A cost-effective method for the quantitative characterization of the magnetostrictive effect in thin films is presented. In this method, a sample's magnetostriction is extrapolated from the tip displacement of a thin-film magnetostrictive cantilever. The tip displacement is measured by monitoring the position of a reflected laser beam using two differentially coupled photodiode positioning sensors. In contrast with alternative optical deflection-angle devices designed for educational purposes, the detection limit of our setup resolves submicron-level displacements from nanoscale thin films. The efficacy of the system is demonstrated through measurements using amorphous 200-nm thick Terfenol-D/Si (100) bimorph cantilevers. In these measurements, magnetostriction values of 106  ±  3.5 ppm at ±4300 Oe applied field were attained, where the voltage noise floor was ±0.05 V (a cantilever displacement uncertainty of ±70 nm). In-plane (IP) and out-of-plane (OOP) magnetization curves and crystallographic x-ray diffraction (XRD) were performed to determine the magnetic behavior and confirm the amorphous nature of the films, respectively. The experimental methods and material characterization systems demonstrated here enhance the understanding of complex magnetic phenomena and introduce common measurement techniques to better equip students with the skills for insightful analysis of fundamental magnetic physics.

1.
N. B.
Ekreem
,
A. G.
Olabi
,
T.
Prescott
,
A.
Rafferty
, and
M. S. J.
Hashmi
, “
An overview of magnetostriction, its use and methods to measure these properties
,”
J. Mater. Process. Technol.
191
(
1–3
),
96
101
(
2007
).
2.
Duc Nguyen
Huu
, “
Giant magnetostriction in Lanthanide-transition metal thin films
,”
Handbook Phys. Chem. Rare Earths
32
,
1
53
(
2001
).
3.
Hiro
Ohzeki
,
Akihiro
Mashine
,
Hideki
Aoyama
, and
Ichiro
Inasaki
, “
Development of a magnetostrictive torque sensor for milling process monitoring
,”
J. Manuf. Sci. Eng.
121
,
615
622
(
1999
).
4.
Fernando
Seco
,
Jose Miguel
Martin
,
Antonio Ramon
Jimenez
, and
Leopoldo
Calderon
, “
A high accuracy magnetostrictive linear position sensor
,”
Sens. Actuators A: Phys.
123–124
,
216
223
(
2005
).
5.
Lothar
Kiesewetter
, “
The application of Terfenol in linear motors
,” in
Proceedings of 2nd International Conference on Giant Magnetostrictive Alloys
(
1988
), p.
15
.
6.
Wei
Wang
,
Huiming
Liu
,
Rongjin
Huang
,
Yuqiang
Zhao
,
Chuangjun
Huang
,
Shibin
Guo
,
Yi
Shan
, and
Laifeng
Li
, “
Thermal expansion and magnetostriction measurements at cryogenic temperature using the strain gauge method
,”
Front. Chem.
6
,
72
(
2018
).
7.
Celso L.
Ladera
,
Guillermo
Donoso
, and
Johnny H.
Contreras
, “
Magnetostriction measured by holographic interferometry with the simple and inexpensive arrowhead setup
,”
Eur. J. Phys.
33
(
2
),
373–383
(
2012
).
8.
Peter S.
Harllee
III
,
George H.
Bellesis
, and
David N.
Lambeth
, “
Anisotropy and magnetostriction measurement by interferometry
,”
J. Appl. Phys.
75
(
10
),
6884
6886
(
1994
).
9.
D.
Laumann
,
P.
Hayes
,
C.
Enzingmüller
,
I.
Parchmann
, and
E.
Quandt
, “
Magnetostriction measurements with a low-cost magnetostrictive cantilever beam
,”
Am. J. Phys.
88
(
6
),
448
455
(
2020
).
10.
Rajdeep
Adhikari
,
Rakesh
Kaundal
,
Anirban
Sarkar
,
Pushpinder
Rana
, and
Amal K.
Das
, “
The cantilever beam magnetometer: A simple teaching tool for magnetic characterization
,”
Am. J. Phys.
80
(
3
),
225
231
(
2012
).
11.
H.
Aireddy
and
A. K.
Das
, “
The cantilever beam magnetometer for the measurement of electric field controlled magnetic property of ferromagnet/ferroelectrics heterostructures
,”
Rev. Sci. Instrum.
90
(
10
),
103905
(
2019
).
12.
