Supplementary information
Thermally assisted electric field control of magnetism in flexible multiferroic
heterostructures
Yiwei Liu1, Qingfeng Zhan1, Guohong Dai1, Xiaoshan Zhang1, Baomin Wang1, Gang Liu1,
Zhenghu Zuo1, Xin Rong1, Huali Yang1, Xiaojian Zhu1, Yali Xie1, Bin Chen1 & Run-Wei Li1
1Key
Laboratory of Magnetic Materials and Devices & Zhejiang Province Key Laboratory of Magnetic
Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering
(NIMTE), Chinese Academy of Sciences (CAS), Ningbo 315201, People’s Republic of China.
1
Intensity (arb. units)
1. Crystalline structure of PVDF
phase PVDF
14 16 18 20 22 24 26 28 30
 (deg)
Figure S1︱X-Ray diffraction pattern of PVDF membrane.
2
2. Calculations of the interfacial coupling factor
z
y
a
L
Y
tp
ta/2
PVDF
b
Y1
ta/2
c
Al/PVDF/Al
Y2
tf
FeGa/Al/PVDF/Al
Figure S2︱Schematic show of the expansion of (a) PVDF membrane, (b) PVDF membrane
coated with Al electrodes on both sides, and (c) FeGa layer deposited on Al/PVDF/Al
membrane along the y direction when decreasing temperature.
When decreasing a temperature, due to the effect of thermal expansion, PVDF
membrane is elongated along the y direction with a displacement of Y, as shown in Figure S2a.
In contrast, when reducing the same temperature for a PVDF coated with Al electrodes on
both sides, due to the clamping effect of Al layers on PVDF, the thermal expansion is reduced
3
a length of Y1, as revealed in Figure S2b. The stress equilibrium of Al/PVDF/Al requires the
balance of force, therefore, we can have the equation
EptpY1/L=Eata(Y-Y1)/L,
(1)
where tp is the thickness of PVDF, ta is the total thickness of the two Al electrodes, Ep and Ea
are the Young’s moduli of PVDF and Al, respectively. For a FeGa layer deposited on
Al/PVDF/Al membrane, the thermal expansion is further reduced a length of Y2, as exhibited
in Figure S2c. The equation of stress equilibrium for FeGa/Al/PVDF/Al can be written as
(Eptp+Eata)Y2/L=Eftf(Y-Y1-Y2)/L,
(2)
where tf is the thickness of FeGa, Ef is the Young’s modulus of FeGa.
The interfacial coupling factor kc is defined as the ratio of the thermal expansion of
FeGa/Al/PVDF/Al to that of a free PVDF. We therefore obtain
kc = (Y-Y1-Y2)/Y =
E pt p
E p t p  Ea t a  E f t f
.
(3)
It is noted that since the thickness of the Au capping layer is 5 nm, we did not take into
account the clamping effect of Au layer in this calculations.
4
3. Coercive fields of FeGa/PVDF film at different temperatures
0.3
M (memu)
0.2
280K
320K
0.1
0.0
-0.1
Hc (320 K)=44 Oe
-0.2
Hc (280 K)=27 Oe
-0.3
-150
-100
-50
0
 (Oe)
50
100
150
Figure S3︱ In-plane magnetic hysteresis loops of FeGa/PVDF film measured along the x
direction at 280 and 320 K.
It should be noted that the coercivity of FeGa films depends on the time scale of
measurement [Sharrock, M. P. Time dependence of switching fields in magnetic recording
media. J. Appl. Phys. 76, 6413 (1994)]. As compared to the hysteresis loops measured within
10 min, the cooling M-T curve shown in Figure 2b is measured in a large time scale of 120
min, which significantly reduces the coercive fields and therefore leads to the appearance of
negative magnetization in the cooling M-T curve.
5
4. Temperature dependence of spontaneous magnetization of FeGa/Si film
0.185
memu
0.180
0.175
H=0 Oe
H=400 Oe
0.170
0.165
280
290
300
310
320
T (K)
Figure S4︱Temperature dependence of magnetization for the 60 nm FeGa film grown on Si
measured at 0 and 400 Oe.
6
5. Remanent magnetization as a function of electric field applied on PVDF
1.0
T=291 K
Mr/Ms
0.8
o
=0
o
=90
0.6
0.4
-300
-200
-100
0
100
200
300
E (kV/cm)
Figure S5︱ The Mr/Ms ratio of FeGa/PVDF film measured with field orientations of θ=0o
and θ=90o at 291 K, when applying on PVDF an electric field ranging from -267 to 267 kV
cm-1.
7