Journal of Magnetic Resonance 254 (2015) 71–74
Contents lists available at ScienceDirect
Journal of Magnetic Resonance journal homepage: www.elsevier.com/locate/jmr
Communication
NMR spin–lattice relaxation time T1 of thin films obtained by magnetic resonance force microscopy Seung-Bo Saun a,1, Soonho Won b,1, Sungmin Kwon a, Soonchil Lee a,⇑ a b
Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea Advanced Metallic Materials Division, Korea Institute of Materials Science, Changwon 642-831, Republic of Korea
a r t i c l e
i n f o
Article history: Received 22 September 2014 Revised 12 January 2015 Available online 7 March 2015 Keywords: MRFM NMR Spin–lattice relaxation time Thin film
a b s t r a c t We obtained the NMR spectrum and the spin–lattice relaxation time (T1) for thin film samples by magnetic resonance force microscopy (MRFM). The samples were CaF2 thin films which were 50 nm and 150 nm thick. T1 was measured at 18 K using a cyclic adiabatic inversion method at a fixed frequency. A comparison of the bulk and two thin films showed that T1 becomes shorter as the film thickness decreases. To make the comparison as accurate as possible, all three samples were loaded onto different beams of a multi-cantilever array and measured in the same experimental environment. Ó 2015 Published by Elsevier Inc.
1. Introduction Nuclear magnetic resonance (NMR) is a very powerful research tool which is widely used in areas such as physics, chemistry, biology and medicine. This technique provides the chemically selective, non-destructive, and local probing of matter from the atomic to the macroscopic scales. The spectrum obtained by NMR basically carries the information regarding the electronic state, which determines the property of matter. One weakness of this powerful tool is its relatively low detection sensitivity, which limits its application only to bulk samples. At present, thin films and devices on the nanometer scale are used in many types of research and industry. Thin film and bulk samples frequently show different physical properties despite the fact that they consist of the same elements. For example, resistivity of the silicon layer sandwiched in silicon oxide increases rapidly with decreasing thickness [1] and BaTiO3 and SrRuO3 lose their ferroelectric [2] and ferromagnetic [3] properties with decreasing thickness, respectively. NMR can present useful information for understanding the properties of thin films and samples on the nanometer scale originating from its quantum size and surface effects once the signal is observed. There have been several schemes which demonstrate the dramatically enhanced detection capability of NMR. Magnetic resonance force microscopy [4,5] (MRFM) is most notable among these in the sense that it is applicable to general samples while the others [6,7] are limited to specially prepared samples. In ⇑ Corresponding author. 1
E-mail address: [email protected] (S. Lee). These authors contributed equally to this work.
http://dx.doi.org/10.1016/j.jmr.2015.02.009 1090-7807/Ó 2015 Published by Elsevier Inc.
MRFM, the magnetic resonance is detected by measuring the coupling force between a magnet and the magnetization of a sample using a cantilever instead of an induced current or impedance change as in conventional NMR. The original goal of MRFM was to detect individual nuclear spin moments with atomic resolution and determine the structure of molecules. Several studies reported in recent years have demonstrated the potential of MRFM in the fields of NMR and magnetic resonance imaging (MRI). Imaging with a 4-nm resolution has been demonstrated by MRFM for virus samples [8]. This represents a 100-million-fold improvement in the volume resolution over conventional MRI. NMR spectrum was obtained by MRFM for micron-scale samples [9], and even double resonance experiment was performed [10]. Also, NMR spectroscopy for a thin film was reported for a 34-nm-thick CaF2 thin film [11]. One of the most useful physical parameters obtained by NMR for condensed matter is the nuclear spin–lattice relaxation time (T1). It can provide important information on the various properties of thin films that differ from those of the bulk. Previous MRFM experiments reported the measurement of the ESR spin–lattice relaxation time [12,13]. NMR spin–lattice relaxation time was also measured by MRFM for a several-microns-thick crystal [14]. The measurement near the surface was difficult because of the broadening of the signal due to the magnetic field gradient. In this work, we report the measurement of the NMR spin–lattice relaxation time for a thin film by MRFM. We avoided the complication with the broadening by working with a very thin sample and using a cylindrical magnet to generate a field that varies primarily in the vertical direction. We measured the T1 of CaF2 thin films and compared the result with that of the bulk.
