Supplementary Information
Electrically controlled non-volatile switching of magnetism in multiferroic
heterostructures via engineered ferroelastic domain states
Ming Liu1,2*, Tianxiang Nan3, Jia-Mian Hu4, Shi-Shun Zhao1, Ziyao zhou1, Chen-Ying Wang2,5,
Zhuang-De Jiang2,5, Wei Ren,1,2 Zuo-Guang Ye,1,2,6 Long-Qing Chen,3 and Nian X. Sun1,3*
1. Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education &
International Center for Dielectric Research, Xi’an Jiaotong University, Xi’an 710049, China
2. Collaborative Innovation Center of High-End Manufacturing Equipment, Xi'an Jiaotong
University, Xi'an,710049, China
3. Electrical and Computer Engineering Department, Northeastern University, Boston, MA 02115,
USA
4. Department of Materials Science and Engineering, Pennsylvania State University, University
Park, Pennsylvania, 16802, USA
5. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University,
Xi’an, 710049, China
6. Department of Chemistry and 4D LABS, Simon Fraser University, Burnaby, British
Columbia,V5A 1S6, Canada
*Corresponding-Authors [email protected], [email protected]
Keywords: Multiferroics, Magnetoelectric coupling, Non-volatile switching
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1. Ferroelectric/ferroelastic domain switching pathways in a PZN-7%PT single crystal
in a rhombohedral Pb(Zn1/3Nb2/3)O3-xPbTiO3 (PZN-PT, x=0.07) single crystal, there are eight
possible polarization directions pointing along the body diagonals of the pseudocubic unit cell,
which correspond to the four structural (ferroelastic) domains (r1, r2, r3, and r4), as shown in the
schematics in the Figure S1. When the polarization is switched by applying an electric field along
the [00-1] direction (Fig. S1a), the rhombohedral PZN-PT can either locally preserve the
ferroelastic state (r1+/r1-) with its electric polarization undergoing a 180o ferroelectric switching to
be antiparallel to the original one or change to a different ferroelastic state (71o or 109o ferroelastic
switching from r1+ to r3- or from r1+ to r2-/r4-) with a different strain state. Analysis of these
ferroelastic domain states suggests that only 109o polarization switching leads to a strong lattice
strain along the diagonal direction in the (001) plane. Such a ferroelectrically coupled ferroelastic
switching will result in a non-volatile tuning of magnetic properties in the mechanically-coupled
magnetic films deposited onto the (001)-oriented PZN-PT crystal. Therefore, to achieve a
homogeneous and dramatically enhanced non-volatile ME coupling, the 180o and 71o polarization
reversals should be avoided. On the other hand, in a (011)-oriented single crystal PZN-PT substrate,
if an electric field is applied in the [0-1-1] direction (Fig. S1b), the polarization switching pathways
include 71o ferroelastic switching from r1+ to r3+/r4-, 109o ferroelastic switching from r1+ tor 3-/r4+
and 180o ferroelectric switching from r1+ to r1-. Based on the analysis of the rhombohedral
distortions, only the 71o ferroelectric/ferroelastic switching contributes to a strong lattice strain
along the [011] and the in-plane [100] directions, during which the electric polarization flips
between the out-of-plane and the in-plane directions. Upon further increasing the electric field, the
PZN-PT (011) single crystal may undergo a phase transition from the rhombohedral to the
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orthorhombic symmetry, resulting in a remarkable lattice strain along the [011] direction, as shown
in Fig. S1c. Such field-induced phase transition is reversible and is expected to display a hysteresis
loop of the lattice strain as a function of the applied field.
Figure S1. Schematics of the electric field-induced ferroelectric/ferroleastic domain switching
pathways (a,b) and ferroelectric/ferroelastic phase transition (c) in the (001)- and (011)-oriented
PZN-PT single crystal substrates.