Cunzheng
Dong
,
Menghui
Li
,
Xianfeng
Liang
,
Huaihao
Chen
,
Haomiao
Zhou
,
Xinjun
Wang
,
Yuan
Gao
,
Michael E.
McConney
,
John G.
Jones
,
Gail J.
Brown
et al, “
Characterization of magnetomechanical properties in FeGaB thin films
,”
Appl. Phys. Lett.
113
(
26
),
262401
(
2018
).
13.
David J.
Dunlop
and
Özden
Özdemir
,
Rock Magnetism: Fundamentals and Frontiers
(
Cambridge U. P
.,
Cambridge
,
2001
), No. 3.
14.
Jian-Gang Jimmy
Zhu
, “
New heights for hard disk drives
,”
Mater. Today
6
(
7–8
),
22
31
(
2003
).
15.
Francisco
De Leon
and
Adam
Semlyen
, “
A simple representation of dynamic hysteresis losses in power transformers
,”
IEEE Trans. Power Delivery
10
(
1
),
315
321
(
1995
).
16.
E.
van de Riet
, “
Deflection of a substrate induced by an anisotropic thin-film stress
,”
J. Appl. Phys.
76
(
1
),
584
586
(
1994
).
17.
Bernard Dennis
Cullity
and
Chad D.
Graham
,
Introduction to Magnetic Materials
(
John Wiley & Sons
,
New York
,
2011
).
18.
David
Jiles
,
Introduction to Magnetism and Magnetic Materials
(
CRC Press
,
Boca Raton
,
2015
).
19.
J.
Mencik
,
E.
Quandt
, and
D.
Munz
, “
Elastic modulus of TbDyFe films—A comparison of nanoindentation and bending measurements
,”
Thin Solid Films
287
(
1–2
),
208
213
(
1996
).
20.
K. P.
Mohanchandra
,
S. V.
Prikhodko
,
K. P.
Wetzlar
,
W. Y.
Sun
,
P.
Nordeen
, and
G. P.
Carman
, “
Sputter deposited Terfenol-D thin films for multiferroic applications
,”
AIP Adv.
5
(
9
),
097119
(
2015
).
21.
Paymon
Shirazi
,
Taehwan
Lee
,
Mohanchandra K.
Panduranga
,
Alpha T.
N'Diaye
,
Anthony
Barra
, and
Gregory P.
Carman
, “
Rare-earth orbital moment contributions to the magnetic anisotropy in magnetostrictive Tb0.3Dy0.7Fe2
,”
Appl. Phys. Lett.
118
(
16
),
162401
(
2021
).
22.
George Gerald
Stoney
, “
The tension of metallic films deposited by electrolysis,” Proc. Royal Soc. London
,
Ser. A, Containing Papers Math. Phys. Character
82
(
553
),
172
175
(
1909
).
23.
Peter
Zaumseil
, “
High-resolution characterization of the forbidden Si 200 and Si 222 reflections
,”
J. Appl. Crystallogr.
48
(
2
),
528
532
(
2015
).
24.
Michael Guevara
De Jesús
,
Mohanchandra K.
Panduranga
,
Paymon
Shirazi
,
Scott
Keller
,
Malcolm
Jackson
,
Kang L.
Wang
,
Christopher S.
Lynch
, and
Gregory P.
Carman
, “
Micro-magnetoelastic modeling of Terfenol-D for spintronics
,”
J. Appl. Phys.
131
(
23
),
234101
(
2022
).
25.
Y.
Hsiao
,
D. B.
Gopman
,
K.
Mohanchandra
,
P.
Shirazi
, and
C. S.
Lynch
, “
Effect of interfacial and edge roughness on magnetoelectric control of Co/Ni microdisks on PMN-PT (011)
,”
Sci. Rep.
12
(
1
),
3919
(
2022
).
26.
Michael Guevara
De Jesus
,
Zhuyun
Xi1ao
,
Maite
Goiriena-Goikoetxea
,
Rajesh V.
Chopdekar
,
Mohanchandra K.
Panduranga
,
Paymon
Shirazi
,
Adrian
Acosta
,
Jane P.
Chang
,
Jeffrey
Bokor
, and
Gregory P.
Carman
, “
Magnetic state switching in FeGa microstructures
,”
Smart Mater. Struct.
31
(
3
),
035005
(
2022
).
27.
A.
Speliotis
and
D.
Niarchos
, “
Magnetostrictive properties of amorphous and crystalline TbDyFe thin films
,”
Sens. Actuators A: Phys.
