Observation of uniaxial strain tuned spin cycloid in a freestanding BiFeO 3ﬁlm Zhe Ding1 2 3Yumeng Sun1 2 3Ningchong Zheng4 5 6 7Xingyue Ma4 5 6 7 Mengqi Wang1 2 3Yipeng Zang4 5 6 7Pei Yu1 2 3Pengfei Wang1 2 3Ya Wang1 2 3

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Observation of uniaxial strain tuned spin cycloid in a freestanding BiFeO3ﬁlm

Zhe Ding,1, 2, 3, ∗Yumeng Sun,1, 2, 3, ∗Ningchong Zheng,4, 5, 6, 7, ∗Xingyue Ma,4, 5, 6, 7, ∗

Mengqi Wang,1, 2, 3 Yipeng Zang,4, 5, 6, 7 Pei Yu,1, 2, 3 Pengfei Wang,1, 2, 3 Ya Wang,1, 2, 3

Yurong Yang,4, 5, 6, 7, †Yuefeng Nie,4, 5, 6, 7, ‡Fazhan Shi,1, 2, 3, 8 and Jiangfeng Du1, 2, 3, §

1CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences,

University of Science and Technology of China, Hefei 230026, China

2CAS Center for Excellence in Quantum Information and Quantum Physics,

University of Science and Technology of China, Hefei 230026, China

3Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China

4National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

5Jiangsu Key Laboratory of Artiﬁcial Functional Materials, Nanjing University, Nanjing 210093, China

6College of Engineering and Applied Science, Nanjing University, Nanjing 210093, China

7Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

8School of Biomedical Engineering and Suzhou Institute for Advanced Research,

University of Science and Technology of China, Suzhou 215123, China

Non-collinear spin order that breaks space inversion symmetry and allows eﬃcient electric-ﬁeld

control of magnetism makes BiFeO3a promising candidate for applications in low-power spintronic

devices[1–4]. Epitaxial strain eﬀects have been intensively studied and exhibit signiﬁcant modulation

of the magnetic order in BiFeO3[5,6], but tuning its spin structure with continuously varied uniaxial

strain is still lacking up to date. Here, we apply in situ uniaxial strain to a freestanding BiFeO3ﬁlm

and use scanning NV microscope to image the nanoscale magnetic order in real-space. The strain is

continuously increased from 0% to 1.5% and four images under diﬀerent strains are acquired during

this period. The images show that the spin cycloid tilts by ∼12.6◦when strain approaches 1.5%.

A ﬁrst principle calculation has been processed to show that the tilting is energetically favorable

under such strain. Our in situ strain applying method in combination with scanning NV microscope

real-space imaging ability paves a new way in studying the coupling between magnetic order and

strain in BiFeO3ﬁlms.

Antiferromagnetic material is robust against external

magnetic ﬁeld disturb, has super-fast spin dynamics and

possesses large magneto-transport eﬀects. Due to the

merits above, antiferromagnetic materials have impor-

tant application in spintronics and other magnetism-

based techniques [7]. Although it is a promising mate-

rial, because of its anti-parallel spin conﬁguration which

leads to zero stray-ﬁeld, antiferromagnetic material can-

not be well studied by normal near-ﬁeld imaging tech-

niques [8]. Non-collinear antiferromagnetic perovskite

compound bismuth ferrite (BiFeO3, BFO) is the only

magnetoelectric multiferroic material under room tem-

perature. Since the non-collinear spin cycloid breaks spa-

tial inversion symmetry, it can be controlled by external

electric ﬁeld and thus costs much less energy compar-

ing to ordinary ferromagnetic devices [8]. BFO owns

spin cycloid because of the Dzyaloshinskii–Moriya in-

teraction (DMI), such cycloid induces an eﬀective mag-

netization which is too weak to detect with normal

methods such as MFM[9] and PEEM[10]. At the same

time, since BFO has ∼2.7eV bandgap[11], sp-STM also

lacks the ability to perform imaging. Scanning NV mi-

croscopy (SNVM) is an emergent real-space scanning

∗These authors contributed equally to this work.

†yangyr@nju.edu.cn

‡ynie@nju.edu.cn

§djf@ustc.edu.cn

method with nanoscale spatial resolution and µT/√Hz

magnetic sensitivity[12,13]. People have utilized SNVM

to study the magnetic structure of BFO epitaxial ﬁlms

at nanoscale [6,8,14].

BFO is a kind of perovskite compound while fulﬁlls

noncentrosymmetric rhombohedral R3cspace group[16].

