We have successfully fabricated single and paired 300 nm×1.5 µm×32 nm Ni80Fe20 bars on a microcantilever using focused ion beam milling. Magnetic interactions of the paired bars were studied by using magnetic force microscopy, microcantilever torque magnetometry, and micromagnetic simulation. Our results clearly indicate that the magnetic switching behavior of the paired Ni80Fe20 bars is affected by magnetostatic interactions. The magnetic hysteresis curves for a sample with eight pairs of Ni80Fe20 bars consist of a series of stable switching states that are related to the domain wall motion in the bars

Chabot, M.D.

Feng, D.Q.

Gao, L.

Liou, Sy_Hwang

Moreland, J.

Porpora, D.

Sabirianov, Renat F.

Yokota, T.

Yuan, Lu

English

DigitalCommons@University of Nebraska

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Si-Hwang Liou Publications Research Papers in Physics and Astronomy 6-1-2004 A study of magnetic interactions of Ni80Fe20 arrays using ultrasensitive microcantilever torque magnetometry L. Gao University of Nebraska - Lincoln D.Q. Feng University of Nebraska-Lincoln, nkfdq@bigred.unl.edu Lu Yuan Physics Department, University of Nebraska, lyuan2@bigred.unl.edu T. Yokota University of Nebraska - Lincoln Renat F. Sabirianov University of Nebraska at Omaha, rsabirianov@mail.unomaha.edu See next page for additional authors Follow this and additional works at: https://digitalcommons.unl.edu/physicsliou  Part of the Physics Commons Gao, L.; Feng, D.Q.; Yuan, Lu; Yokota, T.; Sabirianov, Renat F.; Liou, Sy_Hwang; Chabot, M.D.; Porpora, D.; and Moreland, J., "A study of magnetic interactions of Ni80Fe20 arrays using ultrasensitive microcantilever torque magnetometry" (2004). Si-Hwang Liou Publications. 80. https://digitalcommons.unl.edu/physicsliou/80 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Si-Hwang Liou Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Authors L. Gao, D.Q. Feng, Lu Yuan, T. Yokota, Renat F. Sabirianov, Sy_Hwang Liou, M.D. Chabot, D. Porpora, and J. Moreland This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/physicsliou/80 Artificially Structured Materials III:Patterned Structures Laura Heyderman, ChairmanA study of magnetic interactions of Ni80Fe20 arrays using ultrasensitivemicrocantilever torque magnetometryL. Gao, D. Q. Feng, L. Yuan, T. Yokota, R. Sabirianov, and S. H. Lioua)Department of Physics and Astronomy and Center for Materials Research and Analysis,University of Nebraska, Lincoln, Nebraska 68588M. D. Chabot, D. Porpora, and J. MorelandNational Institute of Standards and Technology, Boulder, Colorado 80305~Presented on 8 January 2004!We have successfully fabricated single and paired 300 nm31.5 mm332 nm Ni80Fe20 bars on amicrocantilever using focused ion beam milling. Magnetic interactions of the paired bars werestudied by using magnetic force microscopy, microcantilever torque magnetometry, andmicromagnetic simulation. Our results clearly indicate that the magnetic switching behavior of thepaired Ni80Fe20 bars is affected by magnetostatic interactions. The magnetic hysteresis curves for asample with eight pairs of Ni80Fe20 bars consist of a series of stable switching states that are relatedto the domain wall motion in the bars. © 2004 American Institute of Physics.