A switchable source for extremely high magnetic field gradients Y. Tao, A. Eichler, T. Holzherr, and C. L. Degen∗ Department of Physics, ETH Zurich,
arXiv:1512.03185v1 [cond-mat.mes-hall] 10 Dec 2015
Otto Stern Weg 1, 8093 Zurich, Switzerland (Dated: December 11, 2015)
Abstract Nanoscale control over magnetic fields is an essential capability in many areas of science and technology, including magnetic data storage [1], spintronics [2], quantum control of spins [3, 4], and nanoscale magnetic resonance imaging [5–7]. The design of nanoscale magnetic sources has always been a compromise between attainable field strength and switching speed. While strong local fields of a few hundred mT and gradients of order 106 T/m can be reached by static ferromagnetic tips [8], dynamical fields and gradients produced by coils or microstrips are at least an order of magnitude smaller [7, 9]. This imposes severe restrictions on many applications such as single spin detection and manipulation. In this work, we demonstrate that the write pole of a commercial hard drive is ideally suited to overcome these restrictions. By scanning a sharp diamond tip [10] over the pole and measuring the induced diamagnetic force with a nanomechanical transducer [11, 12], we are able to image the pole magnetic field with ∼ 10 nm spatial resolution. A gradient of 2.8 · 107 T/m is estimated when the tip is approached to within 5 nm of the surface, roughly 5× higher compared to that of the best static tips [8]. By design, field and gradient are switchable in ∼ 1 ns. Further desirable features include high-vacuum compatibility, low power dissipation, and an extremely flat surface topography amenable to follow-up lithography. Recording heads thus have the potential for important advances in basic research, ranging from single nucleon magnetic resonance [13] to the study of condensed matter under local field variations [14].
1
Magnetic recording heads use intense local magnetic field pulses to write bits of information onto a magnetic medium. Bits are encoded in the magnetization direction of magnetic domains separated by less than 20 nm in state-of-the-art devices [15]. Write fields are thus confined to a very narrow region in space, leading to extremely high local gradients [16]. Aside from net strength, the field must be rapidly switchable in order to achieve fast write rates of ∼ 1 GHz. The writer surface further possesses < 1 nm smoothness to enable controlled fly-by above the magnetic platter disc. With this remarkable list of features, the hard drive industry has created a tool that could enable significant advances in many nanoscale and quantum physics experiments. A considerable challenge in measuring writer fields is their nanometer spatial confinement. While some information can be gained by magnetic force microscopy [17], images barely reach sufficient resolution and are difficult to quantify due to the complicated tip-sample interaction. Here, we present a new variant of scanning probe microscopy to image the write head magnetic field and gradient quantitatively and with high spatial resolution. The technique, which may be best described as diamagnetic force microscopy (DFM), relies on the diamagnetic response of a sharp scanning tip that is positioned over the magnetic source (see Figure 1). Our experiments take advantage of recently-developed diamond nanowires with ∼ 10 nm apex radius [10] that are attached to ultrasensitive cantilever force transducers [11, 12] originally devised for nanomagnetometry and single electron spin detection [18–22]. The write head device shown in Figure 1b-d was extracted from a commercial Seagate hard drive, reconnected to external leads and mounted in a low-temperature scanning force microscope apparatus (see Methods for details). The magnetic force exploited in our study is generated by passing an alternating current I through the write head’s drive coil. The current dynamically magnetizes the write pole and a stray field B appears above the pole. A tip placed in the stray field acquires a small magnetization M = χB/µ0 owing to its magnetic susceptibility χ (typically |χ| < 10−4 ). A weak force develops that attracts or repels the tip from the region of strongest field, depending on whether the tip is paramagnetic (χ > 0) or diamagnetic (χ < 0). For a point-like particle located at position r the force is F (r) = ∇[µ(r) · B(r)] =
χV ∇|B(r)|2 , µ0
(1)
where µ = V M = V χB/µ0 is the magnetic moment and V the volume of the particle. Equation (1) can be understood as the derivative of the magnetostatic energy V χ|B|2 /µ0 2