Figure S2 shows the comparison of the RSM patterns in the vicinity of the (1-13) reflection
upon applying various electric fields along the [001] direction of PZN-PT. Analysis of the RSM
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patterns suggests that the PZN-PT substrate holds three domains of r1, r2, r4 when the sample was
poled positively. Upon applying a negative (along [00-1]) field of -8 kV cm-1 and switching it off,
the polarization flips from the upward to downward directions, exhibiting different RSM patterns.
An additional high intensity reflection spot, corresponding to the r3 domain state, appears,
suggesting two possible domain switching pathways from r1+ to r3- (71o polarization reversal) and
from r2+/r4+ to r3- (109o polarization reversal). According to the lattice parameters of the
rhombohedral distortion in (001) oriented PZN-PT, we firstly calculated the spots distribution in
the (1-1 3) reflection, indicating all possible ferroelectric domain switching. Then, the intensity
for each spot in RSM results has been integrated and overall intensity ratios among these spots
have been achieved. By comparing calculated spot intensity distribution with experimental results
, one can quantitatively determine the domain switching category and the possibility.[1,2] Analysis
results shows that 109o ferroelastic switching (from r1+ to r2-/r4- or from r2+/r4+ to r3-/r1-) takes
place in up to 23% of the entire probed area.
Figure S2. The schematic domain structures and the RSM patterns in the vicinity of the (1-13)
reflection of PMN-PT (001) under various poling states.
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Figure S3 shows the polarization switching pathways in the (011)-oriented PZN-PT by observing
the changes in RSM patterns in the (222) reflection under various poling states. With applying
proper electric fields, the electron polarization can be switched between the in-plane and out-ofplane directions, resulting in a non-volatile tuning of magnetism. Analysis of (022) and (222) RSM
patterns suggests the ferroelastic domain switching (71o) occupies 80% of entire probed area.
Figure S3. The schematic domain structures and the RSM patterns in the vicinity of the (222)
reflection of PMN-PT (011) under various poling states.
Figure S4 shows the electric field dependence of the RSMs in the vicinity of the (002) and (222)
reflections. The coexistence of R and O phase are also observed in (002) and (222) reflections.
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Figure S4. The schematic domain structures and the RSM patterns in the vicinity of the (002) and
(222) reflections of PMN-PT (011) under various poling states.
2. Quantitative determination of the voltage-induced effective magnetic anisotropy through
the FMR measurements in multiferroic heterostructures
The voltage-induced effective magnetic anisotropic field can be quantitatively determined by
measuring the shift of the in-plane ferromagnetic resonance (FMR) field. This can be interpreted
by the Kittel equations: 𝑓 = 𝛾√(𝐻𝑟 + 𝐻𝑒𝑓𝑓 )(𝐻𝑟 + 𝐻𝑒𝑓𝑓 + 4𝜋𝑀𝑠 ) ,
where f is the magnetic resonance frequency in MHz, γ is the gyromagnetic ratio of 2.8 MHz Oe-1,
Hr is the magnetic resonance field, and Heff is the voltage-induced effective magnetic anisotropic
field along the external magnetic field direction. In field-sweeping mode, where the frequency is
fixed, by observing the change in the resonance field Hr at different electrical fields, the voltageinduced effective magnetic field Heff can be quantitatively determined as Heff=ΔHr.
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In our experiments, an X-band (9.3 GHz) Electron Paramagnetic Resonance system was used for
FMR measurements as shown in Fig. S2. The sample was placed in a rectangular cavity working
at TE102 mode. External magnetic fields were applied in the (001) or (011) plane. An electric field
was applied along the thickness direction of the sample.
Figure S5. FMR measurement set up with the FeGaB/PZN-PT multiferroic heterostructure placing
inside the microwave cavity.
