DOI: 10 - Amazon S3 · Web view(c) and (d) Temperature dependence of the saturation magnetization, Ms and coercive field, Hc of the annealing FeGa films at magnetic fields parallel

DOI: 10

Supplementary Information

Coupling of magneto-strictive FeGa film with single-crystal diamond MEMS resonator for high-reliability magnetic sensing at high temperatures

Zilong Zhanga,b, Yuanzhao Wuc, Liwen Sanga, Haihua Wua, Jian Huangb,**, Linjun Wangb, Yukiko Takahashia, Runwei Lic, Satoshi Koizumia, Masaya Todad, Indianto Mohammad Akitad, Yasuo Koidea, and Meiyong Liaoa,*

a National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan

b School of Materials Science and Engineering, Shanghai University, Shanghai 200444, People’s Republic of China

c Chinese Academy of Sciences Ningbo 315201, People’s Republic of China

d Graduate School of Engineering, Tohoku University, Sendai, Miyagi 9808579, Japan

Correspondence: Jian Huang** ([email protected]) and Meiyong Liao* ([email protected])

1. Experimental details

1.1 Device fabrication

Figure S1. Fabrication of FeGa/SCD MEMS magnetic sensor. (i) Ion implantation into the type-Ib SCD substrate. (ii) Deposition of a homoepitaxial SCD layer by micro-wave plasma chemical vapor system. (iii) and (iv) 150 nm-thick Al deposition and lift-off on the SCD epilayer patterned by a laser lithography method. (v) Reactive ion etching by inductively couple plasma (ICP) apparatus in a pure oxygen ambient. Removal the metallization and release of the SCD cantilevers in a boiling acid of H2SO4+HNO3. (vi) Deposition of the FeGa film on the as-fabricated SCD cantilever by the radio frequency magnetron sputtering technology with varying depositing time. The structure FeGa/SCD cantilever was utilized to fabricate the magnetic sensor.

The fabrication of SCD MEMS cantilever resonances was based on the epilayer of SCD substrate. Due to high chemical inertness of the SCD, the process of the SCD cantilever needs a unique step in the last step: the mixture boiling acid of H2SO4+HNO3 were used to release the sample to obtain the SCD cantilever configuration. The fabricated process of the FeGa/SCD cantilever is described in the Figure S1. The process can be described as:

(1) The fabrication of the SCD cantilevers began with the implantation of the high-pressure high-temperature (HPHT) type-Ib SCD (100) substrates with carbon ions at an energy of 180 keV and a dose of 1016 cm−2.

(2) The homoepitaxial diamond layers with different thicknesses from 0.37 to 1.81 μm were grown on the ion-implanted HPHT diamond substrates in a microwave plasma chemical vapor deposition (MPCVD) system. During the growth, a graphite-like layer with a thickness around 200 nm induced by the ion implantation treatment was formed below the diamond surface, which acted as the sacrificial layer to SCD cantilever configuration. An additional annealing at 1100 °C for 3 h under a UHV condition was performed to reduce the number of defects induced by ion implantation.

(3) The SCD cantilever was fabricated by a standard photolithography technique.

(4) In order to etch diamond with oxygen plasma, an aluminum layer with a thickness of around 200 nm was deposited on the patterned diamond epilayer.

(5) The metallization was then removed and wet-etched to remove the graphite. The boiling mixture solution (H2SO4+HNO3) was utilized to release of the SCD cantilevers.

(6) The FeGa film was deposited on the as-fabricated SCD cantilever by the radio frequency magnetron sputtering (RFMS, RG-100) technology, keeping the following process parameters: 10 sccm Ar, chamber pressure of 1 Pa, sputtering power of 100 W, room temperature. The fabrication process of SCD cantilever shows a high reproducibility and uniformity.

The FeGa/SCD cantilever was utilized to fabricate the high-temperature magnetic sensor. In addition, in order to investigate the thermal stability of magnetic properties of the 90 nm-thick FeGa films on SCD, a series of FeGa/SCD samples were annealed at various temperatures for 1 hr in an ultra-high vacuum (UHV, base pressure lower than 10-7 Pa) system.

