Measuring Magnetoelectric and Magnetopiezoelectric Effects
Joe T. Evans*, Scott P. Chapman, Spencer T. Smith, Bob C. Howard, Allen Gallegos
Radiant Technologies, Inc.
Albuquerque, NM 87107 USA
radiant@ferrodevices.com
polarization state for each magnetic field state. Changing the
magnetic field forces the sample to a new polarization state.
The change in polarization will result in charge flowing out of
or into the sample under test provided there is a low impedance
current path available between the plates of the capacitor. If
there is no current path between the plates, the magnetically
generated charge will remain in the capacitor, generating a
voltage by its action across the dielectric constant of the
material. The two test techniques are distinguished by the
input impedance of the measurement instrument.
The authors have developed a test procedure and circuits for
characterizing the charge generation of a magnetoelectric device
when stimulated with a magnetic field. The traditional method
for measuring magnetoelectric effect is to stimulate the sample
with a magnetic field while measuring the voltage generated
across the sample. These voltages can be so small that a lock-in
amplifier is required to pull the signal out of ambient noise.
Charge measurement under the same circumstances produces a
much larger signal and can be related to the voltage response
using the dielectric constant of the material. The charge test is an
exact analog to the traditional electrical hysteresis test with the
exception that the test instrument cycles a magnetic field across
the sample instead of an electric field.
The initial work on the charge-based measurement
technique was published by Dr. Chee Sung Park, then at
CEHMS at Virginia Tech University.
His publication
described how to execute the charge-based measurement and
compared its results with that of the traditional voltage-based
measurement. He found that the correlation was excellent. [1]
Key Words: magnetoelectric coefficient, multiferroic, polarization,
electric charge
I.
INTRODUCTION
The goal of this experiment was to identify the issues
associated with executing a charge-based magnetoelectric
measurement, minimize any negative effects, determine the
accuracy of the measurement sensors, and execute the
measurement on a composite magnetoelectric device.
A capacitor with a nonzero magnetoelectric coupling
coefficient will generate charge, voltage, or a combination of
both when exposed to a magnetic field. The ratio of charge to
voltage generated by the capacitor as a result of a change in an
applied magnetic field is determined by 1) the impedance
across the terminals of the capacitor and 2) the frequency at
which the magnetic field is changing. The capacitor will
generate voltage if the meter across capacitor has a highimpedance input. This arrangement is the traditional method of
characterizing the magnetoelectric coefficient using a lock-in
amplifier as the meter. The coefficient measured in this
manner is ME, defined as
ME = E / H
II.
A. Multiferroic vs Composite Magnetoelectrics
Devices with magnetoelectric properties come in two
flavors. The first has a multiferroic material as the capacitor
dielectric layer.
A multiferroic material has multiple
properties, in this case ferromagnetism together with remanent
polarization or piezoelectricity. With the two properties
coupled in the same device, a change in polarization state could
be forced by a magnetic field or a change in polarization could
be detected by a magnetic sensor. The second type of
magnetoelectric device is a composite made by laminating a
pure ferromagnetic material with a pure piezoelectric or
ferroelectric material. The coupling between the magnetic and
electric properties is through the mechanical interface between
the layers. For instance, a magnetic field will distort the
ferromagnetic material. That distortion will in turn activate the
piezoelectric material to create charge or voltage. In reverse,
activation of the piezoelectric property might create a varying
magnetic field.
(1)
If a virtual ground measurement circuit is connected across the
device, the device will not be allowed to generate a voltage so
the magnetoelectric response will appear as charge. The
coefficient measured at zero electric field is , defined as
 = P/H or  = P/H
(2)
Ferroelectric hysteresis testers use virtual ground measurement
circuits so they are naturally configured to determine the
magnetoelectric coefficient according to (2). The relationship
between  and ME may be algebraically derived as
ME =  / 0r
SAMPLE
(3)
Equation (3) makes sense as  is in units of polarization while
ME is in units of electric field. The dielectric constant  is the
ratio between electric field and polarization.
B. Sample Preparation
The sample used for this experiment was fabricated at
Virginia Tech by Su Chul Yang associated with the Center for
Energy Harvesting Materials and Systems (CEHMS). It
consisted of KNNLS-NZF cut into disks with an area of 0.785
Equation (2) is defined using fundamental thermodynamic
units. The equation means that the capacitor has a unique
1
cm2 and a thickness of 0.5 mm. The disks were laminated to a
nickel foil. The maximum response for this sample occurred at
460 Oersted: 12.5mV/cm/Oe. At 25 Oersted, the sample
generated an ME response of 1.25mV/cm/Oe [2] determined
by CEHMS using the voltage measurement technique.
III.