106
(
1–3
),
298
301
(
2003
).
28.
Ming
Liu
,
Shandong
Li
,
Ziyao
Zhou
,
Shawn
Beguhn
,
Jing
Lou
,
Feng
Xu
,
Tian Jian
Lu
, and
Nian X.
Sun
, “
Electrically induced enormous magnetic anisotropy in Terfenol-D/lead zinc niobate-lead titanate multiferroic heterostructures
,”
J. Appl. Phys.
112
(
6
),
063917
(
2012
).
29.
Julia R.
Downing
,
Suok-Min
Na
, and
Alison B.
Flatau
, “
Compressive pre-stress effects on magnetostrictive behaviors of highly textured Galfenol and Alfenol thin sheets
,”
AIP Adv.
7
(
5
),
056420
(
2017
).
30.
E.
du Trémolet De Lacheisserie
and
J. C.
Peuzin
, “
Magnetostriction and internal stresses in thin films: The cantilever method revisited
,”
J. Magnetism Magn. Mater.
136
(
1–2
),
189
196
(
1994
).
31.
James
Ma
,
Daniel T.
O'Brien
, and
Desiderio
Kovar
, “
Amorphous Terfenol-D films using nanosecond pulsed laser deposition
,”
Thin Solid Films
518
(
1
),
319
323
(
2009
).
32.
Mohanchandra K.
Panduranga
,
Zhuyun
Xiao
,
Joseph D.
Schneider
,
Taehwan
Lee
,
Christoph
Klewe
,
Rajesh
Chopdekar
,
Padraic
Shafer
,
Alpha T.
N'Diaye
,
Elke
Arenholz
,
Rob N.
Candler
et al, “
Single magnetic domain Terfenol-D microstructures with passivating oxide layer
,”
J. Magnetism Magn. Mater.
528
,
167798
(
2021
).
33.
Jennifer Beth
Thoelke
, “
Magnetization and magnetostriction in highly magnetostrictive materials
,” Technical report,
Ames Lab
.,
1993
.
34.
A.
Datta
,
D.
Nathasingh
,
R. J.
Martis
,
P. J.
Flanders
, and
C. D.
Graham
, Jr.
, “
Saturation and engineering magnetostriction of an iron-base amorphous alloy for power applications
,”
J. Appl. Phys.
55
(
6
),
1784
1786
(
1984
).
35.
Alireza
Moridi
,
Haihui
Ruan
,
L. C.
Zhang
, and
Mei
Liu
, “
Residual stresses in thin film systems: Effects of lattice mismatch, thermal mismatch and interface dislocations
,”
Int. J. Solids Struct.
50
(
22–23
),
3562
3569
(
2013
).
36.
Mohanchandra K.
Panduranga
,
Taehwan
Lee
,
Andres
Chavez
,
Sergey V.
Prikhodko
, and
Gregory P.
Carman
, “
Polycrystalline Terfenol-D thin films grown at CMOS compatible temperature
,”
AIP Adv.
8
(
5
),
056404
(
2018
).
37.
Won-Jong
Kim
and
Ali
Sadighi
, “
A novel low-power linear magnetostrictive actuator with local three-phase excitation
,”
IEEE/ASME Trans. Mechatron.
15
(
2
),
299
307
(
2009
).
38.
Masaya
Toda
,
Naoki
Inomata
,
Takahito
Ono
, and
Ioana
Voiculescu
, “
Cantilever beam temperature sensors for biological applications
,”
IEEJ Trans. Electr. Electron. Eng.
12
(
2
),
153
160
(
2017
).
39.
J.
Huang
,
C.
Prados
,
J. E.
Evetts
, and
A.
Hernando
, “
Giant magnetostriction of amorphous Tbx Fe1−x ( 0.10 < x < 0.45) thin films and its correlation with perpendicular anisotropy
,”
Phys. Rev. B
51
(
1
),
297
304
(
1995
).
40.
See supplementary material at https://www.scitation.org/doi/suppl/10.1119/5.0134187 for additional elaboration regarding the calculation and mitigation of thermally-induced strains, photodiode calibration, residual stress approximation, cost-reduction measures and their impact on apparatus efficacy, differential operational-amplifier setup, derivation of the magnetostriction-magnetization relation, the automation software, and the procurement of commercial nanoscale Terfenol-D thin films.

Supplementary Material

AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.