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Communication / Journal of Magnetic Resonance 254 (2015) 71–74
2. Methods Three CaF2 samples were used in the experiment: a bulk sample and two thin films. The bulk sample was a particle of spherical shape with diameter of about 50 lm chosen from CaF2 powder
Fig. 1. (a) Silicon cantilever arrays with loaded CaF2 samples. From the left, 150 nm thin film, 50 nm thin film (inside the dashed rectangles) and a bulk sample with 50 lm diameter. On cantilevers loaded with thin film samples, additional masses were loaded to reduce the cantilever vibration frequency. (b) Schematic drawing of the MRFM setup. The sample-on-cantilever scheme was used.
with a purity of 99.99%. The thin film samples with thicknesses of 50 ± 5 nm and 150 ± 15 nm were deposited directly on top of the cantilevers by e-beam evaporation using the same powder as the source. The thickness of the thin films was measured by spectroscopic reflectometry. The samples are positioned at the ends of the cantilevers, as shown in Fig. 1(a). The spring constant of the cantilevers provided by the manufacturer [15] is 0.01 N/m. Additional masses were loaded onto the cantilevers with the thin film samples to decrease the natural vibration frequency of the cantilevers. This was done because the nuclear magnetization of the sample, which flips periodically in resonance with the vibration of the cantilever, cannot be fully inverted if the frequency is too high [16]. The vibrational frequencies of the cantilevers after the loading of the samples and the additional masses were 1587, 1402, and 1361 Hz. The data was obtained at 18 K and 104 torr. The experiments were carried out at liquid helium temperature but the temperature of the sample was higher than this mainly due to RF heating generated by the coil. The sample temperature can be estimated from the area of the power spectral density of the cantilever’s thermomechanical fluctuation [17], using the fact that the area is proportional to the cantilever temperature. The sample temperature at our experimental condition was obtained by comparing the power spectrum of the cantilever fluctuation with that at liquid nitrogen temperature with rf turned off and exchange gas filled, where the sample temperature should be almost the same with the thermometer located at the other end of the cantilever. Fig. 1(b) shows the experimental setup of the probe part. MRFM is basically a combination of atomic force microscope (AFM) and magnetic resonance techniques. Magnetic resonance is detected by measuring the coupling force between the magnetization of the sample and external magnetic field gradient [5]. In our setup, an iron cylindrical magnet with a 300 lm diameter was used to generate magnetic field gradient mostly in one direction. The magnetic field is relatively constant on the plane of the thin film, though it changes along the direction perpendicular to the plane. The magnetic field gradient along the perpendicular direction is 50 G/lm. The total magnetic field inside the sample is the sum of the homogeneous field generated by a superconducting solenoid surrounding the probe and the inhomogeneous field generated by the magnetized iron magnet located above the sample. The magnet and the optical fiber detecting the cantilever deflection were aligned by three directional nano-positioners. The wavelength of laser used in the optical fiber interferometer [18] was chosen as 1310 nm to avoid cantilever heating as much as possible,
Fig. 2. Timing diagram of the cyclic adiabatic inversion scheme combined with the periodic phase inversion of magnetization. The RF frequency is modulated such that it makes the z component of magnetization oscillate along the z-axis in resonance with the cantilever vibration. The resulting force oscillation is detected by the frequency shift of the cantilever vibration, whose amplitude is forced to remain fixed by feedback circuits. The phase of the RF frequency modulation is flipped every N period of the cantilever oscillation so that the frequency shift changes sign with the same period. This scheme eliminates the white noise and the noise that oscillates in phase with the cantilever.
