow relaxation of SG? but difficult to interpret (see M. Weissman RMP (993)) diluted magn. semicond. Cd0,93 Mn0,07Te AuFe 5% at. Jaroszynski et al., PRL (998) Neuttiens et al. PRB (2000) Here focus on correlations!

13 Theoretical Model H = <i,j> tc i c j + h.c. + i v i c i c i + i Jc i σ c i. S i Random flips Spins assumed randomly frozen Anderson model + Spins scalar disorder v i [ W/2, +W/2] (characterizes a sample) Frozen spins : randomly oriented, but correlated between configurations Spins of magnetic impurities : dephasing of electrons new length L m (J) diffuson/cooperon : reduction of UCF B. Alʼtshuler and B. Spivak, JETP Lett. 42, 447 (985) M. G. Vavilov, L. I. Glazman, and A. I. Larkin, Phys. Rev. B 68, 0759 (2003) D.C. and E. Orignac, Phys. Rev. Lett. 00 (2008) Initial Configuration (characterizes a Spin Glass state) Overlap General idea here : consider a given sample : {v i } 2 spin config. { S () i } and { S (2) i } (2 Spin Glass states) Study correlation between G V,{S () j } and G V,{S (2) j } Ergodic Hypothesis : corresponds to correlation between magnetoconductance traces in 2 Spin Glass states G φ, {S () and G φ, {S (2) j } j } Conductance, same sample, different spins config Flux Through the Sample

14 Techniques H = <i,j> tc i c j + h.c. + i v i c i c i + i Jc i σ c i. S i Spins assumed randomly frozen Anderson model + Spins scalar disorder v i [ W/2, +W/2] (characterizes a sample) Frozen spins : randomly oriented, but correlated between configurations (characterizes a Spin Glass state) Quantitative conductance correlations in a spin glass : Weak localization diagrammatic (perturb.) (D.C. and E. Orignac, Phys. Rev. Lett. 00 (2008)) magnetic dephasing of the cooperons and diffusons Field Theory (non-linear Sigma) (A.A. Fedorenko and D.C., arxiv:0904.0, EPL 200) study crossover between orthogonal and unitary classes, extend to calculations of conductance correlations Numerical Landauer method (G. Paulin and D.C., arxiv: )

15 Flavor of diagrammatic... (or why this idea can work) D.C. and E. Orignac, Phys. Rev. Lett. 00 (2008) We consider the correlation δg V,{S () j } δg V,{S (2) j } V φ(c, { S () }) φ(c, { S (2) }) The 2 components of propagating Diffuson / Cooperon see different spin configurations Same sample (positions of impurities) If two spin configurations similar : weak relative dephasing if two spin configurations different : strong relative dephasing Along a diffusion path : dependance on the overlap e i(js)ŝ() j.σ () e ±i(js)ŝ(2) j.σ (2) Q 2 = N imp + work to lower order in J j different dephasing rate/length for singlet / triplet component L (D,S) = L m / of the Diffuson / Cooperon Q 2, L (D,T ) = L m / : +Q 2 /2 N imp i= S () i. S (2) i L 2 m =2πρ 0 n imp D J 2 S 2

16 Lm(J) : cross-over length scale H = tc i c j + h.c. + v i c i c i + <i,j> i i Elastic scattering time : τ e = 2πρ 0 n i v0 2 G. Paulin and D.C., unpublished Jc i σ c i. S i l e = v F τ e, ξ loc N l e le k k Elastic scattering time : τ m = 2πρ 0 n i J 2 S 2 weak J L m = Dτ m D = v 2 F + τ e τ m Lm le

17 Lm(J) : cross-over length scale H = <i,j> tc i c j + h.c. + i Elastic scattering time : Elastic scattering time : τ e = τ m = v i c i c i + i 2πρ 0 n i v 2 0 2πρ 0 n i J 2 S 2 G. Paulin and D.C., unpublished Jc i σ c i. S i weak J l e = v F τ e, ξ loc N l e L m = Dτ m D = v 2 F + τ e τ m l e L m UCF (universal metal) L φ (T ) ξ loc Length of wire L Strong magnetic disorder : Unitary Class Sensitive to few spin flips

18 Lm(J) : cross-over length scale H = <i,j> tc i c j + h.c. + i Elastic scattering time : Elastic scattering time : τ e = τ m = v i c i c i + i 2πρ 0 n i v 2 0 2πρ 0 n i J 2 S 2 G. Paulin and D.C., unpublished Jc i σ c i. S i weak J l e = v F τ e, ξ loc N l e L m = Dτ m D = v 2 F + τ e τ m l e L m UCF (universal metal) L φ (T ) ξ loc Length of wire L Very Weak magnetic disorder : Orthogonal Class Not Sensitive to spins