Figure S2. The geometrical structure of the 160 μm-length FeGa/ single-crystal diamond (SCD) cantilever. (a) Optical image. (b) the 3D profile image. (c) SEM image of the SCD cantilever suspended above the SCD substrate. (d) The schematic image of the FeGa/SCD cantilever structure. (e) and (f) The height profile of the SCD cantilever without and with deposition of FeGa film.

The images of the as-fabricated magnetic sensor based on the FeGa/SCD cantilever are shown in Figure S2. The 3D laser optical images of the cantilever are shown in the Figure S2(a) and (b). The SEM image of the SCD cantilever suspended above the SCD substrate with a gap of around 200 nm is shown in the Figure S2 (c). The schematic structure of the cantilever is also shown in Figure S2 (d). Furthermore, the cantilever beam is spontaneously bended after releasing, which was confirmed by the 3D laser color image of the as-fabricated SCD (Figure S2 (e) and (f)). Note that the image before FeGa cannot reflect the real case due to the transparence of SCD (the limitation of 3D laser microscopy). After the FeGa film deposition, the laser was effectively reflected, resulting in the good height profile for the FeGa/SCD cantilever, as shown in Fig. S2(f). The continuous bending of the SCD cantilever with FeGa film reveals that the thickness of the FeGa film should be uniform. The bending behavior of SCD cantilever shows little effect on the magnetic sensing performance.

1.2 Measurement characterization of FeGa films on SCD

In this work, we characterized the quality of the SCD MEMS from the viewpoint of materials science. The high crystal quality and uniformity of the as-deposited SCD and the as-fabricated SCD cantilever are confirmed by HRTEM and Raman mapping technologies, as shown in Figure R3. The surface morphology of 90 nm-thick FeGa films were examined by an atomic force microscopy (AFM, Bruker, MM-SPM) system. The microstructures were evaluated by an aberration corrected transmission electron microscope (TEM, JEOL, JEM-ARM200F) system with an accelerating voltage of 200 kV. High resolution TEM (HRTEM), bright-field (BF) and selected area electron diffraction (SAED) images were recorded simultaneously. The samples for the cross-sectional TEM observations were prepared by a focused ion beam (FIB) system. Due to the unique atomic configuration of SCD, the lattice structures of these two materials can be obtained by the TEM images taken under the [110] zone-axis condition. The elemental analysis of the FeGa film were studied by energy dispersion X-ray spectroscopy (EDS) system. The thickness of FeGa film was confirmed by TEM image. The texture orientations of 90 nm-thick FeGa films on SCD were analyzed by X-ray diffraction (XRD, SmartLab) operated on D/tex Ultra 250 diffractometer with Cu K radiation (1.54 Å). The magnetic properties of FeGa films on SCD were measured by the vibrating sample magnetometer (VSM, LakeShore 7410) at various magnetic field orientations of with respect to the sample surface and the physical properties measurement system (Quantum Design, PPMS), respectively.

Figure S3. (a), (b) and (c) HETEM, SEAD and Raman spectrum of the as-grown SCD, respectively. (d) The 2D Raman mapping of the homoepitaxial diamond film with spatial distribution of FWHM. The color bar showing the variation of a full width at half maximum (FWHM) with reference of 2.8 cm−1. The Raman mapping shows the good homogeneity of the SCD layer with a FWHM variation of around 0.1829 rel.1/cm, centered at 1332 cm−1. (e) and (f) 2D Raman mappings of the SCD cantilever. The high crystal quality and crystal uniformity of the SCD cantilever were confirmed by a Raman mapping with a narrow FWHM of 2.80 cm−1 with a deviation less than 0.3 cm−1 throughout the cantilever.

In this work, after deposition of the FeGa film, the bending profile of the FeGa/SCD is shown in the Fig. S2(e). In general, Stoney’s formula is utilized to express the relationship between the bending substrate and the film’s stress and thickness is expressed as [1-3],

where f is the stress per unit of section of the deposited film, ES is the Young’s modulus of the substrate, tS is the thickness of the substrate. vS corresponds to the Poisson’s ratio of SCD, which is vS =0.2. R1 and R0 are the curvature radiuses of the substrate after and before deposition of FeGa film. Based on the curve of the FeGa/SCD in the Fig. S2(e) and (f), the R of the SCD without and with FeGa film is evaluated as 866.4 μm and 1117.7 μm respectively by the curvature measurement method [4]. Therefore, according to the Stoney’s formula, the FeGa film stress induced by the cantilever bending is calculated as -887.3 MPa. Furthermore, the strain of the film on the curved substrate can be evaluated as [5-7],

where the t and R are the thickness of the sample and the curvature radius of the bended substrate, respectively. The strain of the FeGa film on SCD cantilever is -0.0095%. The magnetic anisotropy of the film on curved substrates can be influenced by the film strain [8,9]. In such a strain value of -0.0095%, the magnetic properties of FeGa film such as Hc and Mr/Ms were slightly changed compared to non-strain FeGa film based on the results of the related papers [5-7].