The structure of BFO is shown in ﬁgure 1(c), for the

sake of brevity, we adopt pseudo-cubic unit cell. In each

unit cell, bismuth atoms are at eight corners, while at

the center lays the iron atom contained by an octahe-

dron constructed by six oxygen atoms. The ferroelectric

Curie temperature of BFO is 1103 K[17,18], below which

the ferroelectric polarization is as high as 100 µC/cm2in

high quality grown ﬁlms [19,20]. The antiferromagnetic

order of BFO is characterized as G-type, with N´eel tem-

perature TN= 683 K [21]. 3d electrons of Fe3+ are the

origin of magnetism of BFO, while ferroelectricity and

antiferrodistortive break the spatial inversion symmetry

which gives rise to a DMI. This interaction leads to a

small canting angle between neighbor spins and this pro-

duces an eﬀective spin density as large as 0.02 µBper unit

cell [8,22]. Under proper conditions, spin distribution in

BFO will turn cycloidal, which is an incommensurable

periodic order. A cycloidal order can be described by a

wave vector k, as indicated in ﬁgure 1(c). The magnetic

order of BFO is decided by external ﬁeld, strain, temper-

ature, size and more factors, while the eﬀect of strain has

been intensively studied[5,6,23–26]. Previous works uti-

lized diﬀerent substrates to adjust the epitaxial strain in

arXiv:2210.09548v1 [cond-mat.mtrl-sci] 18 Oct 2022

LaserPhoton

NV probe









 

 











2795 2800 2805 2810 2815 2820

Frequency (MHz)

-0.09

-0.05

(a) (b)

(c)

(d)

Strain

Ferroelectric polarization

Figure 1. Principle of the experiment. (a) The sketch of an SNVM setup. An NV is at the tip of the probe while its structure

is shown in the inset. Under the NV probe, blue and red ball array stands for the antiferromagnetic material imaged during

the experiment. Continuous uniaxial strain (blue two-way arrow) is applied in situ with an organic substrate (not shown in the

sketch). (b) The energy level structure of an NV center. (c) The structure of a BFO pseudo-cubic unit cell. The ferroelectric

state has been polarized along [111] beforehand (brown arrow) and the uniaxial strain (blue two-way arrow) is applied along

[110], which is paralleled to the polarization’s projection to the plane. Possible cycloidal wave vectors (light red arrows) in

bulk BFO are along face diagonals perpendicular to ferroelectric polarization. (d) The demonstration of dual-iso-B protocol.

CW-ODMR data are collected at two frequencies (f1,2) [15].

BFO and found two types of cycloidal order[5,6]. While

these researches provide the phase diagram of BFO mag-

netic order with respect to epitaxial strain, they are not

able to impose adjustable strain to BFO in situ and this

leaves the mechanism of BFO magnetic transformation at

critical point an outstanding open question [5,6,16]. Be-

sides, previous researches mainly focus on biaxial strain

while real-space imaging of magnetic structure under uni-

axial strain has not yet been performed.

In this work, we adopt a new method base on molec-

ular beam epitaxy (MBE) to prepare freestanding BFO

ﬁlm[20,27]. A 75-unit-cell-thick BFO (001) ﬁlm is pre-

pared and transferred to organic substrate Polyethyle-

nenaphthalate(PEN) while epoxy is used as the glue to

conduct strain to the BFO ﬁlm. During experiments,

uniaxial, continuous and in situ strain is imposed

on the BFO ﬁlm by means of mechanically stretching the

PEN substrate [28,29]. In principle, this method is able

to impose arbitrary in-plane tensile strain on the ﬁlm,

while in this work the strain principal axis deviates from

[110] by ∼4.7◦. Such strain breaks the intrinsic R3c

symmetry of BFO and provide a way to tune the spin

cycloid’s direction continuously. A home-built SNVM is

used to perform nanoscale magnetic imaging of its stray

ﬁeld. By using this method, we ﬁnd that the direction

of the cycloidal order is modulated by the uniaxial strain

which conﬁrms to a ﬁrst principle calculation. This phe-

nomenon may help people understanding the transition

mechanism of magnetic order under strain[5,16] whilst

the freestanding ﬁlm based method can be used in strain-

based spintronics, new heterostructure devices and other

new multifunctional devices [20,28,29]. Our new free-

standing ﬁlm based method in combination with SNVM

real-space imaging ability paves a new way to study

strain-magnetism coupling in antiferromagnetic materi-

als.

SNVM has been widely used in condensed matter

physics[30–35], here we apply SNVM to the freestand-

ing BFO ﬁlm to acquire stray ﬁeld distribution near the

surface. The structure of our SNVM setup is demon-

strated in ﬁgure 1(a). The Nitrogen-Vacancy color cen-

ter (NV center) in diamond is a point defect shown in

the inset. It is formed by a nitrogen atom (orange ball

in the inset) and an adjacent vacancy (blue ball in the

inset) in diamond lattice [36]. As shown in ﬁgure 1(b),

the NV center is pumped from ground state (3A2) into

phonon sideband by 532 nm green laser (green arrows)

and relaxes into excited state (3E) with angular momen-

tum conserved (grey arrows). |mS= 0iemits photons

(wavy red arrow) during the transition to ground state

0.0% 0.7% 1.3% 1.5% Uniaxial strain

[110]

1.0

-1.0

(a) (d)

(c)

(b)

(e)

[110]

(f) (i)

(h)

(g)

Figure 2. Spin cycloid variation in real-space during the increasing of strain. (a-d) Images of stray ﬁeld Bpunder diﬀerent

strains. The white scale bar corresponds to 500 nm, a direction reference of [110] and [110] is displayed to the right. Yellow

boxes highlight a local transition of the spin cycloid. (e) The sketch of applied strains corresponding to stray ﬁeld images above.

