Observation of Real Time Magnetization Inversion-recovery 

Using the SPAM Geometry and the CERMIT Protocol

by Dimitri A. Alexson and Doran D. Smith

ARL-TR-5742 September 2011

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Army Research Laboratory

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ARL-TR-5742 September 2011

Observation of Real Time Magnetization Inversion-recovery 

Using the SPAM Geometry and the CERMIT Protocol

Dimitri A. Alexson and Doran D. Smith

Sensors and Electron Devices Directorate, ARL

Approved for public release; distribution unlimited. 
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Observation of Real Time Magnetization Inversion-recovery Using the SPAM 

Geometry and the CERMIT Protocol

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Dimitri A. Alexson and Doran D. Smith

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U.S. Army Research Laboratory

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14. ABSTRACT

We mechanically measure in real time the recovery of nuclear magnetization in an inversion-recovery experiment using a 

force gradient protocol by monitoring the frequency of a driven cantilever. The Ga69 polarization is initially inverted with a 

wide adiabatic rapid passage sweep lasting 20 ms. After inverting the polarization, we observe in real time the initial 

<50 mHz transient decay back to the base line as the polarization realigns along the Zeeman axis with a T1 of approximately 

20 min for T = 4.8 K. The magnetization is shown to be inversely linear with temperature. The RF is on only during the 

adiabatic rapid passage sweep.

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Dimitri A. Alexson

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iii

Contents

List of Figures iv

List of Tables v

1. Introduction 1

2. System Description and Methods 1

3. Optical Interferometer Calibration 4

4. Results and Discussion 8

5. Conclusions 13

6. References 14

List of Symbols, Abbreviations, and Acronyms 15

Distribution List 16
iv

List of Figures

Figure 1. MRFM setup in the SPAM geometry. Shown are the four main elements: the 

sample, bare optical fiber, cantilever with Ni particle attached to the free end and the RF 

coil. B0 is in/out of the page with B1 and the oscillation of the cantilever in the plane of 

the page. The optical fiber is standard 9/125 micron fiber. The RF coil consists of 2.5 

turns of 100 microns diameter 6*9 Cu wire wound with a 500 microns inner diameter...........3

Figure. 2. Interferometer voltage output as a function of optical fiber-cantilever separation 

L, optical path length P, and optical path length phase change . See text for detailed 

discussion...................................................................................................................................5

Figure 3. The RMS value of the AC component of the interferometer output as a function 

of the peak-to-peak value of the optical fiber-cantilever separation LPP, peak-to-peak 

value of the optical path length PPP, and peak-to-peak value of the total optical phase 

change PP. See text for a detailed discussion............................................................................6

Figure 4. Fit of sine wave to raw data. Red dots are raw data, the red line connecting the red 

dots is an aid to the eye, the green curve is a sine wave fit to the data, the green straight 

line is a fit to the sine wave fit near zero. The red line should be ignored. ..............................7

Figure 5. A typical MRFM scan utilizing the CERMIT protocol. Changes in the cantilever’s 

frequency, which are proportional to the magnetization along the Zeeman axis, are shown 

as the background magnetic field B0 is swept. A wide ARP sweep is done through the 

entire region of bulk and slice spins to invert the spins and measure T1 during inversion 

recovery......................................................................................................................................9

Figure 6. The stage interferometer (in red) is used to track the relative position of the sample 

to the cantilever tip while the cantilever frequency (in blue) is being recorded. ARPs are 

used to invert the spins for inversion recovery. (a) A typical example of the sample stage 

not yet in equilibrium. The tip-sample distance is changing, causing an overall gradient 

in the cantilever frequency. (b) Once the system is in equilibrium, T1 can be measured by 

monitoring the cantilever’s frequency. ....................................................................................10

Figure 7 (a–d). Typical inversion recovery data for the recorded temperatures: 4.8; 9.3; 16.6; 

24.9 K. At t = 0 s the ARP is applied using the RF coil which generates the B1, inverting 

the spins in the sample and causing a change in the cantilever’s natural frequency. 

During spin inversion recovery, the cantilever tracks back to the initial condition of spins 

aligned with B0. The curves are fit with the standard inversion recovery exponential 

form..........................................................................................................................................11

Figure 8 (a–b). Magnetization and Relaxation rate as a function of temperature. 

