Mechanical detection of magnetic resonance using nanowire cantilevers: opportunities and challenges

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1 Mechanical detection of magnetic resonance using nanowire cantilevers: opportunities and challenges John Nichol and Raffi Budakian Deparment of Physics, University of Illinois at Urbana Champaign Eric Hemesath and Lincoln Lauhon Department of Materials Science, Northwestern University

2 Outline Motivation Silicon nanowires (SiNWs) at low temperature near a surface Surface dissipation Frequency noise Proposed MRFM protocol using a nanowire cantilever

3 Goal: image single protons with sub nanometer precision MRFM is one promising route Improvements needed in different areas Magnetic moment Number of spins ( μ G) 2 SNR = N S B p Gradient Force noise F Measurement bandwidth ( ) S = 4k T Γ + T Γ F B cant cant surface surface Γ = cant k ω Q c This work Best current: G=70 G/nm with Dy tip S F 1/2 =5 an/rt(hz) near the 300 mk In a 1 Hz BW, single proton SNR =

4 Idea: nanowire cantilevers 3 k R mω Γ= ωq lq Q Potential benefits: Low intrinsic dissipation Low surface dissipation smaller capacitance higher frequency High frequency, new protocols S 1/2 F 3 RT lq w=3μm t=100 nm D=50 nm R l audio frequency lever SiNW cantilever

5 Vapor Liquid Solid Growth Mechanism The VLS process can mediate the growth of semiconductor nanowires nm 1-50 μm Au seed Si substrate Morphology control Composition control Axial & Radial heterostructures 5 nm Position control R. S. Wagner and W. C. Ellis, Appl. Phys. Lett. 4, 89 (1964).

6 GaAs NW spectrum at low temp: Q=95 000! GaAs NWs Xiuling Li, Illinois ECE Larger bandgap, less heating? Higher Qs? GaAs NW 15 microns long, 300nm diam at base, 60 nm diam at tip

7 Polarized fiber optic interferometry at 1550nm E //SiNWaxis E SiNW axis Scattered intensity 50x stronger for TM polarization with D=60nm Shot noise limited displacement sensitivity: 0.5 x m/rt(hz) for 15 µw of light incident on the SiNW at 295 K Nichol et al., APL, (2008).

8 Ultra low dissipation at 295 K representative audio frequency cantilever f=3 10 khz k=100 µn/m Q=20 T=300K Г cant =1.1 x kg/s Г surface =1.5x kg s 10nm spacing nanowire cantilever f=100khz 1.5 MHz k= µn/m Q= Г cant = 2 50 x kg s 1 Г surface = 1.5 x kg s 10nm spacing S 1/2 F = 4k TΓ B

9 λ=2μm to minimize optical absorption 2μm PM free space interferometer operates with near shot noise limited displacement sensitivity

10 4K microscope NW substrate Springs for vibration isolation Sample 0.25 NW 3D piezo walker 8 Optical fiber and lens holder Optical fiber piezo scanner Sample 3D piezo walker z y x 3 axis piezo walker for the NW substrate to locate and focus on specific NWs Piezo bimorph scanner for the optical fiber to image individual NWs 3 axis piezo walker for the sample to locate nanomagnet and microwire underneath NW Spring based vibration isolation

11 Temperature of the SiNW vs. position of the laser spot on the shaft with 8.3 µw incident power Tip of the NW with Au catalyst particle L=12μm Heating by absorption from the Au catalyst particle can be minimized by positioning the laser spot back on the shaft of the SiNW.

12 Temperature of the SiNW vs. laser power with the spot 6 μm back from the tip Q=35000 k=215 µn/m f=630 khz S x 1/2 =1.5 pm/rt(hz) for 1.44 µw optical power incident on the SiNW Assuming T = 6K, S f 1/2 = 0.7 an/rt(hz) 100 Hz

13 Opportunity: ultra low surface dissipation Surface dissipation Total dissipation Native dissipation Stipe et al., PRL, 87, (2001). Surface: Au(111) 295 K 4 K 1 MHz SiNW, surface : Si(100), T = 295K 630 khz SiNW, surface : Al, T sample =4K At low temperature and 10nm from the surface: The SiNW maintains its native dissipation The SiNW has 150x less surface dissipation than the microscale cantilever The SiNW has 300x less total dissipation than the microscale cantilever