(f-i) Wave vector direction in real-space under diﬀerent strains. The white scale bar corresponds to 500 nm. The fan-shaped

colorbar demonstrates the wave vector direction under the frame displayed by green and red arrows below.

and the photons are ﬁnally detected by a single photon

detector. |mS=±1ievolves into ground state through

meta-stable states (1A1,1E) with no detectable photon

emitted (black dotted line arrows). The degeneracy of

|mS=±1iis lifted by Zeeman splitting generated by

external magnetic ﬁeld (γeBp) and resonant microwave

(MW, orange circled arrow) is applied by a copper micro-

antenna to selectively excite one of the spin states. By us-

ing the photon count rate’s diﬀerence between |mS= 0i

and |mS=±1i, it is straight forward to readout the NV

center’s spin state.

In our experiment, by applying green laser and MW

simultaneously and readout the photon counts, we uti-

lize the Continuous Wave Optically Detected Magnetic

Resonance (CW-ODMR) spectrum. In order to acceler-

ate the imaging speed, we adopt the dual-iso-B protocol

shown in ﬁgure 1(d) [8]. Applying this protocol, by sam-

pling at two MW frequencies, we are able to calculate

the projection of the stray ﬁeld to the NV axis[15]. By

scanning across a magnetic ﬁlm edge, we determine that

the distance from the NV center to sample surfaces is

78.5±1.8 nm (with 95% conﬁdence) [15,37,38].

Beforehand, a piezoelectric force microscope (PFM) is

utilized to electrically polarize an area of the BFO ﬁlm

to [111][15]. During the experiment, a uniaxial strain

is applied to the BFO ﬁlm via the PEN substrate. By

employing X-ray diﬀraction (XRD) after the experiment,

we are able to calibrate strains under which the images

are acquired [15].

SNVM imaging is implemented under four diﬀerent

strains: = 0.0%,0.7%,1.3%,1.5%, the results are

shown in ﬁgure 2. The principal axis of strain deviates

from high symmetry direction [110] by 4.7◦, which breaks

R3csymmetry and leads to cycloid tilting. From the

real-space imaging one can ﬁnd that although the coher-

ence length is relatively small, the sample does possess

local cycloidal order, which is modulated by the increas-

ing uniaxial strain. We attribute this small coherence

length to in-homogeneous strain gradient introduced by

epitaxial interface [39]. Be aware that we are using a

novel, organic and soft substrate in combination with a

freestanding ﬁlm to realize in situ strain tuning. With-

out rigid constraint from crystal substrates, freestanding

ﬁlms possess intrinsic unevenness, which may also lead

to the small coherence length [28]. Despite the relatively

small coherence length, spin cycloid’s variation during

the increasing of strain is rather distinct. We calculate

the direction of cycloidal wave vector by minimizing vari-

ances on segments parallel to diﬀerent directions and ap-

ply region growing algorithm to the results to acquire

wave vector direction domain image plotted in ﬁgure 2(f-

i). It is evident that during the application of strain, the

wave vector tilts away from [110].

Be aware that the applied strain also modulates local

distribution of the magnetic order, there are plural non-

trivial local transitions while the applied strain increases.

For example, by retracing with respect to tomography

markers and magnetic patterns, we are able to deter-

mine that the boxed areas in ﬁgure 2are at the same

spot[40]. Two diﬀerent ordered areas at this spot merge

into one when strain approaches 1.5%. This phenomenon

is interpreted as the release of local strain gradient under

external strain.

We have acquired a qualitative result that during the

application of strain, the wave vector tilts away from

[110]. In order to obtain quantitative relation between

the tilting angle and strain, we apply Fourier transfor-

mation (FT) to the initial and ﬁnal real-space scanning

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ObservationofuniaxialstraintunedspincycloidinafreestandingBiFeO3lmZheDing,1,2,3,YumengSun,1,2,3,NingchongZheng,4,5,6,7,XingyueMa,4,5,6,7,MengqiWang,1,2,3YipengZang,4,5,6,7PeiYu,1,2,3PengfeiWang,1,2,3YaWang,1,2,3YurongYang,4,5,6,7,yYuefengNie,4,5,6,7,zFazhanShi,1,2,3,8andJiangfengDu1,2,3,x1CASKe...

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Observation of uniaxial strain tuned spin cycloid in a freestanding BiFeO 3ﬁlm Zhe Ding1 2 3Yumeng Sun1 2 3Ningchong Zheng4 5 6 7Xingyue Ma4 5 6 7 Mengqi Wang1 2 3Yipeng Zang4 5 6 7Pei Yu1 2 3Pengfei Wang1 2 3Ya Wang1 2 3.pdf

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Observation of uniaxial strain tuned spin cycloid in a freestanding BiFeO 3ﬁlm Zhe Ding1 2 3Yumeng Sun1 2 3Ningchong Zheng4 5 6 7Xingyue Ma4 5 6 7 Mengqi Wang1 2 3Yipeng Zang4 5 6 7Pei Yu1 2 3Pengfei Wang1 2 3Ya Wang1 2 3

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