Vortices in Classical Systems
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1 Vortices in Classical Systems
2 4 He-II vortices: Vortices in Quantum Systems STM of NbSe 2 vortices: G. A. Williams, R. E. Packard, Hess PRL (1989). Phys. Rev. Lett. 33, 280 (1974) Pan, Hudson, Davis, RSI (1999) Hall probe image of YBCO film at T = 40 K: Checkerboards in Bi 2 Sr 2 CaCu 2 O 8+x vortices: Gauss s Hoffman et al, Science (2002) 20 um B applied = 1 Gauss
3 Single Vortex Manipulation in Superconducting Nb Vortices in Nb Film Cooled to 5.3K in 100G Eric Straver Jenny Hoffman Dan Rugar Kathryn Moler Δf=2.01Hz 1μm Stanford University Funded by Packard and AFOSR
4 Goals Part I: eliminate i uncontrolled vortex motion bigger magnets efficient power lines quieter sensors & circuits Part II: controlled single-vortex manipulation model for soft condensed matter vortex entanglement t vortex ratchet automaton Luttinger liquid FermiLab
5 Part I: eliminate uncontrolled vortex motion
6 Motivation: eliminate uncontrolled vortex motion H c2 H* (where vortices move) Field (T) 20 YBCO Temperature (K) Larbalestier, Nature 414, 368 (2001)
7 Motivation: eliminate uncontrolled vortex motion H c2 H* (where vortices move) Field (T) 20 YBCO Temperature (K) Larbalestier, Nature 414, 368 (2001) e- e- e- e-
8 Motivation: eliminate uncontrolled vortex motion H c2 H* (where vortices move) Field (T) 20 YBCO Temperature (K) Larbalestier, Nature 414, 368 (2001) Apply current I: Cooper pairs flow without dissipation e- e- e- e-
9 Motivation: eliminate uncontrolled vortex motion H c2 H* (where vortices move) Field (T) 20 YBCO Temperature (K) Larbalestier, Nature 414, 368 (2001) Apply current I: Cooper pairs flow without dissipation Normal electrons in vortex core cause dissipation when moved e- e- e- e- e e- ē- e- e-
10 Vortex Pinning Measurements: Bulk Transport 10 GB, B = 0 Tesla 4 GB, B = 1 Tesla intra-grain (upper scale) grain boundary Redwing et al, APL 75, 3171 (1999). Hogg et al, APL 78, 1433 (2001).
11 Vortex Pinning Measurements: Bulk Transport 10 GB, B = 0 Tesla 4 GB, B = 1 Tesla intra-grain (upper scale) grain boundary Redwing et al, APL 75, 3171 (1999). Hogg et al, APL 78, 1433 (2001). What s really going on here? First detectable Voltage = many, many vortices
12 Examples of Previous Single Vortex Depinning Force Measurements with Transport Current Finnemore and coworkers ongoing work (1988-present) Cabrera and coworkers several other groups
13 Examples of Previous Single Vortex Depinning Force Measurements with Transport Current Finnemore and coworkers ongoing work (1988-present) Cabrera and coworkers 1992 But we d like a more reliable way to know the force at the vortex location; and to detect vortex motion with finer spatial resolution on order ξ ~ nm + several other groups
14 Vortex Pinning Measurements: STM Imaging g reduce field from 3Teslato15Tesla 1.5 estimate pinning force from flux density gradient across twin boundary Maggio-Aprile et al, Nature 390, 487 (1997)
15 Vortex Pinning Measurements: STM Imaging g reduce field from 3Teslato15Tesla 1.5 estimate pinning force from flux density gradient across twin boundary Maggio-Aprile et al, Nature 390, 487 (1997) But we d like a more versatile way to directly measure pinning forces at arbitrary defects.
16 Magnetic Force Microscopy Pros and Cons of MFM Force between tip and sample: F = ( m B) Other signals Image cantilever resonant frequency Δff 0 ~ df z /dz better signal-to-noise Vertical force gradient imaging Horizontal force manipulation Tip Geometry Con: Imperfectly known Pro: Up to 20 nm spatial resolution Signal to Noise Con: Not as good as SQUIDs, Hall probes Pro: Good enough to see vortices Con: See atomic forces too Pro: Simultaneous topography Invasiveness Con: Tip exerts force on vortex Pro: Tip exerts force on vortex
17 Vortex Depinning in Nb T: Decreasing Pinning 5.2K 5.5K 6.0K 6.5K 7.0K 7.5K 4 μm Colormap adjusted separately for each image.