Communication / Journal of Magnetic Resonance 254 (2015) 71–74
because the energy of the photon with 1310 nm wavelength is lower than the energy gap of silicon [19]. The optical power incident on the cantilever is estimated to be about 0.3 lW. An RF field with a frequency of 283.4 MHz generated by a coil changes the magnetization in the localized volume of the sample, called the resonance slice, where the resonance condition is satisfied in the inhomogeneous field. Because the magnetic field gradient is 50 G/lm, the slice thickness of CaF2 having a natural line width of 10 G is 200 nm. The magnetization change induces a change in the force on the cantilever. The magnetization is periodically inverted using the cyclic adiabatic inversion technique in resonance with the natural vibration of the loaded cantilever. During adiabatic inversion, the magnetization along the field direction is inverted by changing the RF frequency across the resonance frequency. Therefore, the RF frequency is modulated as x ¼ x0 þ Xsinð2pf c tÞ, where x0 is the frequency of the magnetic resonance and fc is the vibration frequency of the cantilever. The RF frequency modulation amplitude X is 30 kHz, which corresponds to 7.5 G in the magnetic resonance of fluorine nuclei. The force on the cantilever then oscillates with the same frequency as that of the cantilever vibration and aids or hinders the cantilever vibration depending on the relative phase of the force oscillation. This makes the vibration amplitude change or makes the vibration frequency shift if the amplitude is fixed by a feedback loop of the amplitude control [20]. We chose the frequency-detection scheme that has an advantage over the amplitude detection scheme when the detection time is limited [21]. There are other approaches for measuring magnetic resonance as a frequency shift such as OSCAR [22] or CERMIT [23]. The detection method used in our work is advantageous when the field gradient is relatively small. The amplitude of the cantilever vibration was fixed to 20 nm. During frequency detection, the frequency noise comes from the detector and the fluctuation of the cantilever vibration [24]. The detector noise increases with an increase in the frequency. In our setup, the detector noise starts to exceed the thermal noise of the cantilever above 3 Hz. Noise with frequencies below 0.5 Hz was also detected in our setup, possibly coming from the mechanical vibration of the entire probe set. To eliminate background noise, the phase between the magnetization and the cantilever vibration was inverted every N cycle of cantilever vibration. Fig. 2 shows a timing diagram of the cyclic adiabatic inversion combined with the periodic phase inversion of the magnetization. When the phase between the cantilever vibration and the magnetization oscillation is opposite, the coupling force acts in a way to aid the restoring of the cantilever vibration, and the cantilever frequency shifts in the direction opposite to that in the in-phase case. The frequency shift changes the sign with a frequency of 2 N/fc, as detected by a lock-in amplifier, such that noise data at other frequencies are eliminated. The phase-inversion frequency was 0.5–3 Hz.
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larger than the bulk sample. Whenever the magnetization passes the rotating plane by this repetitive adiabatic inversion, the net magnetization is reduced by the spin–lattice relaxation in the rotating frame, of which the characteristic time T1q is much shorter than T1. After the saturation of the magnetization, the field was shifted to an off-resonance position and left there for a time s, during which the magnetization grew (Fig. 3(a)). The signal was then measured for several different s values to obtain the T1 relaxation curve. The spin–lattice relaxation time of CaF2 is known to depend heavily on the temperature at low temperatures [25,26]. Moreover, the result of the measurement may be sensitive to the experimental setup because the relaxation rate is actually quite small. We tried to compare the relaxation times of three different samples under experimental conditions which were as similar as
3. Results and discussion To measure the spin–lattice relaxation time T1, the magnetization was saturated first and then the recovery process to the thermal equilibrium state was detected. In the experiment at the previous report of T1 measurements of the bulk [14], magnetization was saturated by using the multiple p/2 pulses, which is effective when the RF amplitude is inhomogeneous. In our work, we adiabatically inverted the magnetization repeatedly till it vanished, noting that the spin–lattice relaxation in the rotating frame is much faster than that in the lab frame. For the initial saturation of the whole sample, the magnetic field was swept back and forth repeatedly, crossing the resonance point with RF on at a fixed frequency. The sweep range was broad enough to cover the length
Fig. 3. (a) Scheme of the spin–lattice relaxation (T1) measurement. (b) The NMR spectrum of the bulk CaF2 sample obtained for several different time intervals s. The curve without a symbol is the spectrum of the 50 nm thin film sample obtained for time interval of 200 s. (c) The signal intensity vs. time interval for the bulk and two thin film samples. The solid lines are the fitting curves of the recovery process. The spin–lattice relaxation time decreases as the sample thickness decreases.
