Micromagnets,, and Force-Detected Nuclear Magnetism

Transcription

1 Micro-Oscillators, Micromagnets,, and Force-Detected Nuclear Magnetism John T. Markert Department of Physics, University of Texas at Austin, USA Jae-Hyuk Choi KRISS, Michelle D. Chabot USD, Casey W. Miller UCSD Rosa Cardenas, Han-Jong Chia, Utkur M. Mirsaidov, Yong J. Lee, Samaresh Guchhait, Wei Lu, Michelle Millan and Keeseong Park Supported by Army Research Office Contract No. DAAD C-0064, Robert A. Welch Foundation grant F-1191, and NSF grants DMR & DMR

2 Overview Introduction Principles of NMR-FM Oscillator Microfabrication Double-torsional oscillators Process Micromagnets on Oscillators NMR-FM Experiments (NH 4 ) 2 SO 4 crystal, PMMA thin film, ADP Oscillators and Magnets Resonance slice NMR-FM probe 1-D imaging Summary and future work

3 Magnetic Resonance Force Microscopy MRFM

4 NMR Force Microscopy rf Coil Magnet-Oscillator NMR NMR Sensor Sensor Fiber Optic Interferometer Resonance Slice Sample: PMMA film on Si wafer Magnet on Oscillator H o Detects Detects Motion Motion v v v F( t) = ( M ( t) ) B F min = 4k osc k ω B osc T Q ν

5 Motivations for Double-Torsional Oscillators Thicker necks mechanically easier to fabricate Comparable spring constants Interesting higher-q modes for better force sensitivity

6 Fabrication Process

7 Oscillator Micrographs

8 Torsional Oscillators: Modeling QuickTime and a Microsoft Video 1 decompressor are needed to see this picture. QuickTime and a Microsoft Video 1 decompressor are needed to see this picture. Lower Cantilever Lower Torsional QuickTime and a Microsoft Video 1 decompressor are needed to see this picture. QuickTime and a Microsoft Video 1 decompressor are needed to see this picture. Upper Cantilever Upper Torsional Courtesy of Michelle Chabot, NIST

9 Torsional Oscillators 0.2 µm thick Head Wing 50 µm 100 µm F min N Hz = 4 k B T k Q ω High-Q techniques: Base - Use single crystal silicon 150 µm - Minimize damping to base -Room Temperature Q ~10 4 : F min ~10-16 N/Hz 1/2 -Corresponds to ~10-18 N/Hz 1/2 at 3 He Temps Upper mode of triple torsional Upper torsional mode: I wing I head >>1 E head >>E wing Low damping, high Q Torsional and bending spring constants: k t 3, m t k ω = 4 km t

10 Under-etched Fabrication: KOH Etch Slow etch in the (111) direction: KOH etch rate ratio at room temperature: (110):(100):(111) = 160:100:1 Barely-etched Well-etched Mask Alignment Effects: Mask aligned parallel to (110) flat Mask aligned at 45 degrees to (110) flat

11 e-beam lithography oscillators

12 NMR Force Microscopy rf Coil Magnet-Oscillator NMR NMR Sensor Sensor Fiber Optic Interferometer Resonance Slice Sample: PMMA film on Si wafer Magnet on Oscillator H o Detects Detects Motion Motion v v v F( t) = ( M ( t) ) B F min = 4k osc k ω B osc T Q ν

13 Fiber Optic Interferometer Detection limit < nm / Hz

14 Frequency Scan (Inertia Ratio 6)

15 Noise-driven Spectra Fourier transform of time-series amplitude data Thickness ~ 1 µm Q improvement at low temperature

16 Amplitude (µv) Frequency (Hz) Double-torsional oscillator with Q 10 6

17 Oscillators with Micromagnets External field effects on resonant modes of double-torsional singlecrystal silicon oscillators with individual thin-film micromagnets

18 Permalloy Magnets on Oscillators Oscillator A Oscillator B Mode Resonant Frequency (khz) Quality factor Resonant Frequency (khz) Quality factor Lower Cantilever Lower Torsional Upper Cantilever Upper Torsional µm x15 µm x 32 nm magnet 3 µm x3 µm x 180 nm magnet

19 External Field Effects 0.00 Two regimes observed No magnet Low-field softening New! δf(h)/f o (0) /8 head µ H o High-field stiffening Well known /2 head Whole head µ H o Transition point scales with CoPt volume Zeeman overcomes anisotropy Magnetic Field (T) µ H o µ H o Piezo Driven Scans at 300 K, 100 mtorr Miller et al., J. Appl. Phys., 93 (10), 15 May 2003

20 E/ V = K xsin 2 ξ + K M H(cosβ cosθ sinβ cosϕ) s a y Simple Model Consider cantilever mode (a and c). Magnetic energy of the system can be written as: sin 2 ϕ Low field ω( H ) µ H 2 ω o = 2k o L2 eff 1 H k, x H k 1, yx High field ω( H ) µ HH = 2 ω 2k L ( H o o eff k, x + H k, x ) H k, yx = 2( K y M K s x ) H k, x = 2K M s x

21 Fitting Data k N/m, κ 6x10 N/m M permalloy = 670 ka/m f 0 (B)/f 0 (0) Oscillator A - lower cantilever mode - lower torsional mode f 0 (B)/f 0 (0) Oscillator B - lower cantilever mode - upper cantilever mode B (Tesla) B (Tesla) µ A(fit) = 4.6x10-12 J/T µ A(expected) = 4.6x10-12 J/T H k,x = T H k,y = T µ A(fit) = 0.83x10-12 J/T µ A(expected) = 1.1x10-12 J/T H k,x = -0.6 T H k,y = T

