Mesoscopic physics: normal metals, ferromagnets, and magnetic semiconductors

Transcription

1 Mesoscopic physics: normal metals, ferromagnets, and magnetic semiconductors Douglas Natelson Department of Physics and Astronomy Department of Electrical and Computer Engineering Rice Quantum Institute Rice University

2 Mesoscopic physics: normal metals, ferromagnets, and magnetic semiconductors Normal metals: A. Trionfi, S. Lee, and D. Natelson, cond-mat/ A. Trionfi, S. Lee, and D. Natelson, Phys. Rev. B. 72, (2005). A. Trionfi, S. Lee, and D. Natelson, Phys. Rev. B 70, (R) (2004). Ferromagnetic metals: Z.K. Keane and D. Natelson, Appl. Phys. Lett. 88, (2006) S. Lee, A. Trionfi, and D. Natelson, Phys. Rev. B 70, (2004). Ferromagnetic semiconductors: S. Lee, A. Trionfi, T. Schallenberg, H. Munekata, and D. Natelson, cond-mat/

3 What is quantum coherence? Consider a two-slit experiment. Must add amplitudes and square to find probabilities. Well-defined relative phases of waves results in interference effects. 2Re ψ L ψ R With a detector at one slit, one must consider the state of the detector as well. Result is suppressed interference! 2Re ψ L ψ R Φ0 Φ 0 1

4 Quantum coherence of electrons in metals Electrons exhibit quantum interference phenomena in solids over a scale L φ. Conduction on this scale is actually an interference experiment. Coherence is limited by inelastic processes. Quantum effects are apparent at small scales and low temperatures. 300 K: L φ ~ 0.5 nm. 1 K: L φ ~ 1 μm.

5 Current situation and relevance Pure science: Mesoscopics in metals is relatively mature: should expect quantitative agreement between theory and experiment. Do different coherence effects really tell us the same information? What dominates decoherence in FM materials? Potential applications: Coherence effects are relevant in a number of schemes for quantum computation. Noise and fluctuations in quantum devices clearly relevant.

6 What are mesoscopic effects? Corrections to the conductance (or other measurable quantity) that depend sensitively on the microscopic details of the sample. Often provide a means of assessing quantum coherence information. Examples: Weak localization

7 Weak localization nm wide Au wire ΔR/R B [T] Interference between electron trajectories containing closed loops. Aharonov-Bohm kills interference on field scale related to loop size ( suppression of Cooperon contribution ). Result: Magnetoresistance that may be fit to find L φ (T).

8 What are mesoscopic effects? Corrections to the conductance (or other measurable quantity) that depend sensitively on the microscopic details of the sample. Often provide a means of assessing quantum coherence information. Examples: Weak localization B [T] Universal Conductance Fluctuations (UCF) Magnetic field (MFUCF) ΔR/R nm wide Au wire

9 MF Universal Conductance Fluctuations Conductance is interference from random array of scatterers. ΔR (Ω) nm wide Ag wire 2 K 8 K 14 K AB phase is equivalent to rearranging scatterers magnetofingerprint MFUCF amplitude ~ 2e 2 /h per coherent volume, reduced by ensemble averaging. Correlation field allows inference of L φ (T). B [T]

10 What are mesoscopic effects? Corrections to the conductance (or other measurable quantity) that depend sensitively on the microscopic details of the sample. Often provide a means of assessing quantum coherence information. Examples: Weak localization B [T] Universal Conductance Fluctuations (UCF) Magnetic field (MFUCF) Time dependent (TDUCF) Saturated Unsaturated ΔR/R nm wide Au wire ΔR (Ω) nm wide Ag wire B [T]

11 Two-level systems Localized excitations found in disordered materials. Profoundly affect low temperature properties. Broadly distributed energy and relaxation scales. Toy model developed by Anderson, Halperin, Varma gets most of the essential physics correct. Still mysterious. 2Δ Δ 0 Distribution typically assumed to be flat in Δ with a high energy cutoff, and flat in ln Δ 0 with cutoffs at high and low ends.