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Communication / Journal of Magnetic Resonance 254 (2015) 71–74
possible. Three samples were loaded onto three different beams of a multi-cantilever array, and the fiber and the magnet moved to the position of the sample during measurement. The relaxation times were measured at precisely the same temperature, pressure, and magnetic field, etc. Fig. 3(b) shows how the intensity of the NMR spectrum for the bulk sample grows with the time interval s after the saturation of magnetization. A RF frequency of 283.4 MHz corresponds to 7.08 Tesla in magnetic resonance of the fluorine nuclear spin. The spectrum of the bulk is broad because the sample image is overlapped on the spectrum due to the field gradient of the magnet. The sample size of 50 lm is 250 times larger than the slice thickness, 200 nm. The spectrum of the 50 nm thin film, which is thinner than the slice thickness, plotted together in Fig. 3(b) is quite sharp compared to that of the bulk. The observed cantilever frequency shifts of the bulk and the 50 nm thin film were 170 mHz and 4 mHz, respectively. Using the spring constant of 0.01 N/m and the fixed vibration amplitude of the cantilever of 20 nm, the forces corresponding to these frequency shifts were 50 and 1.1 fN, respectively [20]. The data plotted by the squares in Fig. 3(c) show the signal intensity of the bulk sample vs. the time interval. The data were taken from the peak values of the spectra in Fig. 3(b). This process of magnetization recovery is described by MðtÞ ¼ Mð0Þð1 et=T 1 Þ. The spin–lattice relaxation time of the bulk sample as estimated by fitting this equation to the data was 308 ± 4 s. The data of the 50 nm (circles) and 150 nm (triangles) thin films obtained in the same way are plotted together in Fig. 3(c). The spin–lattice relaxation times estimated by the same fitting are 197 ± 4 and 108 ± 4 s for the 150 and 50 nm samples, respectively. The relaxation time is shorter in the thin films than in the bulk, and its rate increases with a decrease in the thickness of the film. Magnetically active defects, which can be easily generated during the e-beam evaporation process, may influence the spin–lattice relaxation [25]. However, it is doubtful that this is the main source of the enhanced relaxation in CaF2 thin films, because the 50 and 150 nm samples have different relaxation times though they were made by the same process. The discontinuity and defects may induce faster spin–lattice relaxation at the interfaces and spin diffusion from the interfaces make the bulk relaxation faster. The effect should be more dominant with thinner samples. We believe this is the main mechanism of the spin–lattice relaxation time decreasing with the sample thickness. The spin–lattice relaxation processes of the thin film samples are influenced by the interface and 2-D effects. It is usual that the interface effect of a solid is prominent only in several layers from the interface. Therefore, observation of the interface effect in T1 measurements for the 50 and 150 nm samples may be difficult unless the spin–lattice relaxation is practically absent in the bulk state, as in CaF2. 4. Conclusions In conclusion, we obtained the spin–lattice relaxation time of thin films by MRFM. Because the relaxation rate is quite small, we loaded all three samples on different beams of the same multi-cantilever array and attempted to obtain data in conditions as similar as possible. The spin–lattice relaxation time becomes shorter with a decrease in the film thickness, as expected, most
likely due to interface and 2-D effects. This experiment involving a comparison of T1 of bulk and thin film samples is applicable to the characterization of other thin films in various fields. Acknowledgments This work was supported by the National Research Foundation of Korea under Grant No. 2012R1A2A2A01003598 and the HRHR program of KAIST. References [1] P. Zhang, E. Tevaarwerk, B.