22 Cobalt Nanomagnets on Al templates on Si 7x7 Co platetlets of the size of N=2 (5.4 nm edges) (Image: 85nm 85nm)

23 NMR-Force Microscopy rf Coil Fiber Optic Interferometer Resonance Slice PMMA film on Si wafer Magnet on Oscillator H o v v v F( t) = ( M ( t) ) B F min = 4k osc k ω B osc T Q ν

24 NMR-FM Probes RT bio-probe

25 NMR-FM Probe Variable temperature (4-300 K) general purpose probe

26 Low Temperature Cryostat Oxford s HelioxVL 3 He Proble Base temperature of 230 mk Sample approach walker (shown) Two concentric tube piezos excellent thermal stability

27 Cyclic Adiabatic Inversion Effective field in rotating frame: H eff = H 1ˆ' x + ( H o ω γ RF ) zˆ H eff,z H eff, z = H o ω o + Ω sin( ω osct) γ Adiabatic Condition: 2 ( γh 1 ) >> 1 ω oscω Time Spin-Locking: z ω RF ω o adiabatically Ω/γ H eff(max) Mo H eff Mo Η eff,z =(Ω/γ)sin(ωt) H 1 x' H eff = H 1

28 NMR force signal versus quantity determining adiabatic following, Adiabatic Condition Factor = (γη 1 ) 2 /ωω Normalized SNR Adiabatic Condition Factor

29 Resonance Slice Sample

30 Single Shot Force Detection of NMR (nm) MHz 1 H in (NH 4 ) 2 SO MHz Single Shot Force Detection of NMR with SNR ~7 of (15 µm) 3 sample at Room Temperature 2 nm Signal Amplitude Detected Force ~2 x N/Hz 1/2 Expected Force ~2 x N/Hz 1/2 0.3 nm Noise Amplitude Detected Minimum ~3 x N/Hz 1/2 Expected Minimum ~5 x N/Hz 1/2 NMR origin of signal verified Increased carrier frequency by 1 MHz corresponding to ~100 µm shift of resonance slice Detected ~90 µm shift Distance (mm)

31 Magnet-Oscillator NMR Sensor Micromagnets produce immense field gradients! k osc = N/m, f osc = Hz, Q = 6000 F RT = N/ Hz, db/dz = T/m M M min =F min / min =F min / (db/dz) = J/T J/T Hz Hz Flat cylindrical Permalloy magnet 4 µm diameter, 180 nm thick

32 Resonance Slice Resonance slice in CAdI scheme Resonance slice thickness

33 (NH 4 ) 2 SO 4 crystal & PMMA thin film (NH 4 ) 2 SO 4 crystal Large size~1 mm 3 : essentially infinitely thick slab Long spin-lattice relaxation time T 1 10 s Large proton spin density n H = cm -3 Easily cleaved to yield a flat vacuum-sample interface PMMA thin film 300 nm 0.3-µm-thick poly-methyl-methylacrylate (photoresist) film on Si substrate patterned to have a flat region and a region with a 2-D array of ~5.0 µm-diameter polymer islands 200 µm

34 1 D imaging of (NH 4 ) 2 SO 4 crystal NMR-induced amplitude (nm) (NH 4 ) 2 SO 4 crystal Resonance slice position (µm) Noise level: F noise = 2.5 x N NMR-induce amplitude: F expt = 9.7 x N in agreement with the estimation F predicted = 7.6 x N Sharp onset near 2 µm due to a narrow resonance slice and the flat geometry of the crystal

35 1 D imaging of 0.3-µm PMMA film Spatial dependence of NMR-induced amplitude Peak height: N SNR ~ 4 Peak width: ~ 0.5 µm Peak shifts with resonant slice rf frequency determines resonant slice position

36 1 D imaging of PMMA thin film Resonance slice shape and overlapping with PMMA thin film At ~1 µm: Larger gradient Resonance slice is almost flat Maximum overlap with film At ~2 µm: Smaller gradient Resonance slice is curved

37 Summary Adiabaticity: >> really means 6 times greater No magnet 1/8 head 1/2 head External field effects on magnetically capped oscillators: dramatic low field softening observed; f osc and Q stable at high fields Whole head Magnet-on-Oscillator proton NMR-FM demonstrated at RT with ammonium sulfate with 200 nm resonance slices: SNR ~ 4

38 Summary and future work Fabricated sensitive micro-oscillators Studied micromagnet anisotropy and interaction with external field Performed 1-D NMR imaging of (NH 4 ) 2 SO 4 crystal and PMMA thin film in `magnet-onoscillator' scanning mode Sub-micron resolution achieved using permalloy micromagnets; promising for the future scanningmode microscopy of polymer structures 3-D imaging and spin dynamics (T 1 ) experiments are on-going for ADP samples

39 NMRFM ongoing work NMR force microscopy of soft matter (ADP, polymers, biological cells) NMR spectrosopy of individual microcrystals (superconductors, quantum spin systems) MgB2 single microcrystals NMR microscopy below 1 K (local nanometer-scale NMR) Single-spin NMR feasibility studies (demonstrate M min = J/T Hz )

40 Single-Nuclear-Spin Feasibiltiy Study Dual titanium attocube style positioning for 3He Oxfford Heliox VL system Yong J. Lee, Ph.D.

41 Single-Nuclear-Spin Detection requires active control of multimode ultrafloppy oscillators STM low frequency noise Fiber Interferometer thermal (modes)

42 Amplitude Spectral Density [m/ Hz 1/2 ] Q=10,000 Q=3 Frequency [Hz] Ultrafloppy Oscillators Require Control of Thermal Noise even at 0.3 K 0.1 nm required Spectrum Amplitude [m/hz^(1/2)] Q effective = 3 Q = 10, Frequency [Hz]