@DOI: 10.1063/1.1682912#I. INTRODUCTIONMeasuring micrometer and submicrometer scale mag-netic features has proven to be a challenge for conventionalmagnetometers. Thus, more sensitive methods are needed toprobe magnetism on this scale.1–5 Microcantilever torquemagnetometry ~MTM! based on a torsion-mode atomic forcemicroscope ~AFM! is a promising experimental techniquefor measuring submicrometer magnetism due to its highersensitivity than SQUID magnetometry.3–5The main challenge of this measurement technique isobtaining well-defined micromagnetic samples on cantile-vers. Chabot et al. have created a process in which filmdeposition is combined with the cantilever fabricationprocess.6 This method requires using multistep photolithog-raphy process.The interaction of submicrometer-sized arrays is an im-portant topic for micromagnetism. Much work has been donein this area.7–9 However, due to measurement sensitivitylimitations, arrays of hundreds of elements must be fabri-cated to obtain a high enough signal-to-noise ratio. The re-sults are often clouded by statistical variations such as dotshape, size, and spacing. Due to its high sensitivity, MTM isexpected to reduce the statistical variations of the magneticinteraction by studying just a few pairs of magnetic particles.In this work, we use focused ion beam ~FIB! milling, asimple one-step method, to prepare submicrometer bars onthe microcantilever and use magnetic force microscopy~MFM!, microcantilever torque magnetometry, and micro-magnetic simulation to study the magnetic reversal behaviorof these bars.II. EXPERIMENTWe start with a microcantilever which already has a 7mm37 mm332 nm Ni80Fe20 film deposited on the top leftcorner @Fig. 1~a!#. The Ni80Fe20 film was then patterned by aFIB workstation using a Ga1 liquid metal ion source oper-ated at 30 keV ion energy. The ion beam current was ap-proximately 70 pA. A patterning software package allowedus to generate the milled pattern from a bitmap image. TheNi80Fe20 films were patterned into 12 single 300 nm31.5mm332 nm bars @Fig. 1~b!# and 8 pairs of 300 nm31.5mm332 nm bars @Figs. 1~c!#. The milling time was 5 min forboth patterns. The gaps between the edges of bars are 1 mmfor single bars and 40 nm for paired bars.a!Author to whom correspondence should be addressed. electronic mail:sliou@unl.eduFIG. 1. ~a! Microcantilever with Ni80Fe20 film deposited on the top leftcorner. ~b! Focused ion beam patterned Ni80Fe20 arrays with 12 single 300nm31.5 mm332 nm bars and ~c! eight pairs of 300 nm31.5 mm332 nmbars with gap of 40 nm between adjacent bars.JOURNAL OF APPLIED PHYSICS VOLUME 95, NUMBER 11 1 JUNE 200470100021-8979/2004/95(11)/7010/3/$22.00 © 2004 American Institute of PhysicsDownloaded 18 Oct 2006 to 129.93.16.206. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jspField dependent magnetic domain images were obtainedunder ambient conditions with a commercial magnetic forcemicroscopy. Magnetic properties of the patterned Ni80Fe20films were characterized using a microcantilever torque mag-netometer in vacuum. All measurements were done with amagnetic field applied along the long axis of the bars. Mi-cromagnetic simulations were performed to study the mag-netization reversal of the paired Fe20Ni80 bars using theOOMMF software package developed by NIST.10III. RESULTS AND DISCUSSIONFigure 2 shows the domain structures of a single and aset of paired 300 nm31.5 mm332 nm Ni80Fe20 bars underdifferent magnetic fields. All the MFM images were obtainedusing tapping/lift mode with CoPt MFM tips at a lift heightof 20 nm. The tip’s north pole points down, perpendicular tothe sample surface. According to the MFM contrastmechanism,11 the magnetization direction of the bars is fromdark to light. The 300 nm31.5 mm332 nm single bars andpaired bars with a 40 nm gap are observed simultaneously.The sample was saturated with a field of 79.6 kA/m alongthe long axis of the bars. At zero field, the magnetizationdirection of the bars did not change and was still along thedirection of the applied magnetic field @Fig. 2~a!