1.3 Optical readout of magnetic sensor

The optical readout of the resonance frequency of the SCD cantilevers were fulfilled by the Laser Vibormetry (LV 1710) system in a variable temperature chamber with a pressure less than 10-3 Pa. The SCD cantilever was actuated by a micro-probe, which was set above the SCD cantilever and connected to a RF signal. Furthermore, the magnetic fields were applied by the different magnets. The magnets were placed to ensure the magnetic field perpendicular to the cantilever in the same plane, which was confirmed and calibrated by the Gauss meter (EM/C-GM 301). A lock-in amplifier was utilized to read out the optical signal reflected from the vibration of FeGa/SCD cantilever. The resonance frequencies of SCD cantilevers were measured under varying temperature (300~773 K) condition. Moreover, the function of the magnetic sensor based on FeGa/SCD cantilever was implemented with measuring the resonance frequency shifts under applying different magnetic field under heating (300 K to 573 K) and cooling (573 K to 300K) process, which can present the high sensitivity and high stability sensing property of the magnetic sensor.

2. Surface morphologies of the annealed FeGa films on SCD at different temperature

Figure S4. Atom force microscopy (AFM) profiles of 90 nm-thick FeGa films on single crystal diamond (SCD). FeGa films were treated by different annealing temperature (300~8730 K) in 1 hr respectively. A) 300 K 2D-image. B) 300 K 3D-image. C) 473 K 2D-image. D) 473 K 3D-image. E) 573 K 2D-image. F) 573 K 3D-image. G) 673 K 2D-image. H) 673 K 3D-image. I) 773 K 2D-image. J) 773 K 2D-image. K) 873 K 2D-image. L) 473 K 3D-image.

The surface morphologies show a strong temperature dependence (Figure S4). The annealed FeGa films with annealing temperature below 573 K exhibit nanocrystalline grains with ultra-smooth surface, which ensures the better performance and compatibility for the FeGa/SCD configuration utilized as the functional devices. The grain of the annealed FeGa films notably coarsens with temperature above 573 K, resulting in a worse surface. Therefore, the surface of FeGa film on SCD maintained a smooth surface even under annealing at 573 K. This feature enables the fabrication of magnetic sensor based on the FeGa/SCD MEMS device working in harsh environment.

3. Magnetic properties of annealed FeGa films on SCD at various temperature

Figure S5. a) and b) Hysteresis loops for FeGa films on SCD under annealing treatment (300~873 K) measured via vibrating sample magnetometer (VSM) system when the magnetic field is applied parallel and perpendicular to sample surface respectively. (c) and (d) Temperature dependence of the saturation magnetization, Ms and coercive field, Hc of the annealing FeGa films at magnetic fields parallel to the sample surface, respectively.

The magnetization behaviors show only a slight variation up to 573K and gradual degradation at higher temperature, as shown in Figure S5. The high thermal stability of magnetization of the FeGa films contributes to maintaining the high thermal-stability magnetostriction. The coercive field, Hc shows an upward trend with the annealing temperatures. In the Fig. S4 (supplemental information), we can obtain that the grain sizes of the annealed FeGa films increase with annealing temperature. In general, the Hc of the materials shows the positive grain size-dependence. For this case of nanocrystalline soft magnetic materials, a typical model is utilized to depicted the relationship as [10,11],

wherein the pc is the dimensionless pre-factors close to unity. The A is the exchange stiffness, which is a basic parameter. The K1 is magneto-crystalline anisotropy. Js denotes the saturation magnetization. The Hc increases with the grain size with the law of D6. Therefore, the Hc increases with the annealing temperature.

