Introduction to Nanomechanics: Magnetic resonance imaging with nanomechanics

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1 Introduction to Nanomechanics: Magnetic resonance imaging with nanomechanics Martino Poggio Swiss Nanoscience Institute Department of Physics University of Basel Switzerland Nano I, Herbstsemester

2 Nanoscale Magnetic Resonance Imaging (NanoMRI) Micro- and Nanomechanics m Physics of small spin ensembles N Measuring small displacements

3 Magnetic Resonance Imaging (MRI) True 3D imaging Chemically selective Non-destructive BUT Requires nuclei per voxel We want to be able to resolve a single nuclear spin

4 Imaging Techniques Red blood cell Si (111) Human hair T4 phage DNA 30mm 1mm 30 m 1um 30nm 1nm number of spins MRI NMR Magnetic resonance force microscope (MRFM) Atomic force microscope Eye Optical microscope Scanning electron microscope (SEM)

5 Interferometer laser beam Ultrasensitive cantilever F x B x z z 1 H Nuclear spin Magnetic tip Single proton spin in a 10 6 T/m field gradient Van der Waals force between tip and sample Two electrons 100 nm apart Hydrogen atom in Earth s gravity field ~10-20 N ~ N ~10-14 N ~10-26 N

6 Interferometer laser beam Ultrasensitive cantilever F x B x z z 1 H Nuclear spin Magnetic tip

7 New lab in Basel Phani Peddibhotla Michele Montinaro Dennis Weber

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10 Nanoscale Magnetic Resonance Imaging (NanoMRI) Micro- and Nanomechanics

11 What is Nanomechanics? Quantum of Thermal Conductance Nanomechanical Motion Detection Schwab et al., 2000 Casimir Force Measurement Knobel & Cleland, m Single Spin detection 120 m long Decca, 2003 Rugar,

12 What is Nanomechanics? Mass sensing with carbon nanotubes Si nanowires Zettl, 2008 Graphene membranes 1 m Budakian, 2008 Clean nanotube resonators McEuen, m 1 nm Steele,

13 What is Nanomechanics? Si (111) (AFM) DNA (AFM) Giessibl, nm Magnetic Bits (MFM) 500 nm Folks, 2000 Hamon, m Introduction to Nanomechanics 13

14 What is Nanomechanics? Nano-motor in T4 Bacteriophage ScienceDaily,

15 Why Study Nanomechanics? Link between classical mechanics and statistical mechanics Link between classical mechanics and quantum mechanics Smaller sensors are more sensitive

16 Mechanical Force Transducers F x F kx l, w, t are the length, width and thickness of the lever respectively k is the spring constant or stiffness f is the resonant frequency of the cantilever Q or quality factor compares the frequency at which a system oscillates to the rate at which it dissipates its energy T is the temperature x F / k

17 Transduction vs. Sensing A transducer receives energy from one system and transmits it to another, often in a different form. A sensor responds to physical stimuli (e.g. heat, light, pressure, or motion) and generates an electronic signal for detection

18 Mechanical Force Transducers F x F kx k is the spring constant or stiffness f is the resonant frequency of the cantilever Q or quality factor compares the frequency at which a system oscillates to the rate at which it dissipates its energy T is the temperature x F / k k l, w, t are the length, width and thickness of the lever respectively wt l

19 Limits of Mechanical Force Detection m x x kx F(t) Sx( ) ( 0 ) 2 Q SF ( ) 2 m Displacement imprecision of the sensor Transducer thermal motion Transducer zero-point motion 2 x n 2 xth 2 x zp k T B 2 m 0 2m

20 Fluctuation-Dissipation Theorem When limited by thermal fluctuations: S k T F 4 B Gives a minimum detectable force: F min S F B 4k B T B 4k B 0 TkB Q

21 Cantilevers S F 4 k BTkT k Q Q 0 0 k 0 2 wt m 0 l wt 2 a E l 2 2 wt S F l 225 m f ~ 3 khz k ~ 10-5 N/m f ~ 1 MHz k ~ 0.1 N/m 20 m Commercial AFM cantilever 90nm imaging cantilever Small cantilever

22 Cantilevers 3 m thickness: 300 nm 20 m 225 m f ~ 3 khz k ~ 10-5 N/m chip ledge f ~ 1 MHz k ~ 0.1 N/m Commercial AFM cantilever 90nm imaging cantilever Small cantilever

23 Displacement spectral density (Å 2 /Hz) Cantilevers thermal noise at 4 K Q = 380, m Frequency (khz) Commercial AFM cantilever 90nm imaging cantilever Small cantilever

24 Ultrasmall Cantilevers 225 m f ~ 3 khz k ~ 10-5 N/m f ~ 1 MHz k ~ 0.1 N/m f ~ 1 MHz k ~ N/m 20 m Commercial AFM cantilever 90nm imaging cantilever Small cantilever Next generation