(a) Magnetization is linear with the inverse of temperature as predicted by theory (15). 

(b) The relaxation rate 1/T1. T–1(red), T–2(blue) and exp(1/T1) (yellow) curves are 

shown along with the data. The total relaxation rate can depend on several mechanisms 

which become dominant in different temperature regimes (2)................................................12
v

List of Tables

Table 1. Measured T1 and net magnetization values as a function of temperature from fitted 

data shown in figure 7.............................................................................................................12
vi

INTENTIONALLY LEFT BLANK.
1

1. Introduction

A common technique in magnetic resonance is the measurement of T1 with an inversion recovery 

experiment. Knowledge of T1 finds use in many areas, i.e., superconductors (1), semiconductors 

(2), and organic materials (3). Modern electrically detected NMR instruments are only sensitive 

to the transverse magnetization. They perform this measurement while measuring the precession 

of magnetization in the XY plane. In solids, this is typically a very short time, the order of 

100 s. An inversion recovery experiment is performed by inverting the magnetization, waiting 

some fraction of the T1 time, laying the remaining polarization in the XY plane and measuring its 

magnitude by measuring the size of the free induction decay (FID). One must then wait for the 

order of T1 for the magnetization to recover before performing the experiment over again. To 

obtain N points on the T1 curve takes time equal to the order of N*T1. We demonstrate a 

technique suggested by John Marohn (4) where the entire saturation recovery curve is obtained

in one experiment lasting time equal to the order of T1. Using a MEMS cantilever in a 

mechanically detected NMR experiment, we measure the entire inversion recovery curve after a 

single adiabatic rapid passage (ARP) sweep through resonance that inverts the initial 

polarization. The experiments are performed with a magnetic resonance force microscopy 

(MRFM) (5) tool operating in the springiness preservation by aligning magnetization (SPAM) 

(6) geometry using the cantilever enhanced resonance magnetization inversion transients 

(CERMIT) protocol. The signal is registered as a change in the resonant frequency of a soft 

(k~10–4 N/m) cantilever with a Ni sphere attached to the free end, operating in vacuum, at 5 K, in 

a 5 T magnetic field using Ga69 in a GaAs crystal.

2. System Description and Methods

The MRFM probe consists of two major subsystems, a probe body and a probe head. The probe 

body consists of three major parts: (1) a room temperature flange that mates with the top of the

experimental Dewar to which all vacuum, electrical and optical connections are made, (2) the 

probe head body which is a 4 K grease sealed (11) vacuum can, and (3) two thin-walled stainless 

steel tubes that suspend the vacuum can from the room temperature flange. The probe head is 

contained inside the probe head body.

The MRFM probe head body has a 2.5 in outer diameter and is vertically inserted into the 2.5 in

clear bore of a 9 T superconducting magnet. Both the magnet and probe head body are cooled by 

direct immersion in liquid He. One of the two thin walled stainless steel tubes has a 1⁄4 inch 

outside diameter, and the other has a 1⁄2 inch outside diameter. The 1⁄2 inch tube is used to 

evacuate the probe and both tubes carry electrical wires and optical fibers from the room 
2

temperature side to the cold end of the probe. The RF power is fed to the probe head via silver 

coated stainless steel coax that is routed outside the tubes and enters the probe head body just 

above the grease seal. By routing the RF coax through the liquid helium, the heat that conducts 

down the coax, or is generated by RF dissipation, is dissipated in the liquid helium bath and not 

conducted into the probe head.

Inside the probe head body the probe head is suspended from the top of the body by three BeCu 

springs. A Teflon rod with rounded ends is ensheathed by each spring. The Teflon rods act as 

frictional dampers to vibrations traveling down the springs from the probe body to the probe 

head (8). Measurements of probe head vibrations with and without the Teflon rods confirm that 

they do damp vibrations (10). All wires and optical fibers spanning the probe-body probe-head 

gap must not conduct too many vibrations into the probe head. This is especially an issue with 

the RF subsystem, which includes the RF tank circuit and RF coil. The RF dissipates up to 1 W 

in the probe head and the resulting heat must be conducted out without coupling vibrations into 

the probe head. To accomplish this we use three Cu foils 6*9’s pure, 50 microns thick, 1 cm 

wide, and 20 cm long. This is a tradeoff because we need enough Cu foil to conduct the heat out, 

but not so much that vibrations are coupled into the probe head.

