Converse magnetoelectricity in asymmetric magnetoelectric structures
Збережено в:
| Дата: | 2010 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
НТК «Інститут монокристалів» НАН України
2010
|
| Назва видання: | Functional Materials |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/135151 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Converse magnetoelectricity in asymmetric magnetoelectric structures / G.S. Radchenko, M.G. Radchenko // Functional Materials. — 2010. — Т. 17, № 3. — С. 371-374. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-135151 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1351512018-06-15T03:05:12Z Converse magnetoelectricity in asymmetric magnetoelectric structures Radchenko, G.S. Radchenko, M.G. Modeling and simulation 2010 Article Converse magnetoelectricity in asymmetric magnetoelectric structures / G.S. Radchenko, M.G. Radchenko // Functional Materials. — 2010. — Т. 17, № 3. — С. 371-374. — Бібліогр.: 12 назв. — англ. 1027-5495 http://dspace.nbuv.gov.ua/handle/123456789/135151 en Functional Materials НТК «Інститут монокристалів» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Modeling and simulation Modeling and simulation |
| spellingShingle |
Modeling and simulation Modeling and simulation Radchenko, G.S. Radchenko, M.G. Converse magnetoelectricity in asymmetric magnetoelectric structures Functional Materials |
| format |
Article |
| author |
Radchenko, G.S. Radchenko, M.G. |
| author_facet |
Radchenko, G.S. Radchenko, M.G. |
| author_sort |
Radchenko, G.S. |
| title |
Converse magnetoelectricity in asymmetric magnetoelectric structures |
| title_short |
Converse magnetoelectricity in asymmetric magnetoelectric structures |
| title_full |
Converse magnetoelectricity in asymmetric magnetoelectric structures |
| title_fullStr |
Converse magnetoelectricity in asymmetric magnetoelectric structures |
| title_full_unstemmed |
Converse magnetoelectricity in asymmetric magnetoelectric structures |
| title_sort |
converse magnetoelectricity in asymmetric magnetoelectric structures |
| publisher |
НТК «Інститут монокристалів» НАН України |
| publishDate |
2010 |
| topic_facet |
Modeling and simulation |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/135151 |
| citation_txt |
Converse magnetoelectricity in asymmetric magnetoelectric structures / G.S. Radchenko, M.G. Radchenko // Functional Materials. — 2010. — Т. 17, № 3. — С. 371-374. — Бібліогр.: 12 назв. — англ. |
| series |
Functional Materials |
| work_keys_str_mv |
AT radchenkogs conversemagnetoelectricityinasymmetricmagnetoelectricstructures AT radchenkomg conversemagnetoelectricityinasymmetricmagnetoelectricstructures |
| first_indexed |
2025-07-09T21:10:03Z |
| last_indexed |
2025-07-09T21:10:03Z |
| _version_ |
1837205191072415744 |
| fulltext |
Functional Materials, 17, 3, 2010 371
Converse magnetoelectricity in asymmetric
magnetoelectric structures
G.S. Radchenko, M.G. Radchenko*
Institute of Physics, Southern Federal University,
194 Stachki Ave., 344090 Rostov-on-Don, Russia
Pedagogical Institute, Southern Federal University,
33 Bolshaya Sadovaya St., 344022 Rostov-on-Don, Russia
* Rostov Branch, Moscow State Technical University of Civil Aviation,
262b Sholokhova St., 344009 Rostov-on-Don, Russia
Received November 30, 2010
A new computational approach is developed to analyze the asymmetric magnetoelectric struc-
tures. The possibility to enhance considerably the composite main effective parameters is found.
The acoustic and electromagnetic vibrations in such structures are described comprehensively.
Развит новый вычислительный подход к анализу асимметричных магнитоэлектрических
структур. Обнаружена возможность значительного усиления основных эффективных
параметров композита. Приведено полное описание акустических и электромагнитных
колебаний в таких структурах.
1. Introduction
The rapid development of modern electronics requires novel materials with useful proper-
ties. The promising magnetoelectric (ME) heterogeneous materials possessing converse ME effect
(CMEF) are among materials of promise for practical applications. CMEF is the magnetization of
a sample under external electric field. This offers an excellent potential for coil-free electromag-
nets free of eddy-current existence, devices for sensitivity measurements and for development of
ME memory devices and sensors. In literature, the CMEF is a rather new direction and there
are some publications aimed at that matter [1-10]. The structures considered in the present work
and in [1, 3-5, 7, 8, 10, 11] are layered heterogeneous structures containing combination of highly
magnetostrictive and piezoactive substances. The applied external electric field creates mechanical
straining of the piezoelectric plate and then this strain is transferred to magnetic phase, causing a
magnetic flux therein due to the magnetostriction. Then the created flux is registered by a testing
coil [1, 3, 4, 7, 8, 10], two Helmholtz coils [5], one coil above the vibrating magnet [9], or vibrating
sample magnetometer in heterostructures [2]. In the region where the applied electric field is of
resonance frequency, the response is increased drastically and this provides a way for CMEF to be
practically essential. However, almost all these publications are aimed at the symmetric strictures,
there piezo- and magnetostrictive layers are of similar length. However, in reality, the lengths may
be very different, and no attempts to analyze this difference theoretically were made prior to this
G.S. Radchenko, M.G. Radchenko / Converse magnetoelectricity in asymmetric ...