of the particle. For a transducer responsive to forces along the x-direction, the measured force signal is given by Fx (r) = χV ∂x |B(r)|2 /µ0 = 2χV |B(r)|∂x |B(r)|/µ0 , where ∂x |B| ≡ ∂|B|/∂x is the magnetic gradient in x-direction. One of the main targets of our work is to determine the maximum exploitable |B| and ∂x |B|. To generate a diamagnetic force signal that can be distinguished from background fluctuations and spurious electrostatic driving, we modulated the drive current at half the cantilever resonance (fc /2) while measuring the force generated at fc (see Figure 2). For small driving currents I, the write pole is not saturated and the resultant field and gradient are both proportional to I. For a sinusoidal modulation I(t) = I0 sin(πfc t) with amplitude I0 the resulting force has frequency components at d.c. and fc , F (t) = −
χV ∂x |B0 |2 [1 + cos(2πfc t)], 2µ0
(2)
where B0 is the amplitude of the stray field. The force then drives mechanical oscillations x(t) of the cantilever that are detected by optical interferometry [23]. Because the driven mechanical oscillation is phase-coherent, information about the sign of χ can be extracted in addition to the magnitude of the magnetic force. Note that as the current is increased, the write pole eventually becomes saturated resulting in a square-wave response to a sinusoidal drive. This leads to the appearance of higher order terms in the Fourier series. Figure 3 shows a two-dimensional scan where we plot the cantilever oscillation amplitude as a function of XY tip position. The scan clearly shows two regions of high signal, which we identify as the front and back end of the write pole. As expected, the largest force is generated near the trailing gap where the bending of field lines is highest. A finite element simulation [23] of the expected force signal (Figure 3b), based exclusively on the micrograph of Figure 1e, agrees surprisingly well with the scanning experiment. The signal peaks are localized to within ∼ 10 nm, demonstrating the high spatial resolution of the diamagnetic force imaging technique. To confirm that the observed signal is truly due to magnetic driving by the write pole, we have performed several additional tests. Figure 3 plots the signal amplitude as a function of drive current amplitude I. As expected from Eq. (1), the cantilever signal increases quadratically when increasing the driving current from zero to a few mA. We have also varied the shape of the current modulation. When using a rectangular drive, no signal was observed, consistent with the absence of a Fourier component for this modulation pattern (Figure 3D). As the pattern was continuously changed from rectangular to triangular, the 3
cantilever signal first increased, reached a maximum at trapezoidal drive, and then decreased again (see Figure insets). By measuring the phase shift between the cantilever oscillation and the drive current one can determine the sign of the driving force and hence the sign of the magnetic susceptibility χ of the tip material. Figure 4a,b shows two dimensional force images obtained by scanning two types of tips. Tip A was coated with a 10 nm Pt layer and was moderately paramagnetic (χPt = +2.9 · 10−4 ) [24]. Tip B was a bare diamond nanowire and weakly diamagnetic (χdiamond = −2.2 · 10−5 ) [25]. The two images in Figure 4 clearly show how the paramagnetic tip is attracted to the center of the write pole (where the magnetic field is highest), while the diamagnetic tip is repelled from the high field region. Although our measurements record images of the magnetic force Fx , and not the field B, we can rigorously reconstruct the magnetic field and the gradient from a force map. By integrating Eq. (1) along the x-direction, one obtains an expression for the magnetostatic energy of the tip as a function of position, Z x χV |B|2 . W (x) = dx0 Fx (x0 ) = µ 0 −∞
(3)
This expression can be used to deduce the magnetic field, |B| = [µ0 W/(χV )]1/2 . We have quantitatively determined |B| and ∂x |B| for the force map of Figure 4(b) by calibrating the magnitude of the force and the effective tip volume (Veff = 2.9 · 10−24 m3 , tip B) [23]. The resulting field maps are shown in Figure 5a,b. A region of high field is seen over the pole surface, as expected, with a sharp drop of high gradient just to the right. Despite the relatively low drive current (I = 5 mA) and large tip standoff (z = 30 nm), magnetic fields and gradients are already quite sizable with peak values around 100 mT and ∼ 3.2 MT/m, respectively. To estimate the maximum field and gradient that can possibly be generated at the tip location, we measured the dipole force as a function of tip-surface distance z and as a function of the drive current I. These measurements are also presented in Figure 5. As the distance between tip and pole surface was reduced, the signal increased until non-contact friction [10] began to dampen the mechanical oscillation. The signal decayed exponentially with distance with characteristic length δ = 11.3 ± 0.6 nm for tip B (Figure 5c) and δ = 13.5 ± 1.2 nm for tip A (see SI). The signal decay is thus not influenced by the tip shape. We found using numerical modeling that δ is mainly set by the width of the write pole near the trailing gap, which was about 60 nm in our devices. 4
