Strain engineering of the magnetic multipole moments and anomalous Hall effect in pyrochlore iridate thin films
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SCIENCE ADVANCES | RESEARCH ARTICLE
MATERIALS SCIENCE Copyright © 2020
The Authors, some
Strain engineering of the magnetic multipole rights reserved;
exclusive licensee
moments and anomalous Hall effect in pyrochlore American Association
for the Advancement
iridate thin films of Science. No claim to
original U.S. Government
Works. Distributed
Woo Jin Kim1,2*, Taekoo Oh1,2,3*, Jeongkeun Song1,2, Eun Kyo Ko1,2, Yangyang Li1,2, under a Creative
Junsik Mun4, Bongju Kim1,2, Jaeseok Son1,2, Zhuo Yang5, Yoshimitsu Kohama5, Commons Attribution
Miyoung Kim4, Bohm-Jung Yang1,2,3, Tae Won Noh1,2† NonCommercial
License 4.0 (CC BY-NC).
The recent observation of the anomalous Hall effect (AHE) without notable magnetization in antiferromagnets
has suggested that ferromagnetic ordering is not a necessary condition. Thus, recent theoretical studies have
proposed that higher-rank magnetic multipoles formed by clusters of spins (cluster multipoles) can generate
the AHE without magnetization. Despite such an intriguing proposal, controlling the unconventional AHE by
inducing these cluster multipoles has not been investigated. Here, we demonstrate that strain can manipulate the
hidden Berry curvature effect by inducing the higher-rank cluster multipoles in spin-orbit–coupled antiferromagnets.
Observing the large AHE on fully strained antiferromagnetic Nd2Ir2O7 thin films, we prove that strain-induced
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cluster T1-octupoles are the only source of observed AHE. Our results provide a previously unidentified pathway
for generating the unconventional AHE via strain-induced magnetic structures and establish a platform for ex-
ploring undiscovered topological phenomena via strain in correlated materials.
INTRODUCTION easily coupled to both magnetic and electric fields (13), it is very
The anomalous Hall effect (AHE) is a fundamental transport phe- difficult to manipulate the higher-rank cluster multipoles. This
nomenon that has been universally observed in time-reversal sym- imposes substantial limitations on controlled experiments on the
metry broken systems. AHE can arise from two different forms of cluster multipoles and associated AHE.
mechanism (1): extrinsic mechanism, such as skew scattering or Here, we demonstrate that the strain can generate the AHE by
side jump due to magnetic impurities, and intrinsic mechanism inducing the higher-rank cluster multipoles, by using antiferro-
originating from Berry curvature in momentum space. Since the magnetic Nd2Ir2O7 (NIO) thin film. Further investigation reveals
fundamental topological properties of electronic wave functions are that biaxial strain on the pyrochlore lattice can modulate the spin
encoded in the Berry curvature, AHE is considered as a powerful structure and induce certain magnetic octupoles. The induced cluster
tool for probing the topological properties of materials (2, 3). In addi- octupoles can generate the net Berry curvature effect hidden in the
tion to its fundamental interest, AHE can be applied for memory bulk, leading to a finite AHE. We expect that our method could be
devices (4). widely applied to other spin-orbit–coupled topological magnets (10)
Conventionally, AHE has been observed mostly in itinerant and antiferromagnetic spintronics (4, 14).
ferromagnets. Its magnitude is known to be proportional to the
magnetization (5), which is a measure of broken time-reversal symmetry.
Recently, a large AHE has been unexpectedly found in noncollinear RESULTS
antiferromagnets, such as Mn3X (X = Sn, Ge) (6–8) and GdPtBi (9), Strain-induced cluster multipoles in a pyrochlore lattice
which do not exhibit spontaneous magnetization. This unconventional The NIO belongs to the pyrochlore iridates family, R2Ir2O7 (R, rare-
response indicates that ferromagnetism is not a necessary condition earth ions). The members of the family are geometrically frustrated
for AHE and suggests a possible alternative origin of AHE. A recent magnets with complex lattice structures. As shown in Fig. 1A,
theory proposed that higher-rank magnetic multipole (cluster R2Ir2O7 is composed of linked tetrahedrons with R and Ir at each
multipole) moments formed from spin clusters in antiferromagnet vertex. In R2Ir2O7, strong electron correlations and large spin-orbit
can induce a nonzero AHE, beyond the conventional dipoles of ferro- coupling of Ir d electrons result in unique antiferromagnetic spin
magnets (10). Subsequently, the anomalous Nernst (11) and structures, called all-in-all-out (AIAO) ordering (15, 16). As shown
magneto-optical Kerr effects (12) in Mn3Sn have also been attributed in the circle in Fig. 1B, the spins in one tetrahedron point inward
to its cluster octupoles. However, since antiferromagnets are not and those in the neighboring tetrahedron point outward. The Néel
temperatures of the Ir and Nd sublattices of bulk NIO are TIrN ~ 30 K
(15) and TNd
N ~ 15 K (17), respectively. This AIAO ordering breaks
1
Center for Correlated Electron Systems, Institute for Basic Science, Seoul 08826, the time-reversal symmetry, allowing a nonzero Berry curvature
Republic of Korea. 2Department of Physics and Astronomy, Seoul National University,
Seoul 08826, Republic of Korea. 3Center for Theoretical Physics (CTP), Seoul National
distribution and generating correlated topological phases (18, 19)
University, Seoul 08826, Republic of Korea. 4Department of Materials Science and such as a Weyl semimetal.
