Introduction to Nanomechanics: Magnetic resonance imaging with nanomechanics

Introduction to Nanomechanics: Magnetic resonance imaging with nanomechanics Martino Poggio Swiss Nanoscience Institute Department of Physics University of Basel Switzerland Nano I, Herbstsemester 2009 18.11.2009

Nanoscale Magnetic Resonance Imaging (NanoMRI) Micro- and Nanomechanics m Physics of small spin ensembles N Measuring small displacements 18.11.2009 2

Magnetic Resonance Imaging (MRI) True 3D imaging Chemically selective Non-destructive BUT Requires 10 12-10 18 nuclei per voxel We want to be able to resolve a single nuclear spin. 18.11.2009 3

Imaging Techniques Red blood cell Si (111) Human hair T4 phage DNA 30mm 1mm 30 m 1um 30nm 1nm number of spins 10 20 10 15 10 10 10 5 1 MRI NMR Magnetic resonance force microscope (MRFM) Atomic force microscope Eye Optical microscope Scanning electron microscope (SEM) 18.11.2009 4

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 ~10-8...10-10 N ~10-14 N ~10-26 N

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

New lab in Basel http://poggiolab.unibas.ch/ Phani Peddibhotla Michele Montinaro 18.11.2009 Dennis Weber

http://poggiolab.unibas.ch/ 05.11.2009 9

Nanoscale Magnetic Resonance Imaging (NanoMRI) Micro- and Nanomechanics 18.11.2009 10

What is Nanomechanics? Quantum of Thermal Conductance Nanomechanical Motion Detection Schwab et al., 2000 Casimir Force Measurement Knobel & Cleland, 2003 1 m Single Spin detection 120 m long Decca, 2003 Rugar, 2004 18.11.2009 11

What is Nanomechanics? Mass sensing with carbon nanotubes Si nanowires Zettl, 2008 Graphene membranes 1 m Budakian, 2008 Clean nanotube resonators McEuen, 2007 1 m 1 nm Steele, 2009 18.11.2009 12

What is Nanomechanics? Si (111) (AFM) DNA (AFM) Giessibl, 2000 10 nm Magnetic Bits (MFM) 500 nm Folks, 2000 Hamon, 2007 10 m 18.11.2009 Introduction to Nanomechanics 13

What is Nanomechanics? Nano-motor in T4 Bacteriophage ScienceDaily, 2008 18.11.2009 14

Why Study Nanomechanics? Link between classical mechanics and statistical mechanics Link between classical mechanics and quantum mechanics Smaller sensors are more sensitive 18.11.2009 15

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 18.11.2009 16

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. 18.11.2009 17

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 3 3 18.11.2009 18

Limits of Mechanical Force Detection m x x kx F(t) Sx( ) 1 2 2 2 2 2 0 ( 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 0 18.11.2009 19

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 18.11.2009 20

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 18.11.2009 21

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 18.11.2009 22

Displacement spectral density (Å 2 /Hz) Cantilevers 0.020 0.015 thermal noise at 4 K Q = 380,000 0.010 0.005 225 m 0.000 634.7 634.8 634.9 635.0 635.1 Frequency (khz) Commercial AFM cantilever 90nm imaging cantilever Small cantilever 18.11.2009 23

Ultrasmall Cantilevers 225 m f ~ 3 khz k ~ 10-5 N/m f ~ 1 MHz k ~ 0.1 N/m f ~ 1 MHz k ~ 0.001 N/m 20 m Commercial AFM cantilever 90nm imaging cantilever Small cantilever Next generation 18.11.2009 24

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 ~ 0.001 N/m 20 m Commercial AFM cantilever 90nm imaging cantilever Small cantilever Next generation 18.11.2009 25

Displacement spectral density (Å 2 /Hz) Ultrasmall Cantilevers 0.1 Thermal noise at 4K Q = 8,200 0.01 225 m 0.001 300 320 340 360 Frequency (khz) 20 m Commercial AFM cantilever 90nm imaging cantilever Small cantilever Next generation 18.11.2009 26