#. As thefield switched to negative, end domains and vortices wereformed first @Fig. 2~b!#, then domain walls propagate alongthe bars @Fig. 2~c!# and are stopped by the pinning sites. Thepinning sites could be produced by surface or edge rough-ness, defects, or disorder in the film ~such as random anisot-ropy!. The magnetic reversal process for the bars is domainwall motion instead of coherent rotation. At a field of 27kA/m, only one of the paired bars is reversed @Fig. 2~d!#. Asfield changed to 28.1 kA/m, the single bar reversed @Fig.2~e!#, but the magnetization direction of paired bars is stillantiparallel to each other. At larger negative field, all the barsswitched @Fig. 2~f!#. The fact that the switching field ofsingle bars is larger than the reversing field of only one of thepaired bars and less than that of both paired bars shows thatthe magnetostatic interaction exists between the closelypaired bars. The interaction makes the antiparallel magneti-zation directions of paired bars a stable state.To clarify the magnetization reversal of the paired bars,we performed micromagnetic simulations with the followingparameters. The magnetization of Fe20Ni80 was 800 kA/m,the anisotropy constant was 4.53103 J/m3, and the exchangeconstant was 1.3310213 J/m3.12 We used a random anisot-ropy setup to mimic the real medium. The results also showthat the switching of each bar in the paired bars system is notindependent. After saturation, paired bars form a symmetri-cally inverted C state at the remanent state @C state is namedbecause the domain structure resembles the letter C, Fig.3~a!#. With the negative field applied, the magnetization re-versal proceeds through the formation of two vortices ~enddomains! @Figs. 3~b! and 3~c!#. Due to the broken symmetry~random anisotropy!, the reversal of one of the bars happensfirst @Fig. 3~d!#. Although the general picture of the reversalof this bar is similar to the single bar case, there are somedeviations because of the interactions with the second bar.Due to the magnetostatic interactions, the system creates aclosure for the magnetic field ~magnetization of paired barsFIG. 2. Field dependent magnetic domain structures of single Ni80Fe20 bars~300 nm31.5 mm332 nm! and same size paired bars with a gap of 40 nm.The sample was saturated with a field of 79.6 kA/m along the long axis ofthe bars and then decreased to ~a! 0 kA/m, ~b! 22.07 kA/m, ~c! 24.46kA/m, ~d! 27 kA/m, ~e! 28.1 kA/m, and ~f! 29.31 kA/m.FIG. 3. Micromagnetic simulations was performed on the paired Ni80Fe20bars ~300 nm31.5 mm332 nm! with a gap of 40 nm. The sample wassaturated along the long axis of the bars and then decreases to ~a! 24.77kA/m, ~b! 220.69 kA/m, ~c! 226.26 kA/m, ~d! 231.83 kA/m, ~e! 237.40kA/m, and ~f! 242.18 kA/m.7011J. Appl. Phys., Vol. 95, No. 11, Part 2, 1 June 2004 Gao et al.Downloaded 18 Oct 2006 to 129.93.16.206. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jspis aligned in opposite directions!. It is a stable state for thesystem of paired bars. Then at somewhat larger applied field,the system is forced out of this potential well and the secondbar also switches @Fig. 3~f!#. The simulation results are con-sistent with the MFM measurement.Figure 4~a! shows a simulated hysteresis loop for one setof paired bars system. The two steps during the reversal iscaused by the magnetostatic interaction between the pairedbars, which is correlated with the domain structures shown inFigs. 