3. Electric field manipulation of the magnetic resonance spectra in FeGaB/PZN-PT (001)
and FeGaB/PZN-PT (011) multiferroic heterostructures
The ferromagnetic resonance spectroscopy in the field sweep mode was performed on FeGaB
on PZN-PT (001) and PZN-PT (011) substrates at different electric field configurations. Fig. S3 (a)
shows the electric impulse-induced changes in ferromagnetic resonance fields in the FeGaB/PZNPT (001) heterostructrure. The external magnetic field was applied along the [-110] direction of the
PZN-PT which is parallel to the induced magnetic easy axis. The resonance field was shifted by up
to ~60Oe with the application of electric impulse of -8 kV/cm and +6kV/cm. This observation
corresponds to the 109o ferroelastic/ferroelectric domain switching-induced non-volatile lattice
strain.
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In the FeGaB/PZN-PT(011) heterostructure, the external magnetic field was along the [0-11]
direction. As shown in Fig. S3(b), when a negative electric impulse was applied, the polarization
of PZN-PT pointed downward, and a ferromagnetic resonance field of ~680 Oe was obtained. Upon
applying a positive electric impulse of 2.5 kV cm-1, the polarization underwent a 71o switching
from the out-of-plane to the in-plane direction, coupled to the 71o ferroelastic domain switching,
which induced a strong lattice strain along the [0-11] direction and shifted the ferromagnetic
resonance field to ~810 Oe.
Fig. S3 (c) shows the ferroelectric/ferroelastic phase transition-induced ferromagnetic resonance
field shifting. The resonance magnetic field slightly increases upon applying an electric field of 5
kV cm-1 with the external magnetic field applied along the [100] direction. This is due to the linear
piezoelectric effect of the PZN-PT in the rhombohedral phase that produces a compressive strain
along the [100] direction and a tensile strain along the [0-11] direction of PZN-PT, resulting in a
magnetic hard axis in the [100] direction. With further increase of the applied electric field to 7 kV
cm-1, an induced structural phase transition takes place and the PZN-PT is in orthorhombic phase
which results in a strong lattice strain in the [011]-direction. A significant increase in the
ferromagnetic resonance field by 400 Oe was achieved.
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Figure S6. Electric field dependence of ferromagnetic resonance spectra for FeGaB/PZN-PT(001)
(a) and FeGaB/PZN-PT(011) (b).
4. Electric field modulation of magnetic hysteresis loops in FeGaB/PZN-PT(011)
Normalized magnetic hysteresis loops of the FeGaB/PZN-PT(011) heterostructure at different
electric fields shown in Fig. S4 were characterized by a commercial vibrating sample magnetometer
at room temperature. The external magnetic field is applied along the [100] direction. When an
electric field of 7 kV cm-1 was applied, the remnant magnetization dramatically reduced, indicating
a strain-induced magnetic hard axis along the [100] direction. This is due to the electric fieldinduced rhombohedral to orthorhombic ferroelectric/ ferroelastic phase transition, which results in
a strong lattice strain in the [011] direction.
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Figure S7. Magnetic hysteresis loops of the FeGaB/PZN-PT(011) heterostructure measured at
different electric fields.
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5. Investigating the influence of cell size on the magnetization dynamics
Figure S8. Temporal evolution of the average normalized magnetization component <mi>
(i=x,y,z) in the systems of 256Δx × 256Δy × 60Δz (Δx=Δy3.91 nm), 300Δx × 300Δy × 60Δz
(Δx=Δy3.33 nm), 333Δx × 333Δy × 60Δz (Δx=Δy3 nm), and 500Δx × 500Δy × 60Δz (Δx=Δy=2
nm). An identical system size of 1 μm × 1 μm × 120 nm can therefore be achieved by setting
Δz=2 nm in all the testing cases. All simulations start from an initial uniform magnetization
distribution along the [100] direction, upon the application of a static, uniform, 200-Oe-magnetic
field along the [010] direction.
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Co40Fe40B20/Pb(Mg1/3Nb2/3)0.7Ti0.3O3 Structure at Room Temperature. Phys Rev Lett 108,
137203 (2012). doi: 10.1103/PhysRevLett.108.137203
2. Baek, S et al. Ferroelastic switching for nanoscale non-volatile magnetoelectric devices,
Nat. Mater. 9, 309. (2010)
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