For the PPMS tests, in the Fig.2(b) in the manuscript, the results of Hc for the FeGa films were measured under varying temperature from 10 K to 600 K. The reason for the increase in coercivity with decrease in temperature can be understood by considering the effects of thermal fluctuations of the blocked moment across the anisotropy barrier [12]. The Hc is expected to depend on temperature as [12,13],

where H0 is the coercivity at T=0 K, while TB is the superparamagnetic blocking temperature of the nanoparticles. Therefore, the Hc shows the negative temperature-dependence. For PPMS test, the Hc decreases with the temperature increasing.

4. Long-time thermal stability of microstructure and soft magnetic properties of annealed FeGa films on SCD at 573 K.

Figure S6. The surface microstructure of the annealed FeGa films under 573 K for 5 hrs and 15 hrs. a) 2D AFM image for 5 hrs, b) 3D AFM image for 5 hrs. c) 2D AFM image for 15 hrs. d) 3D AFM image for 15 hrs. e) X-ray patterns of the annealed FeGa films at 573 K for 5 hr and 15 hr. f) Hysteresis loops of FeGa film at 573 K for 5 hr and 15 hr measured when the magnetic field is applied parallel to the sample surface.

The annealed FeGa films can maintain high-(110) textured orientation on SCD under 573 K even for 5 hr and 15 hr. Furthermore, the magnetization behavior of annealed FeGa films exhibit outstanding thermal stability under 573 K for long-time of 5 hrs and 15 hrs. The coercive field, Hc maintains an upward trend with the annealing temperatures, changing from 25.8 Oe to 147.1 Oe. The highly textured orientation and long-time magnetization thermal stability under 573 K for the annealed FeGa films can guarantee the high reliability performance of magnetic sensor based on FeGa/SCD scheme working in high temperature environment.

5. The regression analysis process of the temperature dependence of magnetization of the FeGa film and magnetic moments of the FeGa films corresponding to varying magnetic fields under different temperature.

Figure S7. (a) Regression analysis process of the temperature dependence of magnetization for the annealed FeGa film with different temperature based on the experimental data. (b) Hysteresis loops for FeGa films on SCD measured PPMS technology when the magnetic field is applied parallel to sample surface respectively. (c) Temperature dependence of magnetiozation of the FeGa films corresponding to a serie of magnetic fields measured by PPMS system.

The temperature dependence of magnetization of FeGa film can be described as the following express [14],

(1)

where M0 is the low temperature saturation magnetization and Tc is the Curie temperature set as 950 K of Fe81Ga19 film. α and are critical coefficients. The exponents α and can be modified in order to maximize the goodness of the fit. The values of α and are calculated to be 2.20 and 0.64 based on the regression analysis of the curve, as shown in the Figure S7(a). It can be seen that it is a good fit to the curve with the coefficients of determination (R2) greater than 0.945 of the FeGa film on SCD.

Furthermore, we obtain the magnetic moment of the FeGa film under a certain magnetic field based on the PPMS results (Figure 2(a) in the manuscript). The magnetic moments of FeGa film under the series of magnetic fields are shown in Figure S7. The magnetic moment behavior of FeGa film under the series of magnetic fields also shows the high thermal stability up to 573 K, which is consistent with the result of the saturation magnetization.

6. The frequency shift of the bare SCD cantilevers as measurement temperature

Figure S8. Temperature dependence of the resonance frequency shift of the bare SCD cantilevers with varying length dimensions.

The temperature coefficient of resonance frequency (TCF) of SCD cantilever is defined as TCF = (f/f0)/T, where f = f f0. f0 is the fundamental resonance frequency when T=300 K. In general, the resonance frequency of the cantilever beam with bilayers can be described as,

(2)

wherein E is the Young’s modulus, is the effective mass density, t is the thickness, and L is the length of the cantilever. The temperature effect on the cantilever dimensions and the mass density can be neglected due to the ultra-low thermal expansion coefficient of SCD (0~4 ppm/K for 0~1000 K) [16]. Therefore, the resonance frequency is primarily determined by the Young’s modulus under different temperature. In general, the temperature has the negative effect on Young’s modulus of materials [17-19]. A mode was proposed to describe this effect via the express [19],

(3)

where the ET0 is the Young’s modulus of material with the temperature of T0. A is a constant. The high temperature can result in the decrease in Young’s modulus of SCD. According to the express, the resonance frequency decreases with the decrease of E as shown in the Figure S8.