To test the maximum drive current, we have monitored the signal from tip B while increasing the drive beyond the failure current density (Figure 5d). The signal continued to increase up to a breakdown current of ∼ 30 mA, showing that the write pole had not reached magnetic saturation. We have modeled the magnetic response based on a Langevin magnetization curve with a saturation field of 2.4 T (FeCo) [15, 26] and found that the pole magnetization at 30 mA is about 1.57 ± 0.08 T, or roughly 65% of the saturation magnetization [23]. Note that the power dissipation is small even at the maximum driving amplitude. For a write head resistance of R = 3 Ω [15], the dissipated power is only 14 mW even when the coil is continuously driven with 30 mA. In our experiments the total dissipated power was in fact limited by lead and contact resistances, and not the write element. In pulsed mode and at low duty cycle, we expect that saturation can be reached with less than 1 mW average dissipation, eventually permitting Millikelvin operation. Table I collects some key experimental values for the magnetic field |B| and field gradient ∂x |B|, representative for a tip standoff of 5 nm. The values are based on the force map in Figure 4b and on the scaling of the force with drive current I and distance z. The experiment demonstrates that magnetic fields around 0.87 T and gradients around 28 MT/m are present at 30 mA drive, about 5× larger than the gradients observed with static nanoscale ferromagnets [8]. These results are consistent with an independent finite element calculation (that shared no common input parameters) which predicts slightly smaller, but similar values (see Table I). The large gradient is a result of the close access (∼ 5 nm) enabled by the diamond nanowire tips, and also thanks to the recessed nature of the pole that prevents oxidation and allows for sharp, highly magnetized pole edges. Write head gradient sources could enable important steps forward in mechanical detection of electronic and nuclear spins. In Figure 5c, forces up to F = 568 aN were generated with a net magnetic moment of only µ = χV B/µ0 ∼ 4.2 · 10−23 Am, roughly equivalent to ∼ 4.5µB . This represents a force per electron spin of about ∼ 130 aN/µB , almost two orders of magnitude greater than the force encountered in the first demonstration of single electron spin detection [22]. The corresponding force per proton spin would be about 0.40 aN at maximum drive (30 mA). This value is within reach of state-of-the-art force transducers operated below 1 K [27–30]. It is thus conceivable that single nuclear spins could be detected, which would constitute a milestone towards the realization of the long-standing proposal of single nucleon magnetic resonance imaging [13]. Aside from the detection of magnetic forces, the use of write heads may allow for signif5
icant advances in several fields of active research. Perhaps the most important of these is the manipulation of spin systems in the context of quantum technologies. Static magnetic field gradients can be used for rapid spin manipulation by means of electrical fields [4, 31] or quantum dot exchange interaction [32, 33], and for strong and tunable coupling in hybrid quantum systems [34]. The gradient can further be exploited to set up spin registers in quantum simulators [35]. The combination of large field and rapid switching, which to date has been difficult to achieve, will allow the implementation of very fast spin manipulation techniques. At a pulse amplitude of 1 T, the nominal spin flip duration is ∼ 18 ps for electrons and ∼ 12 ns for protons, which would be faster than any previously demonstrated values [36–38]. These flip rates will eventually be limited by the response time of the write head and pole material. Universal spin control requires two orthogonal axes of rotation. Although the write head only provides one axis given by the direction of B(r), there are several possible ways to add a second axis, as proposed in Fig. 6. Beyond spin control, write head devices may finally present creative new opportunities in nanoscale transport. For example, pulsed spin polarized currents could be launched through local magnetization of ferromagnetic electrodes [39]. Electrons in confined geometries, such as quantum point contacts, could be locally deflected and the magnetic potential varied within the ballistic regime. Since write heads have an extremely flat surface made from nonconducting diamond-like carbon, complex lithographic structures including local gates, microwires, constrictions, quantum dots or spin qubits could be conveniently integrated.