14 Opportunity: Estimates for 1 H Imaging 1/3 S F voxel size: 1.2 (SNR = 3) 2 ρ s ( μ pg ) Tmτ s Spin density ρ s ~4 x m 3 Spin lifetime τ s ~30 ms Measurement time T m =60s Temperature T cant =6K Dissipation Force noise Г cant =1.6 x kg s 1 (20 nm from surface) S F =4k B (Г cant T cant ) S F 1/2 =0.7 an/sqrt(hz) G=dB/dx (10 6 T/m) l(nm) sqrt(n spin )

15 Challenge: need to modulate the force from the spins at the cantilever frequency Adiabatic inversions at 500 khz difficult need B1>400G Detecting the Larmor precession is difficult Detecting the z component of the moment by upconversion seems more feasible with parametric CERMIT (invented by John Marohn et al.) F t = μ() t spin modulate via adiabatic inversions at ω mod /2π eg. 2 khz () B z ( x( t) ) x modulate by oscillating cantilever at ω osc =ω cant ω mod eg. 500 khz 2 khz = 498 khz (, ) F x t Fsurface ( x, t) = F( x0, t) + x() t + x x = x Randomly fluctuating force gradients can be upconverted by cantilever oscillation to create force noise. 0

16 Challenge: 1/f frequency jitter from fluctuating force gradients Frequency noise power spectrum Jitter vs. tip sample bias T=8K, xrms=65nm, optimum bias 1/f jitter from fluctuating force gradients Thermal noise Displacement noise 1/f noise observed when sample is 100 μm away! Thermal noise limit not achieved for reasonable amplitude near the surface Probable electronic origin, perhaps low frequency fluctuating electric field gradients

17 Low dissipation cantilevers have increased sensitivity to 1/f force gradient fluctuations Assuming the 1/f frequency fluctuations are due to force gradient fluctuations with a 1/f power spectrum: S k ( f ) = A f S f ( f ) 2 1 f c = 2 kc 2 A f f knee Ultra soft parameters: f=3khz k=86 μn/m Nanowire parameters: f=636khz k=215 μn/m The ratio f/k is 85x larger for the NW than for the ultra soft cantilever S thermal f B ( f ) 2 f knee kt f c = 2π xrmsq kc = x A S 2 rms F

18 Avoiding the added force noise is challenging with the NWs Added force noise experienced by cantilever: S ω x = S ω ω x ( ) ( ) 2 2 k mod pk k cant osc pk To be thermally limited need f mod > f knee f knee ~ 2 khz Need to stop cantilever during spin inversion With f mod = 2kHz, need to start and stop cantilever, and invert the spins in all in 250 μs This is challenging

19 Proposed spin detection protocol Gradient modulation frequency is doubled oscillating near the edge of the hole. S ω ω x ( ) 2 k cant osc pk Now (ω cant ω osc )/2π =250 khz Before (ω cant ω osc )/2π =2kHz in progress

20 Protocol simulation Forcing function has no Fourier component at f cant so cantilever is easier to start and stop Now vulnerable to force gradient fluctuations at 250 khz instead of 2 khz No longer need f mod >f knee

21 Fluctuating electric field curvature creates fluctuating force near f cant 1 E (,) r t F ( δx, t) q x( t) x 2 x 2 = + δ x r= r 0 δx(t) = cantilever displacement r 0 =cantilever equilibrium position Field curvature decreases more rapidly with distance than field gradient E x E E r x r x r 2 1 x 1 x

22 Test the protocol To do list: Determine mechanical properties in magnetic fields Microwire, magnetic gradient source Functionalization of NW with biomolecules Catherine Murphy, Illinois Chemistry

23 Summary 2 μm interferometer compatible with low temperature operation of SiNW cantilevers SiNW cantilevers have ultra low surface dissipation at low temperature S F 1/2 1aN/rt(Hz) close to the surface Frequency jitter must be dealt with Proposed protocol: frequency doubled gradient modulation to avoid excess force noise from frequency jitter Stay tuned work in progress!