The four main elements of the probe head, as shown in figure 1, are a cantilever with a 

ferromagnetic particle attached to its free end, optical fiber, RF coil, and sample mounted on a 

sample stage. The optical fiber is used to sense the position of the cantilever. The RF coil is used 

to generate an RF magnetic field B1 which excites the nuclei in the sample. The sample stage 

moves 5 mm in each of three dimensions and is used to position the sample relative to the fixed 

cantilever. The silicon cantilevers used are typically 450 microns long, 5 microns wide, and 

300 nm thick. They have a 30 micron diameter optical reflection pad centered 70 microns from 

the free end of the cantilever. Attached to the free end of the cantilever and overhanging it is a 

6 microns diameter Ni particle. The several Tesla magnetic field used for the experiments fully 

magnetizes the Ni particle. The cantilever’s amplitude is controlled by a piezoelectric stack that 

vibrates the base of the cantilever in an open loop configuration. The frequency of the cantilever 

is controlled in a closed loop feedback configuration, which keeps the cantilever oscillating at its 

natural frequency. This allows the use of the CERMIT protocol, which relates the change in the 

cantilever’s frequency to a change in the magnitude of the net magnetization along the Zeeman 

axis.
3

Figure 1. MRFM setup in the SPAM geometry. Shown are the four main elements: the sample, bare optical fiber, 

cantilever with Ni particle attached to the free end and the RF coil. B0 is in/out of the page with B1 and 

the oscillation of the cantilever in the plane of the page. The optical fiber is standard 9/125 micron fiber. 

The RF coil consists of 2.5 turns of 100 microns diameter 6*9 Cu wire wound with a 500 microns inner 

diameter.

The four items that constitute the probe head must be positioned within a few micrometers of 

each other. The challenging aspect of the design is the items are positioned at room temperature 

in air, but must remain aligned as the probe head is evacuated and cooled down to 4 K. Small 

mechanical distances and thermally compensated design principles are used. The mechanical 

frame of the probe head, meaning those parts of the probe head responsible for maintaining 

alignment on cool down, are made entirely of type II Ti and are assembled with brass screws. As 

brass shrinks twice as much as Ti does on being cooled from room temperature to 4 K, the probe 

parts are compressed together even tighter once cooled. The position of the cantilever is fixed in 

the probe head. The fiber and RF coil are each independently aligned to the cantilever’s position 

before cool down. The sample stage is approximately aligned before cool down, with final 

alignment occurring once the probe is cold.

The cantilever oscillation is sensed by an optical interferometer operating at 1300 nm. The two 

reflective surfaces that form the Fabry-Perot cavity are the optical reflection pad on the 

cantilever and the 0° angle cleaved face of a single mode optical fiber. The end of the optical 

fiber is positioned approximately 100 microns from the cantilever’s reflection pad. Four percent 

of the light coming down the fiber is reflected at the glass-air interface back up the fiber. The 
4

remaining laser light exits the fiber as a Gaussian beam. A fraction of the laser light strikes the 

cantilever’s reflection pad and is reflected back towards the fiber. This results in two light 

beams traveling back up the fiber. Since the fiber-cantilever gap is smaller than the light’s 

coherence length, the two beams traveling up the fiber are phase coherent. These two beams are 

picked off the fiber with a 90:10 directional coupler and detected with a square law detector. 

The interference of the two beams with each other forms an interferometer sensitive to picometer 

displacements of the cantilever. The total interferometer package, optics plus electronics, has a 

1 pm per root Hz noise floor.

The RF coil is formed from 2.5 turns of 100 micron diameter 6*9 Cu wire wound with a 

500 micron inner diameter. Since B1 falls off with the distance r, for , from the face of the 

coil as 

 

 

 

 where a is the radius the RF coil, the coil is positioned within 150 micrometers 

of the cantilever and the edge of the sample. In this region, where , the drop off in B1 is 

linear with r, so the exact positioning from the sample is more forgiving. The RF circuit 

produces 1.06 mT of B1 for 1 W of RF power.

The sample stage is mounted on the top of a 3D positioning stage manufactured by Attocube. 

The positioning stage’s operation is based on the inertial slider principle (9). Three linear 

positioners give movement in x, y and z at 4 K by the use of piezoelectric elements, hence all 

actuation is done electrically.