Engineering and Research Institute of Advanced Materials, Seoul National University, However, since AIAO ordering preserves the cubic crystalline
Seoul 08826, Republic of Korea. 5Institute for Solid State Physics, The University of symmetry, the net Berry curvature effect vanishes when we integrate
Tokyo, Kashiwa, Chiba 277-8581, Japan.
*These authors contributed equally to this work. over the Brillouin zone (BZ). Unless the cubic crystalline symmetry
†Corresponding author. Email: twnoh@snu.ac.kr is broken, AHE cannot be observed in this system. To break the
Kim et al., Sci. Adv. 2020; 6 : eabb1539 15 July 2020 1 of 7
SCIENCE ADVANCES | RESEARCH ARTICLE
A B
C
octupole
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D
octupole
Fig. 1. The strain engineering concept used to induce magnetic multipoles in a pyrochlore lattice. (A) Pyrochlore lattice structure. Yellow (red) circles depict Nd (Ir)
ions. Note that oxygen ions are not shown. (B) Schematic diagram of epitaxial NIO thin film on the yttria-stabilized zirconia (YSZ) substrate with biaxial strain along [111].
The deformed pyrochlore lattice is schematically displayed in the circle. The blue arrow at each site denotes the spin direction in the AIAO antiferromagnetic configuration.
(C) The spin arrangement of a tetrahedron in the undistorted (i.e., bulk) AIAO configuration. According to the cluster magnetic multipole theory, the AIAO magnetic
ordering can be represented as an A2-octupole. (D) Schematic diagram of the strained magnetic ground state. Biaxial strain along the [111] direction will distort the AIAO
configuration, which can be represented as the superposition of a cluster dipole (M), an A2-octupole, and a T1-octupole (). M represents a ferromagnetic ordering, while
represents an antiferromagnetic ordering other than AIAO. On the basis of symmetry analyses (see section S1 and table S1), we demonstrated that only the T1-octupole
can induce the AHE without magnetization.
cubic symmetry, a magnetic field was applied to pressured NIO single octupole preserves the cubic symmetry, it cannot generate AHE.
crystals (19) and Pr-doped bulk samples (20, 21). However, the spin However, in a strained NIO (s-NIO), the AIAO spin structure
structures modulated by the magnetic field are fragile and easily re- becomes modulated under the strain. The resulting spin configuration
turn once the magnetic field is turned off. Thus, a stable method to is denoted by strained AIAO (s-AIAO), composed of a superposition
break the cubic symmetry is highly desirable; here, we choose a of three kinds of cluster multipoles, namely, a dipole, an A2-octupole,
strain engineering approach and investigate the associated AHE. and a T1-octupole (Fig. 1D). Note that the dipole is just the ferro-
As shown in Fig. 1B, the biaxial strain elongates the unit tetrahedra magnetic ordering, while the T1-octupole is an antiferromagnetic
along the [111] direction. This will naturally break the cubic sym- ordering other than AIAO. Only the T1-octupole can induce the
metry of the system. Since the deformation modulates magnetic AHE without magnetization since it breaks the cubic symmetry as
anisotropy (22), the Ir spin directions should be changed. To system- the dipole does.