18 Vortex Pinning vs. Height at T = 5.5 K A z=576nm B z=518nm C z=461nm D z=403nm E z=346nm F z=288nm G z=230nm H z=173nm 2μ m Δ f (Hz) Δ f=0.63hz I x (μ m) x y Δ f=0.73hz J x (μ m) Δ f=0.85hz -0.2 K x (μ m) Δ f=0.97hz Δ f=1.22hz 0.4 L 1.0M x (μ m) x (μ m) Δ f=1.50hz N x (μ m) Δ f=2.02hz 30O 3.0O x (μ m) Δ f=2.79hz P 500nm vortex motion event Important parameters: k spring = 2.1±0.7 N/m f 0 = Hz λ Nb = 90 nm
19 Model: Monopole Tip Monopole Vortex +M d offset z λ B -M superconductor vortex model vortex as monopole distance λ beneath surface --J. Pearl, J. Appl. Phys. 37, 4139 (1966). df dz z = 2k spr df f = M zφ 2π 0 ( x x 0 ) 2 ( y ( x x ) + ( y y ) + ( z + λ + d ) 5/ offset ) y 0 ) 2 + 2( z + λ + d offset ) 2 )
20 Quantifying the Depinning Force at T = 5.5 K 10-4 df/dz (N/m m) z (nm) B G vs. z 4G vs. z z+λ+d (nm) min
21 Quantifying the Depinning Force at T = 5.5 K 10-4 df/dz (N/m m) z (nm) B G vs. z 4G vs. z 17G vs. z+λ+d λ min 4G vs. z+λ+d 10-5 min z+λ+d (nm) min df z /dz ~ (z+λ+d) -3
22 Quantifying the Depinning Force at T = 5.5 K 10-4 df/dz (N/m m) z (nm) B z (nm) G vs. z G vs. z G vs. z+λ+d λ min 20 4G vs. z+λ+d min z+λ+d (nm) min F z (pn) 10 4 Gauss 17 Gauss df z /dz ~ (z+λ+d) z+λ+d min (nm)
23 Quantifying the Depinning Force at T = 5.5 K 10-4 df/dz (N/m m) z (nm) B z (nm) G vs. z G vs. z G vs. z+λ+d λ min 20 4G vs. z+λ+d min z+λ+d (nm) min df z /dz ~ (z+λ+d) -4 F z (pn) Gauss 17 Gauss fit bound z+λ+d min (nm)
24 Quantifying the Depinning Force at T = 5.5 K 10-4 df/dz (N/m m) z (nm) B G vs. z 4G vs. z 17G vs. z+λ+d λ min 4G vs. z+λ+d 10-5 min z+λ+d (nm) min df z /dz ~ (z+λ+d) -4 F z (pn) z (nm) Gauss 17 Gauss fit bound 5 k spring bound z+λ+d min (nm)
25 Depinning Forces in Two Datasets at 5.5 K z=576nm z=518nm z=461nm z=403nm z=346nm z=288nm z=230nm z=173nm A B C D E F G H 2μ m Δ f=0.63hz Δ f=0.73hz Δ f=0.85hz Δ f=0.97hz Δ f=1.22hz Δ f=1.50hz Δ f=2.02hz Δ f=2.79hz # vortices # vort tices 8 17 Gauss 6 4 Gauss F z (pn) F lateral,max = 0.38*F z,max F depin ranges from 4 to 12 pn at 5.5 K
26 Nb Depinning Forces: Quantitative Comparison f p (pn/μ μm) Breitwisch (PRB 2000): T = 8.55 K; t = 400 nm c Park (PRL 1992): T c = 7.35 K; t = 20 nm Breitwisch Allen (PRB (PRB 1989): 2000): T c = 8.55 T K; t = 400 nm Park (PRL 1992): T c = 7.35 c = 8.91 K; t = 20 nm K; t = 20 nm Allen (PRB 1989): T Allen (PRB 1989): T c = 8.91 c = 5.86 K; t = 50 nm K; t = 20 nm Stoddart (SST 1995): T c = 9.20 K; t = 700 nm Allen (PRB 1989): T c = 5.86 K; t = 50 nm Stoddart (SST 1995): T c = 9.20 K; t = 700 nm T/T c F depin ranges from 15 pn/μm to 40 pn/μm # vort rtices Limits on motion detection from bootstrapping vortex fits: limited by S/N, can be improved r(95%) 60 (nm) z (nm) 8 17 Gauss 6 4 Gauss F z (pn) z (pn)
27 Part II: controlled single-vortex manipulation