The resonance frequencies of the bare SCD cantilevers show the slight temperature dependence. Although the resonance frequency shifts toward the low frequency with the increasing in temperature, the TCF of the bare SCD is -3.2 ppm/K with temperature in the range of 300 K to 773 K. The SCD cantilever can provide a thermal stable platform for the magnetic sensor due to its tiny TCF.

7. Effect of depositing FeGa films on the resonance frequency shift of the SCD cantilevers

Figure S9. Resonance frequency variation of the 160 m-length SCD cantilever without and with deposition of FeGa film. The deposition of FeGa film lead to the resonance frequency shift toward the low frequency, consistent with a bilayer beam configuration. Furthermore, the quality factors of the SCD cantilevers without and with FeGa film show a tiny change.

The resonance frequency of the FeGa/SCD cantilever was measured by Doppler velocity meter before and after depositing FeGa film layer. The resonance frequency of these bilayer system is influenced by the FeGa film. The effective Young’s modulus and mass density of the SCD cantilever with FeGa film can be expressed by [15]

(4)

` (5)

here, Ed, EFeGa, d, FeGa, td and tFeGa are the Young’s modulus, mass density and thickness of the diamond and FeGa film layer respectively.

8. The quality factor (Q) variations of the magnetic sensor at measurement temperature

Figure S10. The Q dependence of the evaluated temperature of the magnetic sensor based on FeGa/SCD cantilever.

The mechanical quality factor of the FeGa/SCD resonator can be easily calculated from the express, Q= f0/Δf, where f0 is the resonance frequency and Δf is the full width at half-maximum of the resonance frequency spectrum fit by the Lorentz function. The Q factor variation of the magnetic sensor is in the range of 3000~7000 at different magnetic fields during heating-cooling process. The high Q factor of the magnetic sensor is beneficial to the high resolution.

9. The magnetic sensing performance of magnetic sensor based on FeGa/SCD cantilever configuration at evaluated temperature

Figure S11. a), d) Schematic diagram of resonance frequency shift of the FeGa/SCD cantilevers magnetic sensor induced by the applying magnetic field under increasing temperature. The response temperature is from 300 K to 573 K. The resonance spectra of the magnetic sensor without and with applying magnet under each temperature is marked by the solid line and dash line. b), e) Resonance frequency shift dependence of temperature for the FeGa/SCD cantilever magnetic sensors at different magnetic fields under heating and cooling treatment respectively. c), f) Resonance frequency shift as a function of the external applying magnetic field under heating-cooling process.

Figure S11 shows the magnetic sensing performance of the magnetic sensor. The resonance frequency of the magnetic sensor decreases with the increasing in temperature without and with magnetic field (Figure S11(a) and (d)). The frequency shift is slightly enhanced with increasing temperature for each magnetic field, as shown in Figure S11(b) and (e). Figure S11(c) and (f) demonstrates the frequency shift linearly increases with the magnetic field. The highest sensitivity is achieved 4.8 Hz/mT at 573K.

10. The axial stress dependence of the resonance frequency of clamp-free beam

We assume the beam is homogenous and isotropic. There is a point force acting in the x axis that causes the beam to deflect in the y direction.

As the clamp-free body profile, the moment can be replaced by the force times the displacement change in out of the plane defection.

We define the variable k to simplify the calculation,

Then, the equation can be rewritten as the following equation,

The nearest above equation is a second-order, linear ordinary differential equation, which has the general solution for position values of k2 (which, of course is the case for our definition of k) is given with two unknown constants, A & B.

For the clamp-free beam system, three boundary conditions are used in a moment.

Using the first two conditions, solving for A and B is straightforward.

So, the general solution can be written as,

Using the third boundary condition, we reduce the above equation to the following,

And so, the above equation will equal zero when kL is equal to the following,

We can now replace k with the relevant variables of our problem, and we will use n=1, since it will require the least bending of the beam, and therefore be the most energetically favorable solution,

Finally, we can rearrange the above equation to solve for F, which will be a critical load that describes the onset of buckling for a beam with a free end and a clamped end.