∗
[email protected]
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Methods: Write heads: The hard disc write heads (WH) used in this study were extracted from Seagate Barracuda 1TB and 4TB desktop drives. The WH’s were fixed on the top of a shapal sample stage. To reconnect the device, we used a silicon jumper chip with lithographically patterned gold pads matching the bonding pads on the side of the WH block. The electrical contact between the WH and jumper chip was made using conductive silver epoxy (Epotek H20E). We used an Asylum Research Cypher MFM to confirm successful electrical control of the write pole magnetization. Diamond nanowire tips: Single-crystal diamond nanowire (DNW) tips were fabricated via inductively-coupled plasma etching following procedures detailed in a previous publication [10]. The nanowires were transferred from their mother substrate to an intermediate silicon wafer chip via PDMS stamping (Gel-Pak 4 padding material). Two tips were prepared for this study; tip A consisted of a diamond nanowire with an apex diameter of ∼ 40 nm coated by 15 nm of YF3 (χ = −1.0 · 10−6 [40]) and 10 nm of Pt (χ = +2.6 · 10−4 [24]). These layers were deposited onto a silicon chip used for tip A via ebeam evaporation. The YF3 was deposited with future
19
F NMR experiments in mind and had no role in this study,
and the Pt was deposited to turn the nanowire paramagnetic as well as to screen electric charges. Tip B was a bare diamond nanowire (χ = −2.2 · 10−5 [25]) with an apex diameter of ∼ 18 nm. High-resolution scanning electron micrographs of both tips are given in the Supplementary Information [23]. Coated and bare DNWs were attached to silicon cantilevers using a micromanipulator system. The custom cantilevers had a length of 120 µm, a shaft width of 4 µm and a thickness of 120 nm [11]. The spring constant was kc = 90 µN/m, the resonance frequencies were between fc = 5 − 6 kHz, and the quality factors were around √ Q = 30, 000 at 4 K, resulting in a nominal force sensitivity of about 4 aN/ Hz. Readers may wish to consult Ref. [10] for fine details of the nanowire handling and transfer processes. Force signal acquisition: All measurements discussed in the main text were performed in a cryostat operated at 4 K and in high vacuum (< 1 · 106 mbar). The WH driving current at fc /2 was generated by an arbitrary waveform generator (NI PXIe-5451). TTL pulses were used to synchronize the lock-in amplifier (Stanford Research SR830) to which the cantilever motional signal from the optical interferometer was sent. An negative feedback loop was used to damp the cantilever to an effective operating Q of about 300 in order to shorten the sensor response time and to keep the driven cantilever oscillation below ∼ 1 nm. The force was calibrated by measuring the thermomechanical noise of the cantilever at 4 K, and comparing 9
the oscillation amplitude of the magnetically driven cantilever with the rms-amplitude of the thermal motion. We have only calibrated the force for tip B, but not for tip A. The phase of the force, which is available as a lock-in output, was calibrated by minimizing the imaginary part of the signal. Finite element modeling:
Finite element simulations were carried out using the COM-
SOL package. The dimensions of the write pole and the surrounding return shield were extracted from Fig. 1d (see Supplementary Information for exact dimensions [23]). The return shield thickness was assumed to be 200 nm based on a focused-ion-beam cut into the write head surface. We assumed a fixed vertical magnetization for the write pole and a µr = 2 · 103 (NiFe) for the return shield. No parameters were adapted to fit the experimental results. Acknowledgments: This work has been supported by the ERC through Starting Grant 309301, the DIADEMS program 611143 by the European Commission, and by the Swiss NSF through the NCCR QSIT. We thank B. Stipe for technical advice on the write head devices, P. Gambardella and M. S. Gabureac for access to the Asylum Research Cypher MFM, and U. Grob, C. Keck, B. Moores, H. Takahashi, O. Zilberberg and the ETH Physics Machine Shop for experimental help and frutiful discussions.