3. Optical Interferometer Calibration

The cantilever interferometer must be calibrated to convert its voltage output to the cantilever’s 

displacement. It is possible to do this by using our knowledge of the value of the wavelength of 

the light used by the interferometer. If the interferometer behaved ideally, the interference 

pattern, as represented by the voltage output of the interferometer, would have a purely 

sinusoidal dependence on the fiber-cantilever separation. However, due to imperfections in the 

interferometer not all the light impinging on the detector is part of the two interfering beams and 

results in a background signal that gives a DC offset to the output voltage, 

  

where L is the equilibrium separation between the end of the fiber and the cantilever and L is 

the displacement of the cantilever. The sinusoidal dependence of V0 on L and L, and the value 

of wavelength of light are used to calibrate the interferometer.

Figure 2 illustrates the details of the signal sizes that the interferometer produces. The figure 

shows interferometer output, Vo versus cantilever displacement, L. Also shown is the extra path 

length P the light must travel when the cantilever experiences a displacement L, and the extra 

phase  this represents in the argument of the sine in the Vo equation. Typically L is the order of 
5

100 microns and L is a few hundred nanometers peak-to-peak. The calibration begins by not 

oscillating the cantilever, L = 0, and adjusting the wavelength of the light source, a 

semiconductor laser operating at ~1300 nm, so that (4πL/ ) hence, . This 

means the cantilever is resting at L = 0 and the AC component of V0 is zero. This locates the 

cantilever at pt. 1 in figure 2. As the cantilever is displaced along +L, Vo increases until at 

 , (pt. 2) where Vo = VAC. At pt. 2 the two beams of light are interfering constructively 

to a maximum extent, i.e., they are perfectly in phase with each other. At this point the light must 

transverse the cantilever displacement twice, hence, . (Depending upon the sign of 

amplification in the electronics, they may instead be in perfect deconstructive interference. For 

the purposes of discussion, and without loss of generality, we assume they are in phase with each 

other.) The optical path length difference of one quarter of one wavelength corresponds to and 

extra /2 phase. If the cantilever is displaced to  , (pt. 3) then Vo = -VAC. At pt. 3 the 

two beams of light are interfering destructively to a maximum extent, i.e., they are  out of phase 

with each other. If the cantilever is oscillated between  (between pts. 2 and 3) the 

cantilever moves a total distance  peak-to-peak and the light travels a total distance 

 which corresponds to an extra phase of .

Figure. 2. Interferometer voltage output as a function of optical fiber-cantilever separation L, optical 

path length P, and optical path length phase change . See text for detailed discussion.

Experimentally it is convenient to measure the RMS value of the cantilever oscillation. The 

information shown in figure 2 is re-plotted as RMS values in figure 3. The cantilever is at 

equilibrium at pt. 1 and at pt. 2, with a peak-to-peak displacement of , Vo has an RMS 
6

amplitude of . This amplitude is less than what it would be if the 

interferometer output did not roll over.

Figure 3. The RMS value of the AC component of the interferometer 

output as a function of the peak-to-peak value of the optical 

fiber-cantilever separation LPP, peak-to-peak value of the optical 

path length PPP, and peak-to-peak value of the total optical phase 

change PP. See text for a detailed discussion.

To determine the interferometer sensitivity, Vo/L as a function of cantilever oscillation 

amplitude the following procedure is used. The laser wavelength is adjusted so that (4πL/ )

 hence locating the cantilever at pt. 1. The cantilever is then driven 

through a series of increasing amplitudes starting at L ~25 nm to over 325 nm peak-to-peak, see 

the red points in figure 4. When the peak-to-peak displacement of L is the amplitude of the 

sine wave  will be at a maximum, 2VAC peak-to-peak. This point occurs 

at an SMU Drive Amp (V) of 2.0 V in figure 4. The SMU Drive Amp is a voltage that 

determines the amplitude of drive voltage used to base drive the cantilever. Using the knowledge 

of the cantilever displacement at pt. 2 allows us to calibrate the rest of the curve for cantilever 

displacement. We assume that a sine wave fits the raw data. The green curve in figure 4 is the 

sine wave fit to the location and amplitude at the curves peak. Given the quality of the sine wave 

fit to the data, we conclude that the conjecture that the data is sinusoidal was valid. Figure 4

displays the cantilever amplitude as an RMS value. The RMS value of the AC part of Vo at pt. 2 

is VAC/ . Some measurements require a knowledge of the interferometer sensitivity near L ~0. 