atically describe the change of spin direction, we adopted the cluster
multipole theory. Since the conduction electrons come from Ir d Characterizations of relaxed and fully s-NIO thin films
orbitals, we considered Ir sublattice only (16). In the cubic pyrochlore To investigate the strain-induced magnetic multipole and associated
lattice, all spin ordering patterns can be classified into five different AHE, we prepared two kinds of NIO thin films on the yttria-stabilized
irreducible representations, carrying 12 distinct cluster multipoles zirconia (YSZ) substrates: relaxed and fully strained films. The biaxial
(18). Among them, certain cluster multipoles that break the cubic strain can arise from the lattice mismatch between the R2Ir2O7 film
symmetry are responsible for the AHE (see section S1). and the YSZ substrate (see Fig. 1B) (23, 24). Since the lattice parameter
In a bulk NIO, the AIAO ordering corresponds to a higher-rank of YSZ is smaller than those of NIO bulk, the NIO film should
be compressively strained. We estimated the strain ( = _ a NIO )
2 a YSZ − a NIO
magnetic multipole called the A2-octupole (Fig. 1C). Since the A2-
Kim et al., Sci. Adv. 2020; 6 : eabb1539 15 July 2020 2 of 7SCIENCE ADVANCES | RESEARCH ARTICLE
to be −0.96%, where aNIO and aYSZ are lattice constants of bulk NIO A B
(10.38 Å) and YSZ (5.14 Å), respectively. * 2.35
YSZ (222)
YSZ (331)
YSZ (111)
*
Nd2Ir2O7 (222)
Nd2Ir2O7 (333)
Nd2Ir2O7 (111)
Intensity (arb. units)
Nd2Ir2O7 (444)
Despite the substantial past efforts (25–27), the in situ growth of
high-quality R2Ir2O7 thin film is notoriously difficult. Under the *
Qz // [111]
proper crystalline growth conditions for pyrochlore oxides (28), the
corresponding R2Ir2O7 phase becomes extremely unstable because * 2.30
of the formation of a gaseous IrO3 phase (29). To avoid this instability, *
*
many studies have used the “solid-phase epitaxy (SPE)” (25, 27) Nd2Ir2O7 (662)
method, which involves the initial growth of amorphous R2Ir2O7 films 10 20 30 40 50 60 70 0.66 0.68
at a lower temperature (T) followed by ex situ thermal annealing in 2θ (º) Qx // [11-2]
a sealed tube. Although SPE can provide a method for the growth of C D
single-phase R2Ir2O7 films, it usually produces relaxed films (25, 26). (222)
Therefore, we developed a previously unknown in situ film growth Nd
(004)
method, i.e., repeated rapid high-temperature synthesis epitaxy Ir (111)
(RRHSE; see section S2 and Materials and Methods) (30). Ir/Nd
The RRHSE method made us successfully grow the fully s-NIO Nd2Ir2O7 Nd2Ir2O7
films on YSZ (111) substrates. Figure 2A shows an x-ray diffraction
-2 scan. The NIO (lll) and YSZ (lll) (l: integer) peaks can be seen, E
indicating epitaxial growth of NIO single phase. Particularly, the
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satellite peaks near the NIO (222) peaks are observed, which is com-
(002)
monly called “thickness fringes.” These interference peaks indicate YSZ (111)
the high quality of a sharp interface between film and substrate. Figure 2B
shows x-ray reciprocal space mapping around the NIO (662) and 2 nm
YSZ (331) Bragg peaks of a 9-nm-thick NIO film. The lattice parameter YSZ
of the (662)-plane, d(662), of bulk NIO is 1.19 Å, and the d(331) of YSZ
is 1.18 Å. Note that the NIO (662) Bragg peak has the same Qx value Fig. 2. Fully s-NIO thin film on a YSZ substrate, grown by the RRHSE method.
(A) X-ray diffraction -2 scans of an epitaxial NIO film grown on a YSZ (111) substrate.
as the YSZ (331) peak, demonstrating that our film becomes fully
The scans reveal that the NIO film was grown coherently with the YSZ substrate.
strained (~1% compressive strain) by the substrate.
(B) Reciprocal space mapping around the YSZ (331) and NIO (662) diffraction peaks.
Figure 2C shows a scanning transmission electron microscopy The Qx values of both peaks are the same, indicating that the film is under ~1%
image that indicates the high quality of our film. The NIO pyrochlore strain. (C) Scanning transmission electron microscopy image with the zone axis
phase is formed with few structural defects or disordered structures. parallel to [1-10]; a clear interface between the film and the substrate can be seen.
Figure 2 (D and E) shows fast Fourier transform patterns from the The distinctly colored circles indicate the pyrochlore structural ordering of the Nd
selected areas in the film and substrate, respectively, marked in and Ir ions. Images of selected areas in (C) were fast Fourier–transformed for (D) the
Fig. 2C. As demonstrated by the red dotted lines, the as-grown NIO NIO thin film, and (E) the YSZ substrate. The three vertical dotted lines between (D)
film has the same inverse lattice constant as the YSZ substrate, which and (E) are plotted without changing the scale. These lines indicate that the in-
also confirms that our film is fully strained. plane lattice constants of NIO and YSZ are the same, providing further direct evi-
dence for the fully s-NIO thin film.