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Figure 1
a
b
c
ultrasensitive cantilever
20 m
0.5 mm sharp tip (dia- or paramagnetic)
d
e
trailing shield
shield
write pole
write pole
diamond tip
z y
FIG. 1.
x
~
18 nm 100 nm
trailing gap
2 m
Geometry of write head experiment and device. a, A sharp diamond needle
(green), attached to a nanomechanical force transducer, is positioned over the write pole of a magnetic recording head. An alternating current periodically switches the pole polarity and induces magnetic gradient forces through dia- or paramagnetism in the tip. Experiments are carried out in a custom scanning force microscope operating at 4 Kelvin and in high vacuum. b, Optical micrograph of a commercial write head. Arrows in b, c and d point in the direction of the trailing edge (in positive x direction). c, Zoom-in on the write/read region of the device. The write pole is at the center of the four arrows. d, The ∼ 90 × 60 nm2 write pole (red) is surrounded by a return shield (yellow) that serves to recollect the field lines. The gradient is largest in the ∼ 20 nm-wide trailing gap between pole and shield. e, Diamond nanowire used to probe the local magnetic force. Inset shows apex of tip B.
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Figure 2
2TC
Write head current I
Write head field B and gradient
Sample magnetization M
|B|
paramagnetic
diamagnetic Magnetic force F
Cantilever oscillation x
TC
Time
FIG. 2. Basic driving protocol for diamagnetic force microscopy. A sinusoidal current with frequency fc /2 is applied to the coil of the write element, generating an oscillating pole magnetic field B and gradient ∇|B|. The oscillating field in turn induces an oscillating sample magnetization M = χB/µ0 . The sample with volume V experiences a magnetic force F = V ∇(M · B) that drives the mechanical resonance fc of an ultrasensitive cantilever force transducer. The amplitude of the resulting cantilever oscillation x is proportional to the force. Tc = 1/fc is one cantilever oscillation period.
12
Figure 3
b
10 nm
75
75
50
50
25
25 Y (nm)
Y (nm)
a
0
0
-25
-25
-50
-50
-75 -100
-50
c
0 X (nm)
50
-75 -100
100
-50
0 X (nm)
d
50
100
0.4
0.2
0 0
FIG. 3.
Cantilever amplitude (a.u.)
Cantilever amplitude (a.u.)