In this region a sine wave is well approximated as a straight line. In figure 4 this straight line is 

green. The slope of this line is . At  the line has a peak-to-peak value of 

πVAC and an RMS value of VAC/ . A cantilever displacement of  corresponds to 

325 nm peak-to-peak or an RMS value of 114.9 nm. 
7

Figure 4. Fit of sine wave to raw data. Red dots are raw 

data, the red line connecting the red dots is an 

aid to the eye, the green curve is a sine wave fit 

to the data, the green straight line is a fit to the sine 

wave fit near zero. The red line should be ignored.

Once the calibration procedure has been accomplished, the output of the cantilever’s 

displacement is converted from voltage to displacement. The next step in characterizing a 

cantilever is to experimentally determine its spring constant, kc. The spring constant is related to 

the cantilever displacement through the equal partition theorem

kcx   kBT

2

where kc is the cantilever spring constant, kB is Boltzmann’s constant, and T is the absolute 

temperature. The temperature can be measured with an independent temperature sensor, kB is a 

known constant, and <x2> is the RMS value of the instantaneous position which we get from the 

converted cantilever displacement. A plot of <x2> versus T is made, resulting in a straight line 

with a zero intercept. The slope is the cantilever’s spring constant. With the calibrated 

cantilever displacement and the cantilever’s spring constant, we can now determine the 

temperature of the cantilever under both undriven and driven circumstances, referred to 

Brownian motion for the undriven case and Frequency Noise in the driven case. For the 

undriven case, the temperature of the cantilever can be found using the equal partition theorem 

stated above. The second technique for measuring Brownian motion involved measuring the 

frequency noise of a driven cantilever. A driven cantilever is excited to constant oscillation 
8

amplitude at its natural resonance frequency. In this case the temperature can be found using the 

following relationship (16),

0

2 2

2

( )

 



k

k T

P f

xrms

therm B

x



where 

0



is the time constant of the cantilever at each temperature measured. It is experimentally 

determined by letting the cantilever ring down.

4. Results and Discussion

Utilizing the CERMIT protocol, we measure the real time recovery of the polarization during an 

inversion-recovery experiment by monitoring the frequency of the driven cantilever. The signal, 

which is proportional to the magnetization along the Zeeman axis, is registered by recording 

changes in the resonance frequency of a driven cantilever. We use a digital frequency controller 

(12) to drive the cantilever at the resonant frequency of its lowest bending mode. The magneticfield gradient from the Ni particle’s magnetic moment interacts with the nuclear spins in the 

sample, causing the resonance frequency of the cantilever to shift slightly as the sample’s 

magnetization is modified, i.e., as part of it, the Ga69, is inverted. The initial Ga69 polarization 

is inverted with a 20 ms long, wide ARP sweep through the entire region of spins contained in 

the bulk (13) and image slice regions, as shown in figure 5. The RF is only on during the 20 ms

ARP, while the spins are being adiabatically inverted. After inverting the polarization, the 

frequency of the driven cantilever is monitored as the polarization realigns along the Zeeman 

axis. The spin-lattice relaxation time T1, can then be directly extracted from the recovery curve 

using the time dependent magnetization relation for inversion recovery:

 

 

 

 

 

 
9

Figure 5. A typical MRFM scan utilizing the CERMIT protocol. Changes in the cantilever’s frequency, which 

are proportional to the magnetization along the Zeeman axis, are shown as the background magnetic 

field B0 is swept. A wide ARP sweep is done through the entire region of bulk and slice spins to 

invert the spins and measure T1 during inversion recovery.

The temperature of the sample was adjusted from the probe’s base temperature of 4.8 K to 9.3, 

16.7 and 24.9 K by directly heating the sample stage holder. At each temperature change, the 

system was allowed to reach thermal equilibrium, as monitored by the probe’s thermometer. 