25 Ultrasmall Cantilevers Cantilever in mid-process 250 nm wide, 70 nm thick 9 µm 225 m f ~ 3 khz k ~ 10-5 N/m Ben Chui IBM/Stanford f ~ 1 MHz k ~ 0.1 N/m f ~ 1 MHz k ~ N/m 20 m Commercial AFM cantilever 90nm imaging cantilever Small cantilever Next generation

26 Displacement spectral density (Å 2 /Hz) Ultrasmall Cantilevers 0.1 Thermal noise at 4K Q = 8, m Frequency (khz) 20 m Commercial AFM cantilever 90nm imaging cantilever Small cantilever Next generation

27 Best Force Resolution Rugar et al. (IBM) 120 m long Lehnert et al. (JILA) F min = 1 an/hz 1/

28 Best Force Resolution? Clean Nanotubes Steele et al. (Delft) Q = 1.5 x 10 5 m = kg 0 = 2 x 500 MHz T = 1 K F min = 0.01 an/hz 1/2 (calculated)

29 Nanoscale Magnetic Resonance Imaging (NanoMRI) Micro- and Nanomechanics Measuring small displacements

30 Transduction vs. Sensing A transducer receives energy from one system and transmits it to another, often in a different form. A sensor responds to physical stimuli (e.g. heat, light, pressure, or motion) and generates an electronic signal for detection

31 Mechanical Force Transducers F x F kx Now we require a sensor for mechanical motion

32 Sensors for Mechanical Motion Tunneling Optical Deflection Optical Interferometry Microwave Interferometry Magnetomotive Piezoelectric Capacitive

33 Displacement Measurements STM Detection

34 Displacement Measurements Laser deflection

35 Displacement Measurements Laser interferometry Fixed mirror spring x P in Movable mirror

36 Displacement Measurements Laser interferometry

37 Displacement Measurements Laser interferometry LIGO Gravitational Wave Detection

38 Displacement Measurements m/ Hz Laser interferometry

39 Displacement Measurements Microwave interferometry capacitive detection K. L. Lehnert, JILA

40 Displacement Measurements m/ Hz K. L. Lehnert, JILA

41 IBM Research Using a quantum point contact as a sensitive detector of cantilever motion M. Poggio, M. P. Jura, C. L. Degen, M. A. Topinka, H. J. Mamin, D. Goldhaber-Gordon, and D. Rugar IBM Research Division, Almaden Research Center and Center for Probing the Nanoscale, Stanford University 2008 IBM Corporation

42 Quantum Point Contact (QPC) Images from: Topinka et al., Science 289, 2323 (2000). and M. P. Jura and D. Goldhaber-Gordon

43 2DEG L e - QPC R 2DEG QPC as a mechanical displacement detector Introduction to Nanomechanics 43

44 cantilever laser QPC

45 The cantilever 2 m 350 x 5 x 1 m Si cantilever 10 m 22 nm of sputtered Pt provides conductive path (~2 kw) to 10/30 nm of Cr/Au on tip

46

47

48

49 The QPC 1 m

50 Spectral Density (Ang 2 / Hz) Spectral Density (Å 2 / Hz) Spectral Density (A 2 / Hz) Spectral Density (Amp 2 / Hz) Measurement of cantilever thermal noise 1 DC V sd drive: 2.0 mv E E E Frequency 5.00 (Hz) 5.25 Frequency (khz) 1E E E E E m / (Hz) 1/

51 Nanoscale Magnetic Resonance Imaging (NanoMRI) Micro- and Nanomechanics m Physics of small spin ensembles N Measuring small displacements

52 Interferometer laser beam Ultrasensitive cantilever F x B x z z 1 H Nuclear spin Magnetic tip Single proton spin in a 10 6 T/m field gradient Van der Waals force between tip and sample Two electrons 100 nm apart Hydrogen atom in Earth s gravity field ~10-20 N ~ N ~10-14 N ~10-26 N

53 Interferometer laser beam Ultrasensitive cantilever 1 H Nuclear spin i rf Magnetic tip Microwire generating 115 MHz magnetic field

54 Interferometer laser beam Ultrasensitive cantilever Resonant slice (B = 2.70 T) 1 H Nuclear spin i rf Magnetic tip Microwire generating 115 MHz magnetic field

55 IBM Research 2008 IBM Corporation 55

56 Nanoscale Magnetic Resonance Imaging (NanoMRI) Micro- and Nanomechanics m Physics of small spin ensembles N Measuring small displacements

57 IBM Research Nanometer-scale magnetic resonance imaging Martino Poggio, Christian Degen, John Mamin, and Dan Rugar IBM Research Division, Almaden Research Center and Center for Probing the Nanoscale, Stanford University 2008 IBM Corporation

58 Almaden Research Center Ultrasensitive Cantilevers Fabricated by B. Chui - IBM 120 µm 100 nm thick shaft S 2k Tk B F 4 fq an Hz 1 µm thick mass loading k = 60 N/m f = 3 khz Q = 50,000 at 4K 2008 IBM Corporation 58