Functional Materials, 17, 3, 2010 372
work. The converse ME susceptibility is poorly analyzed in literature, too. This has stimulated the
present research.
2. Theoretical analysis and results
Let us consider an asymmetric layered structure with different lengths of the components.
The basic equations [11] for strain tensor component S1 and electric and magnetic induction vectors
component D3 and B1 as functions of the x coordinate (X1 direction) can be written as follows (1).
S s T x d Ep p p p
1 11 1 31 3= +( ) *
D x d T x Ep p p p
3 31 1 33 3( ) ( ) *= +e (1)
B x q T x Hm m m m bias
1 11 1 11 1( ) ( )= +m
S x s T x q Hm m m m bias
1 11 1 11 1( ) ( ) .= +
Here s11
p, d31
p and ε33
p are the elastic compliance, piezoelectric coefficient, and dielectric permittivity
of piezoelectric, respectivegly; s11
m, q11
m and μ33
m are the elastic compliance, magnetostrictive coeffi-
cient and magnetic permeability of ferrite, respectively. H1
bias
is the applied bias magnetic field; E3
*,
the electric field equal to the applied one. The mechanical coupling between the phases is supposed
to be ideal.
Using the basic equation governing acoustic oscillations [12] and boundary conditions [11,
12], we get the expression for the strain vector (2)
u x
d h s L E q h s L H
k h L s kL
x
p p m p m m p m bias
p p m
p
( )
cos
*
=
+
æ
è
31 11 3 11 11 1
11 2
çççççç
ö
ø
÷÷÷÷÷
+
æ
è
ççççç
ö
ø
÷÷÷÷÷
æ
è
ççççç
ö
ø
÷÷÷÷÷÷
h L s kLm m p
m
11 2
cos
ssin .kx( ) (2)
The expression (2) is derived for the first time and defines completely the strain of the plate-
like sample due to converse ME interaction and different lengths of the plates. It takes into account
the inertia forces and back moving forces of both the phases. Then we place the obtained result to
the third equation of the set (1). The arising magnetic induction we obtain by averaging it.
The expression for the effective ME susceptibility, taking the above-mentioned average into
account, is given by (3).
a13
31 11 11
11
2
2*
sin
cos
=
æ
è
ççççç
ö
ø
÷÷÷÷÷
d h s L q k L
kL h L s k
p p m p m
m
m p p m LL h L s kLp
m m p
m
2 211
æ
è
ççççç
ö
ø
÷÷÷÷÷
+
æ
è
ççççç
ö
ø
÷÷÷÷÷
æ
è
ççççç
ö
ø
÷cos ÷÷÷÷÷÷
.
(3)
Fig. 1. Theoretical (3) frequency dependence of the L-T
real and imaginary parts of ME susceptibility of PZT-Ter-
fenol compound. The parameters for theory are:
s11
p = 15,3·10–12 m2/N, d31
p
= –175 pC/N;
s11
m = 45,4·10–12 m2/N; q11
m = 4500 м/А;
m11
62 2 10m = × -, Tm/A; Lm = 14 mm, Lp = 16 mm,
hm = 1,2 mm, hp = 2 mm, c = 8000 rad/s,
ρm = 9200 kg/m.
G.S. Radchenko, M.G. Radchenko / Converse magnetoelectricity in asymmetric ...
Functional Materials, 17, 3, 2010 373
The lengths of the plates being taken to be the same, our formula turns into (6) from [4] and
the model is analogous to [11]. To obtain the longitudinal coefficient α33
*, we have to substitute q31
m
for q11
m. It is usually much smaller than transversal due to the influence of demagnetization fields
created by the metal electrode surface currents. The attenuation can be regarded as a complex an-
gular frequency ω = 2πf+iχ.
We can also determine the effective dielectric response (4) which has another resonance fre-
quency.
e e33 3
2
2
3 33
31
2
1*
/
/
*( ) /= ¶
æ
è
çççççç
ö
ø
÷÷÷÷÷÷
¶ = -
( )
-
òL
D x dx E
d
p
L
L
p
p
ss
d h s k L
ks h L s kp
p p m
p
p p p m11
31
2
11
11 11
2
2
+
( )
æ
è
ççççç
ö
ø
÷÷÷÷÷
sin
cos LL h L s kLp
m m p
m
2 211
æ
è
ççççç
ö
ø
÷÷÷÷÷
+
æ
è
ççççç
ö
ø
÷÷÷÷÷
æ
è
ççççç
ö
ø
÷cos ÷÷÷÷÷÷
.