Prior to recording the inversion recovery at each temperature, the sample was positioned at a 

distance of 300 nm from the magnetic particle on the cantilever. The distance is determined by 

an interferometer on the sample stage axis that measures the relative displacement of the sample 

distance from the cantilever tip. The amplitude of the driven cantilever was maintained constant 

by recalibrating the cantilever’s amplitude vs. drive effort at each temperature, while maintaining 

a distance of 300 nm from the surface. Since our signal is registered as changes in the cantilever

frequency and the cantilever frequency is highly dependent on the tip-sample distance, the tipsample distance was set once the probe had reached thermal equilibrium. The sample stage 

interferometer was then used to monitor any displacement of the sample relative to the tip. The 

stage interferometer measured small changes in position over time while the probe head reached 

equilibrium. Two possible sources of this drift are small probe head dimensional changes due to 

thermal contraction or expansion and drift in the sample stage position, possibly due to creep in 

the piezoelectric element. Care was taken to record inversion recovery data only after the probe 
10

head had achieved equilibrium. Figure 6 shows the effect of stage drift on cantilever frequency. 

Figure 6a shows the gradient in cantilever frequency overlaid with the frequency changes as the 

sample stage reaches equilibrium. Since the frequency changes observed here are small it is 

reasonable to assume that stage motion is causing the changes in the cantilever’s frequency. 

Figure 6b is representative of the probe head at equilibrium, and a drift in cantilever frequency or 

stage position is not observed. 

Figure 6. The stage interferometer (in red) is used to track the relative position of the sample to the cantilever tip 

while the cantilever frequency (in blue) is being recorded. ARPs are used to invert the spins for inversion 

recovery. (a) A typical example of the sample stage not yet in equilibrium. The tip-sample distance is 

changing, causing an overall gradient in the cantilever frequency. (b) Once the system is in equilibrium, 

T1 can be measured by monitoring the cantilever’s frequency. 

Figure 7 shows typical inversion recovery data and results of the exponential fits at the four

temperatures of 4.8, 9.3, 16.7, and 24.5 K which are summarized in table 1. Data was collected 

with a B1 of 1.06 mT (requires 1 W of RF power). By keeping B1 constant the same fraction of 

the initial nuclear polarization was inverted each time. This permits a direct comparison of the 

magnetization magnitudes in terms of cantilever frequency changes. Data was collected with a 

tip-sample separation of 300 nm, with the exception of the T = 24.9 K data. It was necessary to 

increase the tip-sample separation for this case because the magnitude of the noise in the 

cantilever frequency caused by surface noise (14) was significant enough to obscure the

measurement. Effects due to surface noise have previously been shown to increase with sample 

temperature. Since the frequency changes became so small at 24.9 K, we also found it necessary 

to increase B1 from 1.06 mT to 1.7 mT to increase the polarization fraction being inverted. 

Figures 7a, b, and c show data collected at B1 = 1.06 mT. Figure 7d shows data collected at both 

B1 = 1.06 and 1.7 mT. The data displaced to the right by 100 s was collected at 1.06 mT, the data 

beginning at 0 s was collected at 1.7 mT. Figure 8 shows the temperature dependence of T1 and 
11

the net magnetization in terms of the measured cantilever frequency. The net magnetization 

behaves linearly with the inverse of the temperature as is predicted by theory (15). Figure 8b 

shows the relaxation rate 1/T1 with temperature. As can be seen in figure 8b, a transition 

temperature occurs near T ~ 20K. This has been previously observed using traditional NMR (2). 

The recovery laws which effect the relaxation rate, can be dominate in different temperature 

regimes. The total spin-lattice relaxation rate has contributions from magnetic relaxation which 

is weakly temperature dependent and, for GaAs, there is time-dependent quadrupolar relaxation 

interaction mechanism which is strongly temperature dependent. As with traditional NMR, 

MRFM can be used to examine the different relaxation rate mechanisms and their temperature 

dependence. The two advantages of MRFM are that T1 can be measured in real time and 

picogram quantities of material can be studied.

Figure 7 (a–d). Typical inversion recovery data for the recorded temperatures: 4.8; 9.3; 16.6; 24.9 K. 

At t = 0 s the ARP is applied using the RF coil which generates the B1, inverting the 

spins in the sample and causing a change in the cantilever’s natural frequency. During 

spin inversion recovery, the cantilever tracks back to the initial condition of spins 

aligned with B0. The curves are fit with the standard inversion recovery exponential 

form.
12

Table 1. Measured T1 and net magnetization values as a 

function of temperature from fitted data shown in 

figure 7.