59 IBM Research Microwire rf source with integrated magnetic tip 4mT RF field (160 khz) < 350 W >10 6 T/m lateral field gradient B tip 200 nm i rf B rf FeCo tip Cu microwire Si substrate M. Poggio et al., Appl. Phys. Lett. 90, (2007) C.Rettner M. Hart M. Farinelli 2008 IBM Corporation 59

60 IBM Research Millikelvin MRFM MRFM cooled by dilution refrigerator Nanowatt fiberoptic interferometer Spring-based vibration isolation 2008 IBM Corporation 60

61 Almaden Research Center Tobacco mosaic virus AFM images of 18 nm diameter TMV deposited on thin gold film 300 nm 18 nm 5 µm scan 1 µm scan AFM imaging by Jane Frommer 2008 IBM Corporation 61

62 1 m Cantilever tip with tobacco mosaic virus

63 Cantilever tip with tobacco mosaic virus 1 m 300 nm

64 Almaden Research Center 3D MRI of Tobacco Mosaic Virus MRFM proton scan data at various tip-sample distances d = 34 nm 46 nm 59 nm 71 nm 100 nm 2008 IBM Corporation 64

65 Point-spread function due to resonant slice resonant slice B = 2.70 T rf = MHz

66 Point-spread function due to resonant slice shell thickness less than 10 nm B = 2.70 T tip diameter ~ 240 nm rf = MHz

67 Point-spread function due to resonant slice regions of strongest field gradient B / dx z tip diameter ~ 240 nm

68 Point-spread function due to resonant slice xy scans tip diameter ~ 240 nm d = 34 nm 46 nm 59 nm 71 nm

69 Point-spread function due to resonant slice MRFM resonant slice response for xy scans d = 34 nm 46 nm 59 nm 71 nm 200 nm 6 nm MRFM response above virus particles Need image reconstruction to recover original image (Landweber algorithm)

70 Almaden Research Center 3D reconstruction of original image d = 34 nm 46 nm 59 nm 71 nm 100 nm After image reconstruction One slice from the 3D reconstruction showing 1 H density 50 nm Scanning electron micrograph 2008 IBM Corporation 70

71 Almaden Research Center 3D MRI of Tobacco Mosaic Virus Y horizontal slice 6 nm 50 nm TMV Z vertical slice z 20 nm x y thin film containing protons 2008 IBM Corporation 71

72 Almaden Research Center 3D MRI of Tobacco Mosaic MRFM proton scan data at various tip-sample distances d = 34 nm 46 nm 59 nm 71 nm 100 nm After image reconstruction One slice from the 3D reconstruction showing 1 H density Scanning electron micrograph 100 nm 100 nm 2008 IBM Corporation 72

73 Almaden Research Center Scanning electron micrograph 2008 IBM Corporation 73

74 Almaden Research Center Lateral resolution of ~6 nm linescan at d = 21 nm distance 6 nm raw image 100 nm Imaging resolution about 1000x finer than best conventional MRI Another factor of ~30x needed for atomic scale imaging 2008 IBM Corporation 74

75 Dan Rugar John Mamin Christian Degen

76 References NanoMRI: Nuclear magnetic resonance imaging with 90-nm resolution H. J. Mamin, M. Poggio, C. L. Degen, and D. Rugar Nature Nanotech. 2, 301 (2007). Nuclear magnetic resonance force microscopy with a microwire rf source M. Poggio, C. L. Degen, C. T. Rettner, H. J. Mamin, and D. Rugar Appl. Phys. Lett. 90, (2007). Nuclear spin relaxation induced by a mechanical resonator C. L. Degen, M. Poggio, H. J. Mamin, and D. Rugar Phys. Rev. Lett. 100, (2008). Nanoscale magnetic resonance imaging C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, and D. Rugar Proc. Nat. Acad. Sci. U.S.A. 106, 1313 (2009). Isotope-selective detection and imaging of organic nanolayers H. J. Mamin, T. H. Oosterkamp, M. Poggio, C. L. Degen, C. T. Rettner, and D. Rugar Nano Letters 9, 3020 (2009). Feedback cooling of resonators: Feedback cooling of a cantilever s fundamental mode below 5 mk M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar Phys. Rev. Lett. 99, (2007). Displacement sensing with an off-board QPC: An off-board quantum point contact as a sensitive detector of cantilever motion M. Poggio, M. P. Jura, C. L. Degen, M. A. Topinka, H. J. Mamin, D. Goldhaber-Gordon, and D. Rugar Nature Phys. 4, 635 (2008). Statistical spin polarizations: Role of spin noise in the detection of nanoscale ensembles of nuclear spins C. L. Degen, M. Poggio, H. J. Mamin, and D. Rugar Phys. Rev. Lett. 99, (2007). Nuclear double resonance between statistical spin polarizations M. Poggio, H. J. Mamin, C. L. Degen, M. W. Sherwood, and D. Rugar Phys. Rev. Lett. 102, (2009)

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