12 TD Universal Conductance Fluctuations ΔR/R d = 5nm, L = 750nm I = 10nA, τ = 3 s T = 81K T = 7.7K time [min] Conductance is interference from random array of scatterers. Scatterers actually do rearrange with time! Result: 1/f noise Noise increases as T is decreased, due to reduced ensemble averaging. Field-dependence of noise power (suppression of Cooperon) allows inference of L φ (T). S(B)/S(B=0) nm wide Ag wire 2 K 14 K 20 K B [T]

13 TD Universal Conductance Fluctuations How big should the TDUCF be? Depends on the microscopic fluctuators. Saturated: Each fluctuator affects conductance in coherent volume by ~ e 2 /h. Unsaturated: Each fluctuator affects conductance in coherent volume by << e 2 /h. Important: Saturated vs. unsaturated determines correct fitting fn for extraction of L φ from noise vs. field! Consistency check: Assuming S G ~ 1/f, how many decades of f needed for S G ( f ) df = var( GMFUCF ) TDUCF are saturated.? If < 20 decades, then By this criterion, every experiment is seen to be in the unsaturated limit.

14 What are mesoscopic effects? Corrections to the conductance (or other measurable quantity) that depend sensitively on the microscopic details of the sample. Often provide a means of assessing quantum coherence information. Examples: Weak localization B [T] Universal Conductance Fluctuations (UCF) Magnetic field (MFUCF) Time dependent (TDUCF) Saturated Unsaturated ΔR/R nm wide Au wire ΔR/R d = 5nm, L = 750nm I = 10nA, τ = 3 s T = 81K T = 7.7K ΔR (Ω) nm wide Ag wire B [T] time [min]

15 Lingering questions Theorists have only reached consensus on coherence agreement within the last two years. Latest theory prediction (Aleiner and Blanter) says that, if e-e scattering is the only low-energytransfer process at work, L φ WL and L φ UCF should agree! Some experimental data suggest that the situation isn t trivial. Are spin-orbit scattering and magnetic impurity scattering important here? Hoadley et al., PRB 60, 5617 (1999)

16 Overall results for AuPd wires a A. Trionfi, S. Lee, and D. Natelson, Phys. Rev. B 70, (R) (2004). b L φ [nm] 10 w = 43 nm c w = 35 nm d 100 w = 500 nm T [K] w = 500 nm, mag. imp WL and nonsaturated TDUCF L f values agree with no adjustable parameters.

17 What about Ag wires? 140 nm wide Ag wire WL (filled) and unsaturated TDUCF (empty) disagree!

18 Pure Au wire 70 nm wide Au wire 1000 L φ WL L φ TDUCF unsat. L φ TDUCF sat. Length [nm] T [K]

19 What s going on here? See this same divergence in pure Au nanowires! Possibility 1: Some decoherence process affects WL and TDUCF differently (!) Possibility 2: The TDUCF and/or the WL coherence lengths are not reflecting the true coherence length. Observation: The saturated functional form for the noise vs. field gives fits of similar quality as the unsaturated form. Hypothesis: Perhaps we are seeing a crossover from unsaturated to saturated TDUCF as T is lowered.

20 Saturated vs. Unsaturated TDUCF 140 nm wide Ag wire

21 How to Test the Hypothesis Try altering the coherence length of the material while leaving the TLS concentration unchanged. Ti adhesion layer causes magnetic scattering that suppresses L φ at low temperatures. Annealing in air eliminates the magnetic scattering! Try changing the TLS concentration while leaving the coherence length unchanged. Surface passivation with alkane monolayer to mitigate surface fluctuators.