Best Force Resolution Rugar et al. (IBM) 120 m long Lehnert et al. (JILA) F min = 1 an/hz 1/2 18.11.2009 27

Best Force Resolution? Clean Nanotubes Steele et al. (Delft) Q = 1.5 x 10 5 m = 10-21 kg 0 = 2 x 500 MHz T = 1 K F min = 0.01 an/hz 1/2 (calculated) 18.11.2009 28

Nanoscale Magnetic Resonance Imaging (NanoMRI) Micro- and Nanomechanics Measuring small displacements 18.11.2009 29

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. 18.11.2009 30

Mechanical Force Transducers F x F kx Now we require a sensor for mechanical motion. 18.11.2009 31

Sensors for Mechanical Motion Tunneling Optical Deflection Optical Interferometry Microwave Interferometry Magnetomotive Piezoelectric Capacitive 18.11.2009 32

Displacement Measurements STM Detection 18.11.2009 33

Displacement Measurements Laser deflection 18.11.2009 34

Displacement Measurements Laser interferometry Fixed mirror spring x P in Movable mirror 18.11.2009 35

Displacement Measurements Laser interferometry 18.11.2009 36

Displacement Measurements Laser interferometry LIGO Gravitational Wave Detection 18.11.2009 37

Displacement Measurements 10 13 m/ Hz Laser interferometry 18.11.2009 38

Displacement Measurements Microwave interferometry capacitive detection K. L. Lehnert, JILA 18.11.2009 39

Displacement Measurements 10 15 m/ Hz K. L. Lehnert, JILA 18.11.2009 40

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

Quantum Point Contact (QPC) Images from: Topinka et al., Science 289, 2323 (2000). and M. P. Jura and D. Goldhaber-Gordon 18.11.2009 42

2DEG L e - QPC R 2DEG QPC as a mechanical displacement detector 13.10.2009 Introduction to Nanomechanics 43

cantilever laser QPC 18.11.2009 44

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 18.11.2009 45

The QPC 1 m 18.11.2009 49

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 10 0 0.1 10-1 0.01 10-2 1E-3 10-3 1E-4 10-4 1E-5 10-5 4500 4750 5000 5250 4.50 4.75Frequency 5.00 (Hz) 5.25 Frequency (khz) 1E-21 10-21 1E-22 10-22 1E-23 10-23 1E-24 10-24 1E-25 10-25 10-12 m / (Hz) 1/2 18.11.2009 50

Nanoscale Magnetic Resonance Imaging (NanoMRI) Micro- and Nanomechanics m Physics of small spin ensembles N Measuring small displacements 18.11.2009 51

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 ~10-8...10-10 N ~10-14 N ~10-26 N

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

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

IBM Research 2008 IBM Corporation 55

Nanoscale Magnetic Resonance Imaging (NanoMRI) Micro- and Nanomechanics m Physics of small spin ensembles N Measuring small displacements 18.11.2009 56

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

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

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, 263111 (2007) C.Rettner M. Hart M. Farinelli 2008 IBM Corporation 59

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

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

1 m Cantilever tip with tobacco mosaic virus

Cantilever tip with tobacco mosaic virus 1 m 300 nm

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

Point-spread function due to resonant slice resonant slice B = 2.70 T rf = 114.8 MHz

Point-spread function due to resonant slice shell thickness less than 10 nm B = 2.70 T tip diameter ~ 240 nm rf = 114.8 MHz

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

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

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)

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

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

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

Almaden Research Center Scanning electron micrograph 2008 IBM Corporation 73

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

Dan Rugar John Mamin Christian Degen 18.11.2009 75

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, 263111 (2007). Nuclear spin relaxation induced by a mechanical resonator C. L. Degen, M. Poggio, H. J. Mamin, and D. Rugar Phys. Rev. Lett. 100, 137601 (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, 017201 (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, 250601 (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, 087604 (2009). 18.11.2009 76