19 Lm(J) : cross-over length scale H = <i,j> tc i c j + h.c. + i Elastic scattering time : Elastic scattering time : τ e = τ m = v i c i c i + i 2πρ 0 n i v 2 0 2πρ 0 n i J 2 S 2 G. Paulin and D.C., unpublished Jc i σ c i. S i weak J l e = v F τ e, ξ loc N l e L m = Dτ m D = v 2 F + τ e τ m l e L m UCF (universal metal) L φ (T ) ξ loc Length of wire L Weak magnetic disorder : Cross-over Sensitive to rearrangement of config. of spins

20 Numerical Landauer Method G. Paulin and D.C., arxiv: G. Paulin and D.C., arxiv: g Transport in Nanowires : Landauer formula g = e2 h modes α,β T αβ µ R j j L R,T Réservoir Réservoir 2 R 2 j j L 2 µ 2 Scattering Matrix S obtained through the Fisher-Lee relations : S G R wave function φ α (y, x) of mode α, velocity v α transmission coefficient ( G R electronic Green s function) : t αβ = i v α v β dy α dy β φ α (y α,x= 0)G R (y α,x=0 y β,x= L)φ β (y β,x= L) Green s function : recursive method Dyson eq. : G R = G R 0 + G R 0 VG + V Build wire row by row Connect the reservoirs G R (,L) G R (L +,L+ ) G R (,L+ ) + +

21 Distribution of Correlations Distribution of G({v i, S () i }) G({v i, S (2) i }) when V = {v i }) varies (5000 samples) G. Paulin and D.C., unpublished

22 Distribution of Correlations Distribution of G({v i, S () i }) G({v i, S (2) i }) when V = {v i }) varies (5000 samples) G. Paulin and D.C., unpublished +,- '"# ' &"# & %"# %!"#!./0/$"!/2 3 /0/!4$$/5/0/#$$$/6789:; )/0/4/*/0/</=/0/$"><>>?)@;;8)9/+,- )/0/</*/0/!4/=/0/$">!%A )/0/>/*/0/!4/=/0/$">!$$ )/0/!$/*/0/!4/=/0/$">$A< )/0/!&/*/0/!#/=/0/$">$><?)@;;8)9/+,- / pair of config. with correlation Q pair of config. with correlation Q2 $"# $ /!!"#!!!$"# $ $"#!!"# ( )!( *

23 Distribution of Correlations Distribution of G({v i, S () i }) G({v i, S (2) i }) when V = {v i }) varies (5000 samples) G. Paulin and D.C., unpublished./0/$"!/2 3 /0/!4$$/5/0/#$$$/6789:; +,- / '"# ' )/0/4/*/0/</=/0/$"><>> &"#?)@;;8)9/+,- )/0/</*/0/!4/=/0/$">!%A )/0/>/*/0/!4/=/0/$">!$$ & )/0/!$/*/0/!4/=/0/$">$A< )/0/!&/*/0/!#/=/0/$">$>< %"#?)@;;8)9/+,- %!"#! $"# / $!!"#!!!$"# $ $"#!!"# ( )!( *./0/!"'/2 3 /0/'$!!/4/0/5!!!/6789:; +,- '% '& '! # $ <)=;;8)9/+,-/>/0/!"???& <)=;;8)9/+,-/>/0/!"??#5 <)=;;8)9/+,-/>/0/!"??#! <)=;;8)9/+,-/>/0/!"??@A <)=;;8)9/+,-/>/0/!"?#?? <)=;;8)9/+,-/>/0/!"?#!$ <)=;;8)9/+,-/>/0/!"?'!! <)=;;8)9/+,-/>/0/!"%$!@ <)=;;8)9/+,-/>/0/!"&$?$ <)=;;8)9/+,-/>/0/!"!!&! <)=;;8)9/+,-/>/0/!/B8C8: / Evolution of PDF of correlations of g when correlation of spins Q varies % &! /!!"#!!"$!!"%!!"&!!"&!"%!"$!"# ( )!( *

24 Distribution of Correlations Distribution of G({v i, S () i }) G({v i, S (2) i }) when V = {v i }) varies (5000 samples) Variance : Probe of overlap *+,-./0,/23* ,7 "%$& "%$( "%$' "%$$ "%$ "%!& "%!( "%!' "%!$ "%! δg V,{S () j } :3;3<3"%"=:3>? 3<3&"" :3;3<3"%"=:3>? 3<3!$"" :3;3<3"%"=:3>? 3<3!("" δg V,{S (2) Q = j } S () i. S N (2) i i G. Paulin and D.C., unpublished V = F (L/L m,q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

25 Distribution of Correlations Distribution of G({v i, S () i }) G({v i, S (2) i }) when V = {v i }) varies (5000 samples) δg Variance : Probe of overlap V,{S () j } δg V,{S (2) Q = j } S () i. S N (2) i i,-.-"'"( G. Paulin and D.C., unpublished V = F (L/L m,q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

26 Perspectives Specificities a spin glass nanowire : dimensional cross-over of dynamics? Effects of short range correlations between spins (T>Tg) new type of material (spins implanted in pure metal) Perspectives : characterization of T-chaos, aging, comparison between successives quenches magnetoconductance at lower fields B dynamics at low T (<Tg/0) and high fields (AT line?) Thank You!