28 Motivation: soft condensed matter physics Do vortices split or tilt and do vortices entangle? surface pancake vortex vortex core interlayer Josephson vortex Clem, PRB 43, 7837 (1991) Reichhardt & Hastings, PRL 92, (2004)
29 Motivation: Luttinger liquid physics STM: twin boundary in CuO chain plane of YBa 2 Cu 3 O 7-x y pin vortices in twin boundary plane x 0.21nm 100 Å Eric Hudson, et al Vortices are like 1D bosons in Luttinger liquid!! L τ nm z x L x Polkovnikov, PRB 71, (2005) vortex wandering in z-direction 1D particles moving in time y x
30 Motivation: vortex ratchet computing Fabricated defects in a superconductor, used to pin vortices Real material parameters for MgB 2 : Maximum speed: simulations show 315 MHz, pair-breaking is in the THz range. Minimum size: λ ~ 100nm Power dissipation: Joules / single cell flip NAND gate: Hastings, Reichhardt, Reichhardt, PRL 90, (2003)
31 Our Procedure for Single Vortex Manipulation using Magnetic Force Microscopy surveillance height manipulation height
32 Vortex Manipulation Results A B C D E Δ f=79mhz Δ f=87mhz Δ f=96mhz Δ f=74mhz Δ f=70mhz 2μ m T = K h = 288 nm 1μm T = 5.53 K h = 86.4 nm Δf=3.21Hz Δf = Hz
33 Goals Part I: eliminate i uncontrolled vortex motion bigger magnets efficient power lines quieter sensors & circuits Part II: controlled single-vortex manipulation model for soft condensed matter vortex entanglement t vortex ratchet automaton Luttinger liquid FermiLab
34 Vortex studies in YBCO Future directions Better MFM tips: - model as monopole 20μm 200nm Deng, APL (2004) nanotube on cantilever tip - better AFM spatial resolution, correlate with topography 100 nm Hawley, Science, 1991 STM studies: image with ξ ~ 15 Å resolution, 100 better than λ ~ 150 nm
35 Spatial Resolution 8μm SQUID 0.5μm Hall Probe MFM STM 0.5 Gauss 1.1 Gauss 100 Gauss 5 Tesla 10μm 550Å
36 Future: How to Pin Vortices in YBCO? (1) Screw dislocations (2) Chemical inclusions (3) Oxygen dopants (4) Twin boundaries STM: spiral growth patterns 100 nm Hawley, Science, 1991 STM: impurities in Bi 2 Sr 2 CaCu 2 O 8+x Ni 10Å Zn Vacancy(?) Hudson et al, Nature 411, 920 (2001). Pan et al, Nature 403, 746 (2000). Hudson et al, Physica B 329, 1365 (2003). STM: superconducting gap STM: twin boundary in CuO inhomogeneity in Bi 2 Sr 2 CaCu 2 O 8+x chain plane of YBa 2 Cu 3 O 7-x Vortex imaging in Bi 2 Sr 2 CaCu 2 O 8+x 0.21nm 100 Å 20 Δ (mev) Lang et al, Nature 415, 412 (2002) Å Eric Hudson, unpublished. 0.00nm 100Å Hoffman, Science (2002).
37 ummary Manipulate single vortices with nanoscale control Measured directly the depinning i forces in Nb 1μm already applying same technique to YBCO P Δf=3.21Hz Δf = Hz Eric Straver Nick Koshnick Ophir Ausleander # vort tices Next: correlate depinning forces with topography (Moler) STM studies to explore higher fields (Hoffman) nm 8 17 Gauss 6 4 Gauss 4 2 vortex motion event F z (pn)
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