2 and 3. Figure 4~b! shows the M -H curve obtainedwith microcantilever torque magnetometry for a cantileverwith eight sets of paired bars patterned on the 32 nm film, asshown in Fig. 1~c!. The hysteresis curves are obtained bysweeping the external field from 231.83 kA/m to 131.83kA/m. The torque field and cantilever resonant frequencyused are 85 A/m and 25.4 kHz, respectively. We have yieldeda saturation magnetization of 870 kA/m for the eight sets ofpaired bars with a magnetic volume of 2.3310219 m3. Theexperimental magnetization is within 10% of the bulk valueof 800 kA/m. The error may be due to difficulty in estimatingthe thickness of the film and the actual value of the torquefield. The observed series of stable switching states duringthe magnetization reversal process is likely due to the do-main wall motion in the bars. A possible explanation for thedifference between the simulation and the measured loop isthat the simulation is performed only on one paired barsunder ideal conditions but MTM includes all the switching ofeight paired bars in which each bar may have a differentreversal field due to different defect structures formed duringthe FIB processing.IV. CONCLUSIONSThe focused ion beam milling is a convenient way toobtain arbitrary patterns on a microcantilever. Domain struc-ture and micromagnetic simulation results show that the re-versal of the paired 300 nm31.5 mm332 nm bars is affectedby the magnetostatic interactions. We used MTM to measureeight sets of paired Ni80Fe20 bars. The hysteresis curve con-sists of a series of stable switching states. This is related tothe domain wall motion in the bars. We show that microcan-tilever torque magnetometry is a suitable method for measur-ing magnetic interactions in submicrometer-sized magneticsamples. Future work will improve the sensitivity of theMTM by optimizing the cantilevers. This will allow thestudy of the magnetization reversal of only one set of pairedbars.ACKNOWLEDGMENTSResearch was supported by NSF MRSEC Award Nos.DMR-0213808 and DMR-0116780 and Army Research Of-fice DAAD Grant No. 19-03-1-0298. T. Yokota was sup-ported by a Grant-in-Aid for JSPS Fellows, Grant No.00000652.1 B. C. Stipe, H. J. Mamin, T. D. Stowe, T. W. Kenny, and D. Rugar, Phys.Rev. Lett. 86, 2874 ~2001!.2 J. G. E. Harris, D. D. Awschalom, F. Matsukura, H. Ohno, K. D. Mara-nowski, and A. C. Gossard, Appl. Phys. Lett. 75, 1140 ~1999!.3 M. Lo¨hndorf, J. Moreland, P. Kabos, and N. Rizzo, J. Appl. Phys. 87,5995 ~2000!.4 M. D. Chabot and J. Moreland, J. Appl. Phys. 93, 7897 ~2003!.5 J. Moreland, J. Phys. D 36, R39 ~2003!.6 M. D. Chabot and J. T. Markert, Proc. SPIE 3875, 104 ~1999!.7 J. F. Smyth, S. Schultz, D. R. Fredkin, D. P. Kern, S. A. Rishton, H.Schmid, M. Cali, and T. R. Koehler, J. Appl. Phys. 69, 5262 ~1991!.8 S. Y. Chou and L. Kong, J. Appl. Phys. 79, 5855 ~1996!.9 V. Novosad, M. Grimsditch, J. Darrouzet, J. Pearson, S. D. Bader, V.Metlushko, K. Guslienko, Y. Otani, H. Shim, and K. Fukamichi, Appl.Phys. Lett. 82, 3716 ~2003!.10 J. Donahue and R. D. McMichael, Physica B 233, 272 ~1997!.11 S. H. Liou and Y. D. Yao, J. Magn. Magn. Mater. 190, 130 ~1998!.12 M. Klaui, C. A. F. Vaz, L. Lopez-Diaz, and J. A. C. Bland, J. Phys.:Condens. Matter 15, 985 ~2003!.FIG. 4. ~a! Simulated magnetic hysteresis loop of the paired Ni80Fe20 bars~300 nm31.5 mm332 nm! with a gap of 40 nm. ~b! Hysteresis loop of theeight sets of paired bars with same size is obtained with a microcantilevertorque magnetometer. Inset: Close-up view of series of stable switchingstates.7012 J. Appl. Phys., Vol. 95, No. 11, Part 2, 1 June 2004 Gao et al.Downloaded 18 Oct 2006 to 129.93.16.206. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp

A study of magnetic interactions of Ni\u3csub\u3e80\u3c/sub\u3eFe\u3csub\u3e20\u3c/sub\u3e arrays using ultrasensitive microcantilever torque magnetometry

UNL | Libraries

University of Nebraska - Lincoln 
DigitalCommons@University of Nebraska - Lincoln 
Si-Hwang Liou Publications Research Papers in Physics and Astronomy 
6-1-2004 
A study of magnetic interactions of Ni80Fe20 arrays using 
ultrasensitive microcantilever torque magnetometry 
L. Gao 
University of Nebraska - Lincoln 
D.Q. Feng 
University of Nebraska-Lincoln, nkfdq@bigred.unl.edu 
Lu Yuan 
Physics Department, University of Nebraska, lyuan2@bigred.unl.edu 
T. Yokota 
University of Nebraska - Lincoln 
Renat F. Sabirianov 
University of Nebraska at Omaha, rsabirianov@mail.unomaha.edu 
See next page for additional authors 
Follow this and additional works at: https://digitalcommons.unl.edu/physicsliou 
 Part of the Physics Commons 
Gao, L.; Feng, D.Q.; Yuan, Lu; Yokota, T.; Sabirianov, Renat F.; Liou, Sy_Hwang; Chabot, M.D.; Porpora, D.; 
and Moreland, J., "A study of magnetic interactions of Ni80Fe20 arrays using ultrasensitive microcantilever 
torque magnetometry" (2004). Si-Hwang Liou Publications. 80. 
https://digitalcommons.unl.edu/physicsliou/80 
This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at 
DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Si-Hwang Liou Publications 
by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 
Authors 
L. Gao, D.Q. Feng, Lu Yuan, T. Yokota, Renat F. Sabirianov, Sy_Hwang Liou, M.D. Chabot, D. Porpora, and J. 
Moreland 
This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/
physicsliou/80 
Artificially Structured Materials III:
Patterned Structures Laura Heyderman, Chairman
A study of magnetic interactions of Ni80Fe20 arrays using ultrasensitive
microcantilever torque magnetometry
L. Gao, D. Q. Feng, L. Yuan, T. Yokota, R. Sabirianov, and S. H. Lioua)
Department of Physics and Astronomy and Center for Materials Research and Analysis,
University of Nebraska, Lincoln, Nebraska 68588
M. D. Chabot, D. Porpora, and J. Moreland
National Institute of Standards and Technology, Boulder, Colorado 80305
~Presented on 8 January 2004!
We have successfully fabricated single and paired 300 nm31.5 mm332 nm Ni80Fe20 bars on a
microcantilever using focused ion beam milling. Magnetic interactions of the paired bars were
studied by using magnetic force microscopy, microcantilever torque magnetometry, and
micromagnetic simulation. Our results clearly indicate that the magnetic switching behavior of the
paired Ni80Fe20 bars is affected by magnetostatic interactions. The magnetic hysteresis curves for a
sample with eight pairs of Ni80Fe20 bars consist of a series of stable switching states that are related
to the domain wall motion in the bars. © 2004 American Institute of Physics.
@DOI: 10.1063/1.1682912#
I. INTRODUCTION
Measuring micrometer and submicrometer scale mag-
netic features has proven to be a challenge for conventional
magnetometers. Thus, more sensitive methods are needed to
probe magnetism on this scale.1–5 Microcantilever torque
magnetometry ~MTM! based on a torsion-mode atomic force
microscope ~AFM! is a promising experimental technique
for measuring submicrometer magnetism due to its higher
sensitivity than SQUID magnetometry.3–5
The main challenge of this measurement technique is
obtaining well-defined micromagnetic samples on cantile-
vers. Chabot et al. have created a process in which film
deposition is combined with the cantilever fabrication
process.6 This method requires using multistep photolithog-
raphy process.
The interaction of submicrometer-sized arrays is an im-
portant topic for micromagnetism. Much work has been done
in this area.7–9 However, due to measurement sensitivity
limitations, arrays of hundreds of elements must be fabri-
cated to obtain a high enough signal-to-noise ratio. The re-
sults are often clouded by statistical variations such as dot
shape, size, and spacing. Due to its high sensitivity, MTM is
expected to reduce the statistical variations of the magnetic
interaction by studying just a few pairs of magnetic particles.
In this work, we use focused ion beam ~FIB! milling, a
simple one-step method, to prepare submicrometer bars on
the microcantilever and use magnetic force microscopy
~MFM!, microcantilever torque magnetometry, and micro-
magnetic simulation to study the magnetic reversal behavior
of these bars.
II. EXPERIMENT
We start with a microcantilever which already has a 7
mm37 mm332 nm Ni80Fe20 film deposited on the top left
corner @Fig. 1~a!#. The Ni80Fe20 film was then patterned by a
FIB workstation using a Ga1 liquid metal ion source oper-