D. Measuring the Magnetic Field
Due to the presence of the electrical shield box, a Hall Effect
sensor could not be placed in the vicinity of the sample to
collect magnetic field strength during stimulus. The authors
used a high speed current sensor in line with the Helmholtz coil
to determine the magnetic field at the sample while in the
central cylinder of uniformity of the Helmholtz coil.
Comparison of the current sensor to a calibrated gaussmeter
indicated an accuracy of 97.5% for the current sensor at 1 Hz.
TEST CONFIGURATION
The charge-based magnetoelectric response test is executed
by substituting a magnetic waveform for the traditional voltage
stimulus in a polarization hysteresis test. The substitution is
accomplished by placing a current source on the voltage output
of the hysteresis tester to drive a Helmholtz coil. The sample is
placed inside the coil at the center of the coil. Either a current
sensor in line with the Helmholtz coil or a Hall Effect sensor
placed at the sample location captures the magnetic field during
the stimulus waveform.
E. DC Field Bias
Many magnetoelectric devices exhibit higher coefficients
when exposed to a DC magnetic bias field during stimulation.
A uniform DC bias field can be achieved by placing the sample
and the Helmholtz coil at the center of a much larger field coil
driven by its own high power amplifier. A non-uniform bias
can be applied with a permanent magnet set next to the
Helmholtz coil as in Fig. 1. No bias was applied to the sample
for this experiment.
Magnetoelectric measurement conducted in this manner is
subject to a variety of limitations and parasitics.
A. Frequency Limitations
The inductance of the Helmholtz coil limits the maximum
frequency that may be applied to the sample.
VCoil = L I/t
F. Small Signal Capacitance
The mathematical steps to convert the  coefficient to the
ME coefficient require the use of the small signal capacitance
of the device under test. Dividing the magnetoelectric charge
measured under zero impedance by the sample’s small signal
capacitance should predict the voltage the sample would
generate under open circuit conditions. Most magnetoelectric
devices vary their small signal capacitance as a function of
magnetic field. The composite device under test exhibited a
1% variance in its small signal capacitance as a DC magnetic
field varied over ±50 gauss. The small signal capacitance as a
function of magnetic field is measured by executing the classic
small signal capacitance electrical test on the sample as it rests
inside the Helmholtz coil while the coil generates DC values of
the fields to be used in the test.
(4)
The voltage limit of the current amplifier used by the authors in
Fig. 1 becomes Vcoil in (4). Combined with inductance L of the
coil, it limited the maximum frequency to 20 Hz. Distortion of
the stimulus waveform sets in at frequencies below the limit,
the reason why 1 Hz was used as the test frequency for this
experiment.
B. Charge Loss
The most sensitive charge measurement requires an
electrometer for the RETURN channel in Fig. 1. Electrometers
leak and this leakage limits the minimum frequency at which
the test may be run. The Radiant Technologies Precision
Multiferroic nonlinear materials tester used for the experiment
in Fig. 1 was characterized for charge loss by executing a
traditional voltage-driven hysteresis test on a precision 10pF
reference capacitor. At one volt, the capacitor should generate
10pC of charge plus or minus the precision of the reference
capacitor, in this case a NIST-traceable 0.1% quality standard.
The tester retained 99% of the charge during a 10 Hz test and
98.1% of the charge during a 1 Hz test.
G. Parasitic Cable Capacitance
A major advantage of the charge-based measurement approach
is the use of the virtual ground across the sample. With zero
volts across the coaxial cables connecting the sample to the
tester, the parasitic capacitance of the cable cannot affect the
test. The same is not true for the volt-based measurement
using a lock-in amplifier. The charge generated by the sample
is spread across the capacitance of the cables and the input of
the lock-in amplifier, reducing the value of the measured
voltage from the value the sample would generate if it were
truly isolated. This parasitic effect for the voltage-based
measurement must be measured and subtracted.
C. Ambient Electric Noise
The charge measured during the experiment was so small it
was easily swamped by ambient electric noise in the room.
Polarization hysteresis systems measure absolute charge so
ambient noise cannot be eliminated by lock-in techniques. The
ambient noise was eliminated by placing the sample inside an
aluminum electrical shield box grounded to the tester. The box
fit inside the Helmholtz coil and coaxial cables were used to
connect the sample inside the shield box to the tester.
H. Induced Charge
The cables connecting the sample to the test must intrude
inside the AC magnetic field generated by the Helmholtz coil.
The AC magnetic field will induce current in the cables as the
field varies amplitude.
However, the magnetic field
commanded in the Helmholtz coil by the polarization tester
moves in steps, stopping at intermediate magnetic field levels
to allow the sample to stabilize and for the tester to measure the
total amount of charge captured from or given to the sample at
2
that point in the waveform. Because each charge measurement
is made with the magnetic field in a static condition, there will
be no magnetically-induced charge included in the measured
charge.