-N. Park, D.E. Savage, G.K. Celler, I. Knezevic, P.G. Evans, M.A. Eriksson, M.G. Lagally, Electronic transport in nanometer-scale silicon-on-insulator membranes, Nature 439 (2006) 703–706. [2] J. Junquera, P. Ghosez, Critical thickness for ferroelectricity in perovskite ultrathin films, Nature 422 (2003) 506–509. [3] J. Xia, W. Siemons, G. Koster, M.R. Beasley, A. Kapitulnik, Critical thickness for itinerant ferromagnetism in ultrathin films of SrRuO3, Phys. Rev. B 79 (2009) 140407. [4] J.A. Sidles, J.L. Garbini, K.J. Bruland, D. Rugar, O. Züger, S. Hoen, C.S. Yannoni, Magnetic resonance force microscopy, Rev. Mod. Phys. 67 (1) (1995) 249–265. [5] D. Rugar, C.S. Yannoni, J.A. Sidles, Mechanical detection of magnetic resonance, Nature 360 (1992) 563–566. [6] J.M. Kikkawa, D.D. Awschalom, All-optical magnetic resonance in semiconductors, Science 287 (2000) 473–476. [7] D.R. McCamey, J. van Tol, G.W. Morley, C. Boehme, Fast nuclear spin hyperpolarization of phosphorus in silicon, Phys. Rev. Lett. 102 (2009) 027601. [8] C.L. Degen, M. Poggio, H.J. Mamin, C.T. Rettner, D. Rugar, Nanoscale magnetic resonance imaging, Proc. Natl. Acad. Sci. USA 106 (2009) 1313–1317. [9] C.L. Degen, Q. Lin, A. Hunkeler, U. Meier, M. Tomaselli, B.H. Meier, Microscale localized spectroscopy with a magnetic resonance force microscopy, Phys. Rev. Lett. 94 (2005) 207601. [10] Q. Lin, C.L. Degen, M. Tomaselli, A. Hunkeler, U. Meier, B.H. Meier, Magnetic double resonance in force microscopy, Phys. Rev. Lett. 96 (2006) 137604. [11] S. Won, S.-B. Saun, S. Lee, S.-G. Lee, K. Kim, Y. Han, NMR spectroscopy for thin films by magnetic resonance force microscopy, Sci. Rep. 3 (2013) 3189. [12] W. Dougherty, K. Bruland, S. Chao, J. Garbini, S. Jensen, J. Sidles, The Bloch equations in high-gradient magnetic resonance force microscopy: theory and experiment, J. Magn. Reson. 143 (2000) 106–119. [13] R. Budakian, H. Mamin, D. Rugar, Suppression of spin diffusion near a micronsize ferromagnet, Phys. Rev. Lett. 92 (3) (2004) 037205. [14] O. Klein, V.V. Naletov, H. Alloul, Mechanical detection of nuclear spin relaxation in a micron-size crystal, Eur. Phys. J. B 17 (2000) 57–68. [15] Concentris. . model: CLA-750-010-08. [16] C.P. Slichter, Principles of Magnetic Resonance, third ed., Springer-Verlag, New York, 1992. pp. 24. [17] J.L. Hutter, J. Bechhoefer, Calibration of atomic-force microscope tips, Rev. Sci. Instrum. 64 (7) (1993) 1868–1873. [18] D. Rugar, H.J. Mamin, P. Guethner, Improved fiber-optic interferometer for atomic force microscopy, Appl. Phys. Lett. 55 (25) (1989) 2588–2590. [19] D. Rugar, B.C. Stipe, H.J. Mamin, C.S. Yannoni, T.D. Stowe, K.Y. Yasumura, T.W. Kenny, Adventures in Attonewton force detection, Appl. Phys. A 72 (2001) S3– S10. [20] S.-G. Lee, S.H. Won, S.-B. Saun, S. Lee, Magnetic resonance force microscopy in fast-relaxing spins using a frequency-modulation mode detection method, Nanotechnology 18 (2007) 375505. [21] T.R. Albrecht, P. Grütter, D. Horne, D. Rugar, Frequency modulation detection using high-Q cantilever for enhanced force microscope sensitivity, J. Appl. Phys. 69 (2) (1991) 668–673. [22] B.C. Stipe, H.J. Mamin, C.S. Yannoni, T.D. Stowe, T.W. Kenny, D. Rugar, Electron spin relaxation near a micron-size ferromagnet, Phys. Rev. Lett. 87 (2001) 277602. [23] S.R. Garner, S. Kuehn, J.M. Dawlaty, N.E. Jenkins, J.A. Marohn, Force-gradient detected nuclear magnetic resonance, Appl. Phys. Lett. 84 (2004) 5091–5093. [24] E.W. Moore, S.-G. Lee, S.A. Hickman, L.E. Harrell, J.A. Marohn, Evading surface and detector frequency noise in harmonic oscillator measurements of force gradients, Appl. Phys. Lett. 97 (2010) 044105. [25] N. Bloembergen, On the interaction of nuclear spins in a crystalline lattice, Physica 15 (1949) 386–426. [26] S.M. Day, E. Otsuka, B. Josephson Jr., Spin-lattice relaxation of F19 in CaF2 at low temperatures, Phys. Rev. 137 (1965) 108–112.
Contents lists available at ScienceDirect
Journal of Magnetic Resonance journal homepage: www.elsevier.com/locate/jmr
Communication
NMR spin–lattice relaxation time T1 of thin films obtained by magnetic resonance force microscopy Seung-Bo Saun a,1, Soonho Won b,1, Sungmin Kwon a, Soonchil Lee a,⇑ a b
Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea Advanced Metallic Materials Division, Korea Institute of Materials Science, Changwon 642-831, Republic of Korea
a r t i c l e
i n f o
Article history: Received 22 September 2014 Revised 12 January 2015 Available online 7 March 2015 Keywords: MRFM NMR Spin–lattice relaxation time Thin film
a b s t r a c t We obtained the NMR spectrum and the spin–lattice relaxation time (T1) for thin film samples by magnetic resonance force microscopy (MRFM). The samples were CaF2 thin films which were 50 nm and 150 nm thick. T1 was measured at 18 K using a cyclic adiabatic inversion method at a fixed frequency. A comparison of the bulk and two thin films showed that T1 becomes shorter as the film thickness decreases. To make the comparison as accurate as possible, all three samples were loaded onto different beams of a multi-cantilever array and measured in the same experimental environment. Ó 2015 Published by Elsevier Inc.