Temperature [K] T1 (s) Magnetization 

[mHz]

4.8 1340.224 0.0300335

9.3 876.458 0.0247917

16.7 184.114 0.0102456

24.9 25.39 0.00713975

Figure 8 (a–b). Magnetization and Relaxation rate as a function of temperature. (a) Magnetization is linear 

with the inverse of temperature as predicted by theory (15). (b) The relaxation rate 1/T1. T–1

(red), T–2(blue) and exp(1/T1) (yellow) curves are shown along with the data. The total 

relaxation rate can depend on several mechanisms which become dominant in different 

temperature regimes (2).
13

5. Conclusions

The technique demonstrated here significantly reduces the experimental time required for a spinlattice inversion recovery measurement. Real time monitoring of the spin-lattice relaxation time 

T1 as a function of sample temperature has been demonstrated with MRFM using a force 

gradient detection protocol. The temperature dependence is in line with previous studies done on 

GaAs (2). Changes in the net magnetization stored along the Zeeman axis is registered as a 

change in the driven cantilever’s resonant frequency. By tracking the cantilever’s resonant 

frequency, after an inversion in the sample’s magnetization, an entire inversion recovery curve 

can be obtained in a time the order of T1. Using traditional NMR T1 measurement techniques 

capturing the entire inversion recovery curve in N points would require N measurements spaced 

~T1 apart for a total time the order of N*T1.
14

6. References

1. Takigawa, M.; Reyes, A. P.; Hammel, P. C.; Thompson, J. D.; Heffner, R. H.; Fisk, Z.;

Ott,K. C. Cu and O NMR Studies of the Magnetic Properties of YBa2Cu3O6.63 (Tc=62 K). 

Phys Rev B 43 1991, , 247–257.

2. McNeil, J. A.; Clark, W. G. Nuclear Quadrupolar Spin-lattice Relaxation in Some IIIV Compounds. Phys. Rev. B 13 1976, 4705.

3. Schoeniger, J. S.; Aikenm N.; Hsu, E.; Blackband, S,J. Relaxation-time and Diffusion NMR 

microscopy of single neurons. J Magn Reson B. 1994 Mar, 103 (3), 261–73.

4. Private communication, John Marohn, 2005

5. Sidles, J. A., et al. Magnetic Resonance Force Microscopy. Rev. Mod. Phys. 1 Jan. 1995, 67

(1), 249.

6. Marohn, J. A.; Fainchtein, R.; Smith, D. D. An Optimal Magnetic Tip Configuration for 

Magnetic-resonance Force Microscopy of Microscale Buried Features. Appl. Phys. Lett. 21 

Dec. 1998, 74 (25), 3778.

7. Garner, S. R., et al. Force-gradient Detected Nuclear Magnetic Resonance. Appl. Phys. Lett.

21 June 2004, 84 (25), 5091.

8. Private communication, Raul Fainchtein, 1996

9. Pohl, D. W. Sawtooth Nanometer Slider: A Versatile Low Voltage Piezoelectric Translation 

Device. Surface Sci. 1 March 1987, 181 (102), 174.

10. Doran Smith, unpublished results

11. Swartz, E. T. Efficient He-4 Cryostats for Storage Dewars. Rev. Sci. Instrum. 1986, 57 (11), 

p. 2848.

12. SC-Solutions Frequency Controller, model number scFDC.

13. Suter, A., et al. Probe-Sample Coupling in the Magnetic Resonance Force Microscopy. J 

Magn. Res. 2002, 154, 210.

14. Yazdanian, S. M.; Marohn, J. A.; Loring, R. F. Dielectric Fluctuations in Force Microscopy: 

Noncontact Friction and Frequency Jitter. J. Chem. Phys. 2008, 128, 224706.

15. Abragam, A. The Principles of Nuclear Magnetism, p. 2, equ. 2, 1961.

16. Marohn, J. Frequency Noise, white paper, Cornell University, 24 February 2008.
15

List of Symbols, Abbreviations, and Acronyms

ARP adiabatic rapid passage

CERMIT cantilever enhanced resonance magnetization inversion transients

FID free induction decay

MRFM magnetic resonance force microscopy

SPAM springiness preservation by aligning magnetization
16

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