1.0 0.6
1 2 3 4 Drive current I (mA)
0.8 0.6
0.2 0 0.0
5
Tramp Tc
0.4
0.2
0.4
0.6
0.8
1.0
R
Magnetic force above the write pole surface. Two lobes of increased signal are
visible at the front and back end of the pole where the gradient ∂x |B| is largest. The contours indicate the write pole (dashed) and shield (dotted). The traces above (a,b) show the signal intensity |Fx |2 along the x-direction. a, Experimental data, recorded with tip A and an integration time of 3 seconds per point. Point spacing was 2 nm and drive current was 5 mA. b, Independent finite element simulation based on the micrograph from Fig. 1d. c, Signal as a function of drive current amplitude, well below magnetic saturation of the pole. Solid line is ∝ I 2 . d, Signal amplitude while changing the current modulation from rectangular (R = 0) to triangular (R = 1), as sketched in the figure. R = 2Tramp /Tc is the fraction of time spent on ramping the current. For (c,d), the scanning tip was parked at the center of the right lobe where the signal was highest.
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Figure 4
50
a Y (nm)
25 0
-25
b
-50 50
Y (nm)
25 0
-25 -50 -75
-50
-25
0 25 X (nm)
50
75
Force
FIG. 4.
Paramagnetic and diamagnetic response. a, Force image recorded by the param-
agnetic Pt-coated tip A. b, Same image for the diamagnetic bare diamond tip B. Arrows point in the direction of the force. Color bar scale is linear. Scan height was 15 nm for tip A and 30 nm for tip B, and drive was 5 mA.
14
Figure 5
a
b
50
0
25
0
Y (nm)
Y (nm)
25
50
80 60
-25
2
0
3
-25
40
-50 -75
1
-1
20 -50 -25
0 25 X (nm)
50
-50 -75
75
c
-50
-25
0 25 X (nm)
d
75
20 600
400
force (aN)
force (aN)
15
200
~5 nm
400
10
200
5 ~30 mA
0
0
10
20 30 40 tip standoff z (nm)
0
50
0
20 40 drive current I (mA)
write pole magnetization (kOe)
600
50
0 60
FIG. 5. Quantitative field maps and estimated limits. a,b, Two-dimensional images of the magnetic field (a) and field gradient (b) for 5 mA drive and 30 nm standoff (see text). Contour labels are mT and MT/m, respectively. c, Force signal as a function of tip standoff z, measured at the XY location with the highest signal. The solid line is an exponential fit with decay length δ = 11.3 ± 0.6 nm. The dashed line is the prediction by the finite element model that was vertically scaled to fit the data. Drive was 12 mA. e, Cantilever signal as the drive was increased beyond the breakdown current of ∼ 30 mA. The solid line is a fit based on the magnetization curve of FeCo [23]. The dashed line (right scale) is the associated pole magnetization. Tip standoff was 20 nm. All data are from tip B.
15
Figure 6
a
b superconducting solenoid spin
microwire
write pole
c
FIG. 6.
shield
d
mechanical shuttling in gradient
anisotropy field
Proposed arrangements for ultrafast spin manipulation. Write head field is
symbolized by solid red field lines and orthogonal auxiliary field is symbolized by dashed blue field lines. a, Auxiliary microwire serving as electromagnet [7, 9]. b, Auxiliary macroscopic solenoid. c, An ac field is generated by rapid motion of spin in the pole gradient, for example, with a mechanical resonator [34] or by an electrical field [4, 31]. d, Internal anisotropy provides the orthogonal field, such as the crystal field of a nitrogen-vacancy center [41].
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Table 1
Field |B|
Gradient ∂x |B|
12 mA
30 mA
saturation
12 mA
30 mA
saturation
Experiment 0.51 T
0.87 T
—
17 MT/m
28 MT/m
—
Model
0.64 T
0.98 T
10 MT/m
19 MT/m
29 MT/m
0.34 T
TABLE I. Estimated pole field and field gradient produced at z = 5 nm tip location for drive currents of 12 mA (pole magnetization 0.83 ± 0.07 T), 30 mA (1.57 ± 0.08 T), and for magnetic saturation (2.4 T), respectively. The estimated error for the experimental values is +28%/ − 11% due to the uncertainty in the tip volume. The model values are probably slightly overestimated due to the few-nm thick protective layer of diamond-like carbon and Pt on top of the write pole. See supplementary material for details [23].
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