If, to obtain the axial stress , we will divide this load by the cross-sectional area of the beam,

As discussed in the paper, the resonance frequency for the cantilever beam in the first mode can be depicted as,

Therefore, the relationship between f and can be expressed as,

(6)

11. The measurement of the thermomechanical noise and minimum detectable magnetic field for the magnetic sensor

Figure S12. (a) The magnetic noise spectrum of the FeGa/SCD MEMS testing under 300 K. (b) Dependence of the resonance frequency shift on magnetic field under different temperature during the heating-cooling treatment. (c) The detectable force of FeGa/SCD cantilever under 300 K and 573 K with the applying magnetic fields

The magnetic noise of the magnetic sensor based on the bilayer cantilever were measured to illustrate the magnetic sensing performance. The magnetic noise spectrum was measured at 300 K, as shown in the Figure S12 (a). For the cantilever, the magnetic noise level is ~4 nT/√Hz, which is close to that of the estimation by the equation. Furthermore, in general, thermomechanical noise arises from the thermally actuated mechanical fluctuation of the device and can be understood using fluctuation-dissipation theorem [20]. From the fluctuation-dissipation theory, the thermomechanical noise arises from a white equivalent noise force exerted on the device by the heating surrounding environment.

We calculated the minimum magnetic field based on the experimental data on the resonance frequency shift vs magnetic field. The magneto-strictive stress induced by the FeGa film can be converted into longitudinal force applied to the FeGa/SCD cantilever, which affects the resonance frequency of the cantilever. For a homogeneous beam system subjected to the longitudinal force F, the fundamental resonant frequency fr can be expressed as [21],

(7)

where f0, Eeff, l, t and w are the resonance frequency, effective Young’s modulus, length, thickness and width of the FeGa/SCD cantilever. For the fundamental mode, the constant 0 is 0.295. Therefore, the resonance frequency shift of magnetic sensor shows strong relationship with the F. In our work, the frequency shift increases linearly with the magnetic field, as shown in the Figure S12(b). The detected force dependences of magnetic field under 300 K and 573 K are shown in Figure S12(c), illustrating the high force sensitivity. On the other hand, one can also estimate the minimum detectable force for a rectangular cantilever, which can be expressed as [22],

(8)

where k is spring constant, kB is the Boltzmann’s constant. T is the measurement temperature. Therefore, the minimum detectable force for the 160 µm-long FeGa/SCD cantilever was calculated to be 1.6810-14 N and 310-14 N at 300 K and 573 K, respectively. According the relationship between force and the resonance frequency, the minimum resonance frequency shift can be obtained based on the minimum detectable force. Therefore, the minimum detectable magnetic field (Hmin) of the magnetic field sensor can be approximately calculated based on the experimental data, as the follow,

(9)

The dH/df is shown in the inset of Figure S12(b). The minimum detectable magnetic field (Hmin) of the magnetic sensor are 1.3210-10 T (132 pT) and 1.5910-10 T (159 pT) at 300 K and 573 K, respectively.

12. The on-chip SCD MEMS magnetic sensor with more compact electrical readout system

Figure S13. (a) Optical image of the FeGa/SCD cantilever based magnetic sensor for the electrical readout measurement. (b) The resonance frequency spectra shift of the cantilever induced by the increasing magnetic field. (c) Resonance frequency vs measurement magnetic field of the FeGa/SCD cantilever. (d) Dependence of the resonance frequency shift on the applying magnetic field.

we have fabricated the FeGa/SCD magnetic sensor with all electrical actuation by using Au electrode as the driving gate and the electrical readout by using the variation of the resistance of FeGa as the sensing part. Indeed, the optical readout system is not suitable for a compact sensor. However, the optical readout system has the best sensitivity and simplicity for device demonstration, which is widely utilized in the Lorenz force based magnetic sensors and magneto-strictive effect based magnetic sensors. For the practical applications, electrical readout is necessary.

The scheme of the on-chip SCD MEMS magnetic sensor with more compact electrical readout system and the related sensing results are shown in Figure S13. Here, we just replaced the Source-Drain electrodes with FeGa thin film. We successfully demonstrated the on-chip magnetic sensing with compact structure, although the performance can be further improved.

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21

102 104 106 108

Without FeGa

With FeGa

Amplitude (a.u.)

Frequency (kHz)

L=160um

Shift

300 400 500 600

2

3

4

5

6

7

2.82 mT

1.97 mT

1.77 mT

0.77 mT

0.39 mT

Q

(

10

3

)

Temperature (K)

With magnet