1. Introduction Nuclear magnetic resonance (NMR) is a very powerful research tool which is widely used in areas such as physics, chemistry, biology and medicine. This technique provides the chemically selective, non-destructive, and local probing of matter from the atomic to the macroscopic scales. The spectrum obtained by NMR basically carries the information regarding the electronic state, which determines the property of matter. One weakness of this powerful tool is its relatively low detection sensitivity, which limits its application only to bulk samples. At present, thin films and devices on the nanometer scale are used in many types of research and industry. Thin film and bulk samples frequently show different physical properties despite the fact that they consist of the same elements. For example, resistivity of the silicon layer sandwiched in silicon oxide increases rapidly with decreasing thickness [1] and BaTiO3 and SrRuO3 lose their ferroelectric [2] and ferromagnetic [3] properties with decreasing thickness, respectively. NMR can present useful information for understanding the properties of thin films and samples on the nanometer scale originating from its quantum size and surface effects once the signal is observed. There have been several schemes which demonstrate the dramatically enhanced detection capability of NMR. Magnetic resonance force microscopy [4,5] (MRFM) is most notable among these in the sense that it is applicable to general samples while the others [6,7] are limited to specially prepared samples. In ⇑ Corresponding author. 1
E-mail address: [email protected] (S. Lee). These authors contributed equally to this work.
http://dx.doi.org/10.1016/j.jmr.2015.02.009 1090-7807/Ó 2015 Published by Elsevier Inc.
MRFM, the magnetic resonance is detected by measuring the coupling force between a magnet and the magnetization of a sample using a cantilever instead of an induced current or impedance change as in conventional NMR. The original goal of MRFM was to detect individual nuclear spin moments with atomic resolution and determine the structure of molecules. Several studies reported in recent years have demonstrated the potential of MRFM in the fields of NMR and magnetic resonance imaging (MRI). Imaging with a 4-nm resolution has been demonstrated by MRFM for virus samples [8]. This represents a 100-million-fold improvement in the volume resolution over conventional MRI. NMR spectrum was obtained by MRFM for micron-scale samples [9], and even double resonance experiment was performed [10]. Also, NMR spectroscopy for a thin film was reported for a 34-nm-thick CaF2 thin film [11]. One of the most useful physical parameters obtained by NMR for condensed matter is the nuclear spin–lattice relaxation time (T1). It can provide important information on the various properties of thin films that differ from those of the bulk. Previous MRFM experiments reported the measurement of the ESR spin–lattice relaxation time [12,13]. NMR spin–lattice relaxation time was also measured by MRFM for a several-microns-thick crystal [14]. The measurement near the surface was difficult because of the broadening of the signal due to the magnetic field gradient. In this work, we report the measurement of the NMR spin–lattice relaxation time for a thin film by MRFM. We avoided the complication with the broadening by working with a very thin sample and using a cylindrical magnet to generate a field that varies primarily in the vertical direction. We measured the T1 of CaF2 thin films and compared the result with that of the bulk.
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Communication / Journal of Magnetic Resonance 254 (2015) 71–74
2. Methods Three CaF2 samples were used in the experiment: a bulk sample and two thin films. The bulk sample was a particle of spherical shape with diameter of about 50 lm chosen from CaF2 powder
Fig. 1. (a) Silicon cantilever arrays with loaded CaF2 samples. From the left, 150 nm thin film, 50 nm thin film (inside the dashed rectangles) and a bulk sample with 50 lm diameter. On cantilevers loaded with thin film samples, additional masses were loaded to reduce the cantilever vibration frequency. (b) Schematic drawing of the MRFM setup. The sample-on-cantilever scheme was used.
with a purity of 99.99%. The thin film samples with thicknesses of 50 ± 5 nm and 150 ± 15 nm were deposited directly on top of the cantilevers by e-beam evaporation using the same powder as the source. The thickness of the thin films was measured by spectroscopic reflectometry. The samples are positioned at the ends of the cantilevers, as shown in Fig. 1(a). The spring constant of the cantilevers provided by the manufacturer [15] is 0.01 N/m. Additional masses were loaded onto the cantilevers with the thin film samples to decrease the natural vibration frequency of the cantilevers. This was done because the nuclear magnetization of the sample, which flips periodically in resonance with the vibration of the cantilever, cannot be fully inverted if the frequency is too high [16]. The vibrational frequencies of the cantilevers after the loading of the samples and the additional masses were 1587, 1402, and 1361 Hz. The data was obtained at 18 K and 104 torr. The experiments were carried out at liquid helium temperature but the temperature of the sample was higher than this mainly due to RF heating generated by the coil. The sample temperature can be estimated from the area of the power spectral density of the