22 Au results w/ Ti layer nm wide Au with 1.5 nm Ti Length [nm] 100 L φ WL no annealing L φ WL annealing 1 10 T [K]

23 Au results w/ Ti layer 1000 Length [nm] L φ WL L TDUCF φ unsat. L TDUCF φ sat T[K]

24 Noise Power before and after SAM 70 nm wide Au wire (no Ti, 2K) 1E-11 S [Hz -1 ] 1E-12 1E-13 pre-sam post-sam f [Hz]

25 SAM Au results 70 nm wide Au sample (no Ti) 1000 L φ WL L φ TDUCF unsat. L φ TDUCF sat. Length [nm] T [K]

26 SAM Au results 70 nm wide Au sample (no Ti) 1000 L φ WL L φ TDUCF unsat. L φ TDUCF sat. Length [nm] T [K]

27 Conclusions and a new hypothesis Both Ti and surface passivation results are consistent with a crossover from unsaturated to saturated TDUCF at low temperatures. So, what is wrong with the simple consistency check that tells us we d need hundreds of decades of 1/f noise to equal the MFUCF? New hypothesis: somewhere at frequencies higher than we measure, there is excess noise above the 1/f expectation.

28 Atomic scale FM contacts Mesoscopic effects in ferromagnets are comparatively unexplored. We have used three systems to study mesoscopic effects in FM materials: nanoscale contacts, FM metal nanowires, and InMnAs wires. Atomic-scale FM contacts - motivation Ballistic magnetoresistance? Molecular electronics applications Garcia et al., PRL 82, 2923 (1999)

29 Ni point contacts Use controlled electromigration to make nanoscale constriction between Ni pads with well-defined magnetizations.

30 Ni point contacts 100 nm 30 nm Controlled electromigration can be very precise and allow atomicscale constrictions or gaps to be formed. Nanoconstrictions tend to be short-lived even at low temperatures.

31 Ni point contacts In-plane field Out-of-plane field R ~ 80 Ω R ~ 5.8 kω R ~ 13 kω R ~ 10 MΩ Z.K. Keane and D. Natelson, Appl. Phys. Lett. 88, (2006)

32 Ni point contacts conclusions Large (same order as tunneling MR) magnetoresistive effects exist, but no huge BMR. Enormous variation from device to device in shape and even sign of the magnetoresistance. Looks like magnetic configuration at those last couple of atoms depends in detail on the surroundings! Confirmed independently by Dan Ralph s group at Cornell.

33 Quantum coherence mesoscopics in ferromagnetic metals theory motivation Electronically correlated state possesses low-lying environmental degrees of freedom not seen in normal metals: Spin waves What do the correlations and these excitations do to coherence? Coherent propagation through spatially inhomogeneous magnetic fields. Berry s phase effects

34 Complicating effect: Anisotropic magnetoresistance Resistance [kω] B I B S = 0.59 T AMR effect at 8K : 3-4 % 4.9 Switching field, B S ~ T B-field [T] Noise measurement scheme nulls away AMR effects, except when domains are propagating in the bridge arms.

35 Our efforts in FM metal nanowires Try to measure time-dependent UCF in lithographically defined permalloy (Ni0.8Fe0.2) wires. Permalloy is a soft ferromagnet by controlling shape, use geometry to get uniaxial anisotropy. Use nonmagnetic leads to avoid disturbing magnetization of ferromagnet. Same basic noise measurement scheme as in AuPd case. 10μm S. Lee, A. Trionfi, and D. Natelson, Phys. Rev. B 70, (2004).

36 Domain configurations 1μm (a) 450nm wire with multiple domain walls (b) 27nm wire with domain wall (c) 27nm wire without domain walls

37 Single-domain case Cooperon suppression 1E-10 w = 50 nm 0 T 8 T transverse 8 T parallel S R /R 2 [Hz -1 ] 1E-11 1E-12 1E T [K] This wire is believed to be in a single-domain state for all 3 sets of data. No noise reduction at high fields implies no Cooperon contribution!

38 What about domain walls? 1E-10 w = 50 nm 0 T 8 T transverse 8 T parallel 0.57 T transverse S R /R 2 [Hz -1 ] 1E-11 1E-12 1E T [K] Transverse field set where domain propagation is favored leads to increased noise, but only over a limited temperature range!