ated at 30 keV ion energy. The ion beam current was ap-
proximately 70 pA. A patterning software package allowed
us to generate the milled pattern from a bitmap image. The
Ni80Fe20 films were patterned into 12 single 300 nm31.5
mm332 nm bars @Fig. 1~b!# and 8 pairs of 300 nm31.5
mm332 nm bars @Figs. 1~c!#. The milling time was 5 min for
both patterns. The gaps between the edges of bars are 1 mm
for single bars and 40 nm for paired bars.
a!Author to whom correspondence should be addressed. electronic mail:
sliou@unl.edu
FIG. 1. ~a! Microcantilever with Ni80Fe20 film deposited on the top left
corner. ~b! Focused ion beam patterned Ni80Fe20 arrays with 12 single 300
nm31.5 mm332 nm bars and ~c! eight pairs of 300 nm31.5 mm332 nm
bars with gap of 40 nm between adjacent bars.
JOURNAL OF APPLIED PHYSICS VOLUME 95, NUMBER 11 1 JUNE 2004
70100021-8979/2004/95(11)/7010/3/$22.00 © 2004 American Institute of Physics
Downloaded 18 Oct 2006 to 129.93.16.206. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
Field dependent magnetic domain images were obtained
under ambient conditions with a commercial magnetic force
microscopy. Magnetic properties of the patterned Ni80Fe20
films were characterized using a microcantilever torque mag-
netometer in vacuum. All measurements were done with a
magnetic field applied along the long axis of the bars. Mi-
cromagnetic simulations were performed to study the mag-
netization reversal of the paired Fe20Ni80 bars using the
OOMMF software package developed by NIST.10
III. RESULTS AND DISCUSSION
Figure 2 shows the domain structures of a single and a
set of paired 300 nm31.5 mm332 nm Ni80Fe20 bars under
different magnetic fields. All the MFM images were obtained
using tapping/lift mode with CoPt MFM tips at a lift height
of 20 nm. The tip’s north pole points down, perpendicular to
the sample surface. According to the MFM contrast
mechanism,11 the magnetization direction of the bars is from
dark to light. The 300 nm31.5 mm332 nm single bars and
paired bars with a 40 nm gap are observed simultaneously.
The sample was saturated with a field of 79.6 kA/m along
the long axis of the bars. At zero field, the magnetization
direction of the bars did not change and was still along the
direction of the applied magnetic field @Fig. 2~a!#. As the
field switched to negative, end domains and vortices were
formed first @Fig. 2~b!#, then domain walls propagate along
the bars @Fig. 2~c!# and are stopped by the pinning sites. The
pinning sites could be produced by surface or edge rough-
ness, defects, or disorder in the film ~such as random anisot-
ropy!. The magnetic reversal process for the bars is domain
wall motion instead of coherent rotation. At a field of 27
kA/m, only one of the paired bars is reversed @Fig. 2~d!#. As
field changed to 28.1 kA/m, the single bar reversed @Fig.
2~e!#, but the magnetization direction of paired bars is still
antiparallel to each other. At larger negative field, all the bars
switched @Fig. 2~f!#. The fact that the switching field of
single bars is larger than the reversing field of only one of the
paired bars and less than that of both paired bars shows that
the magnetostatic interaction exists between the closely
paired bars. The interaction makes the antiparallel magneti-
zation directions of paired bars a stable state.
To clarify the magnetization reversal of the paired bars,
we performed micromagnetic simulations with the following
parameters. The magnetization of Fe20Ni80 was 800 kA/m,
the anisotropy constant was 4.53103 J/m3, and the exchange
constant was 1.3310213 J/m3.12 We used a random anisot-
ropy setup to mimic the real medium. The results also show
that the switching of each bar in the paired bars system is not
independent. After saturation, paired bars form a symmetri-
cally inverted C state at the remanent state @C state is named
because the domain structure resembles the letter C, Fig.
3~a!#. With the negative field applied, the magnetization re-
versal proceeds through the formation of two vortices ~end
domains! @Figs. 3~b! and 3~c!#. Due to the broken symmetry
~random anisotropy!, the reversal of one of the bars happens
first @Fig. 3~d!#. Although the general picture of the reversal
of this bar is similar to the single bar case, there are some
deviations because of the interactions with the second bar.
Due to the magnetostatic interactions, the system creates a
closure for the magnetic field ~magnetization of paired bars
FIG. 2. Field dependent magnetic domain structures of single Ni80Fe20 bars
~300 nm31.5 mm332 nm! and same size paired bars with a gap of 40 nm.
The sample was saturated with a field of 79.6 kA/m along the long axis of
the bars and then decreased to ~a! 0 kA/m, ~b! 22.07 kA/m, ~c! 24.46