The voltage-based measurement is a dynamic
measurement so induced charge will be added to the sample
response and must be subtracted from the result.
Dividing (6) by the area of the sample results in the equation
that calculates the  coefficient of the sample at the specified
magnetic field.
P/H = 0.00255h-0.00408 pC/cm2/Oe
At 25 Oe,  equals 0.06 pC/cm2/Oe.
The ME coefficient is calculated from (6), not (7), by dividing
that charge prediction by the small signal capacitance of the
sample at the magnetic field strength of interest (758pF) to
convert to units of volts. That result is divided by the sample
thickness (0.5mm) to convert to electric field.
I.
Parasitic Charge
As mentioned earlier in the section about parasitic cable
capacitance, the test fixture contributes no parasitic charge to
the results when a virtual ground instrument is used. Parasitic
charge does arise from inside the polarization tester itself.
This parasitic charge can easily be measured by simply
disconnecting the tester from the sample and running the same
test.
ME = 5.28x10-5 h - 8.44x10-5 mV/cm/Oe (8)
At 25 Oe, ME is predicted to be 1.24mV/cm/Oe.
J.
Voltage Bias
It is possible with the test configuration used for this
experiment to apply a voltage bias to the sample during
magnetic field AC actuation. That was not done for this
experiment. The sample electrodes were shorted with ground
referenced on one plate and the polarization tester virtual
ground input on the other.
IV.
(7)
ANALYSIS
The error in the charge measurement consists of the 0.5%
specification provided by the manufacturer for the Precision
Multiferroic tester used in the test plus the charge leakage from
its electrometer circuit, measured at 1.9%. Thus, the charge
measurement error for this experiment extended from -2.4% to
+0.5%. The magnetic field measurement error was measured
to be ±2.5%. The  coefficient is found by dividing the charge
by the magnetic field. Using the maximum charge uncertainty
against the minimum magnetic uncertainty and vice versa
yields a maximum error range of +3.1% to -4.8%. Therefore
there is a reasonable expectation that the  value of
0.06pC/cm2/Oe and the ME of 1.24mV/cm/Oe calculated for
this sample at 25 Oersted are accurate to within ±5%.
RESULTS
A single test was run on the sample over ±25 Oe. The
measurement was made with and without the sample in place
in order to capture the parasitic charge generated by the
polarization tester. Both measurements are plotted against each
other in Fig. 2.
The ME value measured by Su Chul Yang at Virginia Tech
for this sample at 25 Oe was 1.25 mV/cm/Oe, a difference of
1% from that measured above. This is an excellent correlation
but more work remains to be done. The next step in our
research will be for the authors to work with CEHMS at
Virginia Tech to perform the same error source evaluation on
the traditional voltage-based method that measures ME and
then comparing the two test techniques on a single knowngood sample.
Subtracting the parasitic induced charge from the
measurement should yield values close to the true
magnetoelectric charge generation of the sample.
The
difference can be fitted with a polynomial equation which can
then be used to predict 1) the charge the sample will generate at
any H-field, 2) the value of  for the sample at a specific Hfield, and 3) the value of ME at a specific H-field. The
difference between the sample response and the induced charge
is plotted in Fig. 3 along with its polynomial fit. Also shown in
the plot is the equation of the fit. Since the charge plotted in
Fig. 3 is an absolute response of the sample to the applied
magnetic field, its  coefficient at each magnetic field value is
the slope of the polarization generated at that field. The
charge generation result in Fig. 3 was fit with a polynomial
resulting in (5) having an R2 value of 0.9767.
ACKNOWLEDGMENT
The authors wish to acknowledge the invaluable assistance
of Dr. Shashank Priya, Su Chul Yang, and Shashaank Gupta
from CEHMS at Virginia Tech.
REFERENCES
Q = 0.001h2 - 0.0032h + 0.0084 pC(Oe) (5)
[1]
The derivative of (5) gives the equation that calculates the
slope of the charge response in Fig. 3 at a specified magnetic
field.
Q/H = 0.002h - 0.0032 pC/Oe
[2]
(6)
3
C. S. Park, J. Evans, and S. Priya, “Quantitative understanding of the
elastic coupling in magnetoelectric laminate composites through the
nonlinear polarization-magnetic (P-H) response,” Smart Mater. Struct.,
vol. 20, 6pp., 2011.
Sample synthesized by Su Chul Yang of the Center for Energy
Harvesting Material and Systems. All data rights are retained by
CEHMS.
Figure 1: Magnetoelectric test configuration.
4
Figure 2: Magnetoelectric charge response of the CEHMS composite laminated sample plus parasitic
charge.
5
Q/H
Figure 3: The true magnetoelectric charge response of the CEHMS composite laminated sample plus
polynomial fit.
6