39 What are the fluctuators in ferromagnets? Noise power in Py samples is very similar in magnitude to that in AuPd samples. Similar volume scaling as well. No major effect of 8 T magnetic field. S R (2 K)/R Permalloy AuPd Suggests that the same fluctuators present in AuPd are at work here w [nm]

40 Possible unusual dephasing mechanisms? nm AuPd : B = 0 T S R /R 2 [Hz -1 ] T [K] 35nm AuPd : B = T 50nm Py : B = 0 T 50nm Py : B = 8 T The expected 2d result: S R ( T ) ~ L 2 φ ~ τ ( T ). φ Low T dependence of noise power in permalloy is ~ T -2. Not consistent with typical e-e scattering decoherence mechanisms.

41 Conclusions for permalloy wires First observations of TDUCF in a ferromagnetic metal. No field-dependence of noise - clearly demonstrates prediction that Cooperon contribution to UCF is suppressed in this ferromagnet. Implies that weak localization effects should be similarly suppressed! Measurements when domain walls are present show increased low-t UCF noise, consistent with coherent scattering of electrons by domain walls. Unusual temperature dependence of noise power implies that, if standard two-level systems are the fluctuators, the decoherence mechanism is unusual in this ferromagnet.

42 Ferromagnetic semiconductors Another interesting system Particularly so because the exchange that leads to the FM phase is mediated by the itinerant holes! During our experiments, some very pretty work out in GaMnAs: Wagner et al., PRL 97, ; Vila et al., cond-mat/

43 InMnAs In 1-x Mn x As, x ~ 0.058, nm thick layer p ~ 1.9 x cm -3 ρ ~ mω-cm Patterned by e-beam lithography and Ar + sputter etching. Widths ~ 6.5 microns, segment lengths ~ 40 microns High resistivity measurements at much lower T.

44 InMnAs Resistivity [ x10-3 Ω cm ] (a) (c) Temperature [K] Hall Resistance, ρ Hall [Ω] (b) (d) 2K 40K 60K 100 2K 25K K Magnetic Field [T] Reasonable magnetic charateristics, though new growth techniques can get much more metallic samples with higher T c.

45 InMnAs - MFUCF 4 (a) 1 2K (b) 0 0 4K ΔR [Ω] (c) K 1 2K 4K K Magnetic Field [T] (d) With bridge scheme, can see MFUCF at 2 K.

46 InMnAs - TDUCF Normalized Noise Power [1/Hz] (a) (b) perpendicular Parallel 2K 2K 4K 4K 15K 15K ~T -2 ~T Temperature [K] Magnetic Field [T]

47 InMnAs - conclusions At lowest temperatures, low field noise power grows like 1/T 2, as seen in permalloy material previously. At lowest temperatures, noise is suppressed at high fields, independent of field orientation Zeeman suppression of fluctuating magnetic disorder? Spin-glassiness? MFUCF do appear need much better statistics, but consistent with order-of-magnitude estimate of L φ (2 K) ~ nm.

48 Take-home messages Though mesoscopics in metals is mature, questions remain in trying to understand meoscopic effects, even in normal metals. It is possible to do similar experiments in ferromagnetic systems, and the results suggest that new physics may be present. Unusual measurement techniques can allow examination of such effects even in systems that can be difficult to probe by normal means.

49 Mesoscopic physics: normal metals, ferromagnets, and magnetic semiconductors Normal metals: A. Trionfi, S. Lee, and D. Natelson, cond-mat/ A. Trionfi, S. Lee, and D. Natelson, Phys. Rev. B. 72, (2005). A. Trionfi, S. Lee, and D. Natelson, Phys. Rev. B 70, (R) (2004). Ferromagnetic metals: Z.K. Keane and D. Natelson, Appl. Phys. Lett. 88, (2006) S. Lee, A. Trionfi, and D. Natelson, Phys. Rev. B 70, (2004). Ferromagnetic semiconductors: S. Lee, A. Trionfi, T. Schallenberg, H. Munekata, and D. Natelson, cond-mat/