kA/m, ~d! 27 kA/m, ~e! 28.1 kA/m, and ~f! 29.31 kA/m.
FIG. 3. Micromagnetic simulations was performed on the paired Ni80Fe20
bars ~300 nm31.5 mm332 nm! with a gap of 40 nm. The sample was
saturated along the long axis of the bars and then decreases to ~a! 24.77
kA/m, ~b! 220.69 kA/m, ~c! 226.26 kA/m, ~d! 231.83 kA/m, ~e! 237.40
kA/m, and ~f! 242.18 kA/m.
7011J. Appl. Phys., Vol. 95, No. 11, Part 2, 1 June 2004 Gao et al.
Downloaded 18 Oct 2006 to 129.93.16.206. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
is aligned in opposite directions!. It is a stable state for the
system of paired bars. Then at somewhat larger applied field,
the system is forced out of this potential well and the second
bar also switches @Fig. 3~f!#. The simulation results are con-
sistent with the MFM measurement.
Figure 4~a! shows a simulated hysteresis loop for one set
of paired bars system. The two steps during the reversal is
caused by the magnetostatic interaction between the paired
bars, which is correlated with the domain structures shown in
Figs. 2 and 3. Figure 4~b! shows the M -H curve obtained
with microcantilever torque magnetometry for a cantilever
with eight sets of paired bars patterned on the 32 nm film, as
shown in Fig. 1~c!. The hysteresis curves are obtained by
sweeping the external field from 231.83 kA/m to 131.83
kA/m. The torque field and cantilever resonant frequency
used are 85 A/m and 25.4 kHz, respectively. We have yielded
a saturation magnetization of 870 kA/m for the eight sets of
paired bars with a magnetic volume of 2.3310219 m3. The
experimental magnetization is within 10% of the bulk value
of 800 kA/m. The error may be due to difficulty in estimating
the thickness of the film and the actual value of the torque
field. The observed series of stable switching states during
the magnetization reversal process is likely due to the do-
main wall motion in the bars. A possible explanation for the
difference between the simulation and the measured loop is
that the simulation is performed only on one paired bars
under ideal conditions but MTM includes all the switching of
eight paired bars in which each bar may have a different
reversal field due to different defect structures formed during
the FIB processing.
IV. CONCLUSIONS
The focused ion beam milling is a convenient way to
obtain arbitrary patterns on a microcantilever. Domain struc-
ture and micromagnetic simulation results show that the re-
versal of the paired 300 nm31.5 mm332 nm bars is affected
by the magnetostatic interactions. We used MTM to measure
eight sets of paired Ni80Fe20 bars. The hysteresis curve con-
sists of a series of stable switching states. This is related to
the domain wall motion in the bars. We show that microcan-
tilever torque magnetometry is a suitable method for measur-
ing magnetic interactions in submicrometer-sized magnetic
samples. Future work will improve the sensitivity of the
MTM by optimizing the cantilevers. This will allow the
study of the magnetization reversal of only one set of paired
bars.
ACKNOWLEDGMENTS
Research was supported by NSF MRSEC Award Nos.
DMR-0213808 and DMR-0116780 and Army Research Of-
fice DAAD Grant No. 19-03-1-0298. T. Yokota was sup-
ported by a Grant-in-Aid for JSPS Fellows, Grant No.
00000652.
1 B. C. Stipe, H. J. Mamin, T. D. Stowe, T. W. Kenny, and D. Rugar, Phys.
Rev. Lett. 86, 2874 ~2001!.
2 J. G. E. Harris, D. D. Awschalom, F. Matsukura, H. Ohno, K. D. Mara-
nowski, and A. C. Gossard, Appl. Phys. Lett. 75, 1140 ~1999!.
3 M. Lo¨hndorf, J. Moreland, P. Kabos, and N. Rizzo, J. Appl. Phys. 87,
5995 ~2000!.
4 M. D. Chabot and J. Moreland, J. Appl. Phys. 93, 7897 ~2003!.
5 J. Moreland, J. Phys. D 36, R39 ~2003!.
6 M. D. Chabot and J. T. Markert, Proc. SPIE 3875, 104 ~1999!.
7 J. F. Smyth, S. Schultz, D. R. Fredkin, D. P. Kern, S. A. Rishton, H.
Schmid, M. Cali, and T. R. Koehler, J. Appl. Phys. 69, 5262 ~1991!.
8 S. Y. Chou and L. Kong, J. Appl. Phys. 79, 5855 ~1996!.
9 V. Novosad, M. Grimsditch, J. Darrouzet, J. Pearson, S. D. Bader, V.
Metlushko, K. Guslienko, Y. Otani, H. Shim, and K. Fukamichi, Appl.
Phys. Lett. 82, 3716 ~2003!.
10 J. Donahue and R. D. McMichael, Physica B 233, 272 ~1997!.
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FIG. 4. ~a! Simulated magnetic hysteresis loop of the paired Ni80Fe20 bars
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https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1079&amp;context=physicsliou

A study of magnetic interactions of Ni\u3csub\u3e80\u3c/sub\u3eFe\u3csub\u3e20\u3c/sub\u3e arrays using ultrasensitive microcantilever torque magnetometry

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