cantilever’s thermomechanical fluctuation [17], using the fact that the area is proportional to the cantilever temperature. The sample temperature at our experimental condition was obtained by comparing the power spectrum of the cantilever fluctuation with that at liquid nitrogen temperature with rf turned off and exchange gas filled, where the sample temperature should be almost the same with the thermometer located at the other end of the cantilever. Fig. 1(b) shows the experimental setup of the probe part. MRFM is basically a combination of atomic force microscope (AFM) and magnetic resonance techniques. Magnetic resonance is detected by measuring the coupling force between the magnetization of the sample and external magnetic field gradient [5]. In our setup, an iron cylindrical magnet with a 300 lm diameter was used to generate magnetic field gradient mostly in one direction. The magnetic field is relatively constant on the plane of the thin film, though it changes along the direction perpendicular to the plane. The magnetic field gradient along the perpendicular direction is 50 G/lm. The total magnetic field inside the sample is the sum of the homogeneous field generated by a superconducting solenoid surrounding the probe and the inhomogeneous field generated by the magnetized iron magnet located above the sample. The magnet and the optical fiber detecting the cantilever deflection were aligned by three directional nano-positioners. The wavelength of laser used in the optical fiber interferometer [18] was chosen as 1310 nm to avoid cantilever heating as much as possible,
Fig. 2. Timing diagram of the cyclic adiabatic inversion scheme combined with the periodic phase inversion of magnetization. The RF frequency is modulated such that it makes the z component of magnetization oscillate along the z-axis in resonance with the cantilever vibration. The resulting force oscillation is detected by the frequency shift of the cantilever vibration, whose amplitude is forced to remain fixed by feedback circuits. The phase of the RF frequency modulation is flipped every N period of the cantilever oscillation so that the frequency shift changes sign with the same period. This scheme eliminates the white noise and the noise that oscillates in phase with the cantilever.
Communication / Journal of Magnetic Resonance 254 (2015) 71–74
because the energy of the photon with 1310 nm wavelength is lower than the energy gap of silicon [19]. The optical power incident on the cantilever is estimated to be about 0.3 lW. An RF field with a frequency of 283.4 MHz generated by a coil changes the magnetization in the localized volume of the sample, called the resonance slice, where the resonance condition is satisfied in the inhomogeneous field. Because the magnetic field gradient is 50 G/lm, the slice thickness of CaF2 having a natural line width of 10 G is 200 nm. The magnetization change induces a change in the force on the cantilever. The magnetization is periodically inverted using the cyclic adiabatic inversion technique in resonance with the natural vibration of the loaded cantilever. During adiabatic inversion, the magnetization along the field direction is inverted by changing the RF frequency across the resonance frequency. Therefore, the RF frequency is modulated as x ¼ x0 þ Xsinð2pf c tÞ, where x0 is the frequency of the magnetic resonance and fc is the vibration frequency of the cantilever. The RF frequency modulation amplitude X is 30 kHz, which corresponds to 7.5 G in the magnetic resonance of fluorine nuclei. The force on the cantilever then oscillates with the same frequency as that of the cantilever vibration and aids or hinders the cantilever vibration depending on the relative phase of the force oscillation. This makes the vibration amplitude change or makes the vibration frequency shift if the amplitude is fixed by a feedback loop of the amplitude control [20]. We chose the frequency-detection scheme that has an advantage over the amplitude detection scheme when the detection time is limited [21]. There are other approaches for measuring magnetic resonance as a frequency shift such as OSCAR [22] or CERMIT [23]. The detection method used in our work is advantageous when the field gradient is relatively small. The amplitude of the cantilever vibration was fixed to 20 nm. During frequency detection, the frequency noise comes from the detector and the fluctuation of the cantilever vibration [24]. The detector noise increases with an increase in the frequency. In our setup, the detector noise starts to exceed the thermal noise of the cantilever above 3 Hz. Noise with frequencies below 0.5 Hz was also detected in our setup, possibly coming from the mechanical vibration of the entire probe set. To eliminate background noise, the phase between the magnetization and the cantilever vibration was inverted every N cycle of cantilever vibration. Fig. 2 shows a timing diagram of the cyclic adiabatic inversion combined with the periodic phase inversion of the magnetization. When the phase between the cantilever vibration and the magnetization oscillation is opposite, the coupling force acts in a way to aid the restoring of the cantilever vibration, and the cantilever frequency shifts in the direction opposite to that in the in-phase case. The frequency shift changes the sign with a frequency of 2 N/fc, as detected by a lock-in amplifier, such that noise data at other frequencies are eliminated. The phase-inversion frequency was 0.5–3 Hz.