(4)
The dielectric response ε33
* consists of frequency-independent part (rigidly fixed sample) and
resonance dynamic part, which at f→0 transforms ε33
* into the low-frequency response at constant
stress.
It is impossible to divide the piezoelectric and magnetoelectric contributions to the strain
(both phases vibrate in the same manner). Thus, to calculate the effective converse piezoresponse,
we need to consider the strains in both the phases according to the average from the total strain.
The effective piezoelectric coefficient is determined by formula (5)
d
d h s L k L L k Lp p m p
m
m
p
31
31 11
2
2 2*
sin sin
=
æ
è
ççççç
ö
ø
÷÷÷÷÷
+
æ
è
ççççç
ö
ø
÷÷÷÷÷÷
æ
è
ççççç
ö
ø
÷÷÷÷÷÷
æ
è
ççççç
ö
ø
÷÷÷÷÷
+kL h L s kL h Lm p p m
p
m m
11 2
cos ss kLp
m
11 2
cos
.
æ
è
ççççç
ö
ø
÷÷÷÷÷
æ
è
ççççç
ö
ø
÷÷÷÷÷÷
(5)
The resonance frequencies are determined by assuming the denominators in (3-5) to zero
and are dependent on the elastic properties of both the phases and their volume densities and all
the dimensions. If the oscillations of the external electric field are at the resonance frequencies, the
sharp increase of induced magnetic induction (3), dynamic polarization (4), and mechanical vibra-
tions (5) will occur in the sample.
The physical nature of resonance frequency independence of other integral composite param-
eters in this work and in [4], in contrast to [11], consists in what follows. The magnetic field and
magnetic induction play opposite parts in the electromagnetic interactions in comparison with elec-
tric field and induction. This results, for example, in the absence of the average induced magnetic
Fig. 2. Theoretical (4) frequency dependence of the
real and imaginary parts of effective dielectric per-
mittivity ε33
* of PZT-Terfenol compound. The pa-
rameters for theory are the same as in Fig. 1.
Figure 3. Theoretical (5) frequency dependence of the
transversal real and imaginary parts of piezoelectric
coefficient d31
* of PZT-Terfenol compound. The param-
eters for theory are the same as in Fig. 1.
G.S. Radchenko, M.G. Radchenko / Converse magnetoelectricity in asymmetric ...
Functional Materials, 17, 3, 2010 374
field H inside the sample due to the converse effect. The ME voltage coefficient is determined in [11]
under open electric chain conditions (average D is equal to zero) as E/H comprises fields which play
physically opposite roles. Therefore, αE depends upon most of the integral parameters.
The attenuation can be regarded as a complex angular frequency ω = ω’+iχ. Here χ is the
attenuation parameter. So we also take into account the attenuation as it was done in [11] for
direct effect and in [4] for converse one. The resonant enhancements of the most important physi-
cal constants are shown in Figs. 1-3. All the considered effective constants show a large resonance
enhancement (both in real and imaginary parts). At low frequencies, the ME and other constants
are much lower and practically independent of the frequency.
3. Conclusion
So, in this work we have investigated and analyzed the converse magnetoelectric effect with-
in the frames of resonance theory. The considerable resonance enhancement of basic effective pa-
rameter in plate-like ME composites is shown. These results can help in designing of ME devices,
magnetostrictive and piezoelectric transducers, actuators, and other technical devices.
References
1. Y. M. Jia, S. W. Or, H. L. W. Chan et al., Appl. Phys. Lett. ,88, 242902 (2006).
2. W. Eerenstein, M. Wiora, J. L. Prieto et al., Nature Mater. Lett., 6, 348 (2007).
3. C. Popov, H. Chang, P. M. Record et al., J. Electroceram, 20, 53 (2008).
4. Y. K. Fetisov, V. M. Petrov, G. Srinivasan, J. Mater. Res., 22, 2074 (2007).
5. J. P. Zhou, W. Zhao, Y.-Y. Guo et al., J. Appl. Phys., 105, 063913 (2009).
6. X. Fang, N. Zhang, Z.L. Wang, Appl. Phys. Lett., 93, 102503 (2008).
7. Y.-M. Jia et al., Composites Sci. . Techn., 68, 1440 (2008).
8. Y. Wang et al., Appl. Phys. Lett., 93, 113503 (2008).
9. W. Y. Wong et al., J. Appl. Phys., 101, 09N508 (2007).
10. Y. Jia, H. Luo, S. W. Or et al., Chin. Sci. Bull., 53, 2129 (2008).
11. D. A. Filippov, Fiz. Tverd. Tela, 47, 1118 (2005).
12. G.S. Radchenko, J. Phys. D: Appl. Phys., 41, 155421 (2008).
Зворотна магнітоелектричність
в асиметричних магнітоелектричних
структурах
Г.С.Радченко, М.Г.Радченко
Розвинуто новий обчислювальний підхід до аналізу асиметричних магнітоелектричних
структур. Виявлено можливість значного підсилення основних ефективних параметрів
композиту. Подано повний опис акустичних та електромагнітних коливань у таких
структурах.
|