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larger than the bulk sample. Whenever the magnetization passes the rotating plane by this repetitive adiabatic inversion, the net magnetization is reduced by the spin–lattice relaxation in the rotating frame, of which the characteristic time T1q is much shorter than T1. After the saturation of the magnetization, the field was shifted to an off-resonance position and left there for a time s, during which the magnetization grew (Fig. 3(a)). The signal was then measured for several different s values to obtain the T1 relaxation curve. The spin–lattice relaxation time of CaF2 is known to depend heavily on the temperature at low temperatures [25,26]. Moreover, the result of the measurement may be sensitive to the experimental setup because the relaxation rate is actually quite small. We tried to compare the relaxation times of three different samples under experimental conditions which were as similar as
3. Results and discussion To measure the spin–lattice relaxation time T1, the magnetization was saturated first and then the recovery process to the thermal equilibrium state was detected. In the experiment at the previous report of T1 measurements of the bulk [14], magnetization was saturated by using the multiple p/2 pulses, which is effective when the RF amplitude is inhomogeneous. In our work, we adiabatically inverted the magnetization repeatedly till it vanished, noting that the spin–lattice relaxation in the rotating frame is much faster than that in the lab frame. For the initial saturation of the whole sample, the magnetic field was swept back and forth repeatedly, crossing the resonance point with RF on at a fixed frequency. The sweep range was broad enough to cover the length
Fig. 3. (a) Scheme of the spin–lattice relaxation (T1) measurement. (b) The NMR spectrum of the bulk CaF2 sample obtained for several different time intervals s. The curve without a symbol is the spectrum of the 50 nm thin film sample obtained for time interval of 200 s. (c) The signal intensity vs. time interval for the bulk and two thin film samples. The solid lines are the fitting curves of the recovery process. The spin–lattice relaxation time decreases as the sample thickness decreases.
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possible. Three samples were loaded onto three different beams of a multi-cantilever array, and the fiber and the magnet moved to the position of the sample during measurement. The relaxation times were measured at precisely the same temperature, pressure, and magnetic field, etc. Fig. 3(b) shows how the intensity of the NMR spectrum for the bulk sample grows with the time interval s after the saturation of magnetization. A RF frequency of 283.4 MHz corresponds to 7.08 Tesla in magnetic resonance of the fluorine nuclear spin. The spectrum of the bulk is broad because the sample image is overlapped on the spectrum due to the field gradient of the magnet. The sample size of 50 lm is 250 times larger than the slice thickness, 200 nm. The spectrum of the 50 nm thin film, which is thinner than the slice thickness, plotted together in Fig. 3(b) is quite sharp compared to that of the bulk. The observed cantilever frequency shifts of the bulk and the 50 nm thin film were 170 mHz and 4 mHz, respectively. Using the spring constant of 0.01 N/m and the fixed vibration amplitude of the cantilever of 20 nm, the forces corresponding to these frequency shifts were 50 and 1.1 fN, respectively [20]. The data plotted by the squares in Fig. 3(c) show the signal intensity of the bulk sample vs. the time interval. The data were taken from the peak values of the spectra in Fig. 3(b). This process of magnetization recovery is described by MðtÞ ¼ Mð0Þð1 et=T 1 Þ. The spin–lattice relaxation time of the bulk sample as estimated by fitting this equation to the data was 308 ± 4 s. The data of the 50 nm (circles) and 150 nm (triangles) thin films obtained in the same way are plotted together in Fig. 3(c). The spin–lattice relaxation times estimated by the same fitting are 197 ± 4 and 108 ± 4 s for the 150 and 50 nm samples, respectively. The relaxation time is shorter in the thin films than in the bulk, and its rate increases with a decrease in the thickness of the film. Magnetically active defects, which can be easily generated during the e-beam evaporation process, may influence the spin–lattice relaxation [25]. However, it is doubtful that this is the main source of the enhanced relaxation in CaF2 thin films, because the 50 and 150 nm samples have different relaxation times though they were made by the same process. The discontinuity and defects may induce faster spin–lattice relaxation at the interfaces and spin diffusion from the interfaces make the bulk relaxation faster. The effect should be more dominant with thinner samples. We believe this is the main mechanism of the spin–lattice relaxation time decreasing with the sample thickness. The spin–lattice relaxation processes of the thin film samples are influenced by the interface and 2-D effects. It is usual that the interface effect of a solid is prominent only in several layers from the interface. Therefore, observation of the interface effect in T1 measurements for the 50 and 150 nm samples may be difficult unless the spin–lattice relaxation is practically absent in the bulk state, as in CaF2. 4. Conclusions In conclusion, we obtained the spin–lattice relaxation time of thin films by MRFM. Because the relaxation rate is quite small, we loaded all three samples on different beams of the same multi-cantilever array and attempted to obtain data in conditions as similar as possible. The spin–lattice relaxation time becomes shorter with a decrease in the film thickness, as expected, most
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