Electronic structures of relaxed and fully s-NIO thin films
We compared these fully s-NIO films grown by RRHSE with the
relaxed NIO (r-NIO) films grown by the SPE (see section S3). The (the r-NIO film in our case) explains its insulating nature. The energy
resistivity (T) curve of a 9-nm-thick s-NIO film exhibits a semi- gap opens with a value of about 13 meV (Fig. 3B), which agrees well
metallic behavior at most T. As shown in Fig. 3A, the s-NIO film has with the bulk value (32). Under 1% compressive strain, the valence
(T) an order of magnitude smaller than that of the r-NIO film. and conduction bands move, which slightly increases the direct gap
The (T) curve of an 80-nm-thick r-NIO film exhibits a metal- at most k regions. However, some valence and conduction bands
insulator transition around ~30 K (black dashed line in Fig. 3A), in become crossed with Fermi level; thus, small electron and hole pockets
agreement with its bulk counterpart (17, 31). The strong upturn of develop near L1,2,3,4 (Fig. 3C), creating a semimetallic state. These
the r-NIO film is due to its insulating nature below TNIr ~ 30 K model calculations can explain why the s-NIO film has a much
(17, 31). The (T) curve of the r-NIO film follows the Arrhenius plot smaller (T) than the r-NIO film.
(not shown here) in the low T region, indicating a bandgap opening.
In contrast, the (T) curve of the s-NIO film has a positive slope for Large AHE in fully s-NIO thin films
most T (orange line in Fig. 3A), suggesting that the film should be Besides, the s-NIO film shows a much larger anomalous Hall
in a semimetallic state. Converting the resistivity into conductivity, conductivity (AHC) compared to the r-NIO film. Figure 3D shows
the s-NIO film has xx ~ 1600 ohms−1 cm−1 at 2 K. The tiny upturn the magnetic field (H)–dependent AHC xAy ( H)at 2 K, obtained
below ~30 K might arise from disorder effects. after subtracting the ordinary Hall contribution from the total Hall
To understand the corresponding electronic structure changes, conductivity (see Materials and Methods). The A
xy curves of s- and
we performed mean-field calculations using the Hubbard model r-NIO films are displayed by the circles and the dashed line, respectively.
(see section S4). The previous study shows that the most valence The xAy (H = − 9 T)values of the s- and r-NIO films are 2.4 and
and conduction bands near the Fermi energy come mainly from Ir 0.2 ohms−1 cm−1, respectively. The spontaneous Hall conductivity
5d electrons (16). Our calculated electronic structure of the bulk (SHC) xAy (H = 0)of the s-NIO films is 1.04 ohms−1 cm−1, which
Kim et al., Sci. Adv. 2020; 6 : eabb1539 15 July 2020 3 of 7SCIENCE ADVANCES | RESEARCH ARTICLE
A B Relaxed (insulator)
100
Energy (meV)
101 50
0
ρ (milliohms cm)
EF
r-Nd2Ir2O7 film −50
−100
xx C 100
1% strained (semimetal)
Energy (meV)
50
100 s-Nd2Ir2O7 film
0
EF
−50
0 100 200 300 −100
T (K) Γ L1 K1 L2 Γ L3 K2 L4 Γ
s-Nd2Ir2O7 film
D r-Nd2Ir2O7 film E F
100
H=0 kz
Ω(111) (k)
2 0
−100
1
=0
(ohms−1 cm−1)
A
−200 Relaxed L3
L1
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0 K2 Γ
100 ky
H=0 K1
Ω(111) (k)
−1 kx L4 L2
0
A
−2 2K A
≠0 1% strained
−100
−9 −6 −3 0 3 6 9 Γ L1 K1 L2 Γ L3 K2 L4 Γ
µ0H (T)
Fig. 3. Transport properties and electronic ground states of relaxed and fully s-NIO films. (A) Orange solid (black dashed) line indicates the resistivity, xx, of the
fully s(r)-NIO film, prepared by the RRHSE (SPE) method. xx reveals that the electronic structure of NIO could be changed under strain. The calculated band structure of
the (B) bulk and (C) 1% biaxial s-NIO is shown. The insulator-to-semimetal transition can explain the large change in xx in (A). (D) Measured AHC A
xyof fully s-NIO (circle)
and r-NIO (dashed line) films. Note that the A
xyof s-NIO is an order of magnitude larger than that of r-NIO. Orange circles and dashed arrows depict H-field sweep results
between −9 and 9 T; antihysteresis-like behavior can be seen. (E) Corresponding Berry curvature calculation results along the high-symmetry lines in (B) and (C). Although
→
the Berry curvature of the bulk seems larger, the net contribution of A
xy(k )becomes zero (i.e., hidden), resulting in xy= 0 under cubic symmetry. On the other hand, the
summation of the Berry curvature for the s-NIO could emerge because of the broken cubic symmetry. (F) Schematic of the BZ for the pyrochlore structure.
→
is much larger than that of the r-NIO film. Note that the small ( k ) at the L1,2,3,4 points in the BZ (Fig. 3F) exists for both the r- and
AHC and SHC in the r-NIO film might be induced by the net mag- s-NIO systems. The Berry curvature at each high-symmetry point for
netization of AIAO domain walls (33). However, the large AHC the r-NIO is somewhat larger than that for the 1% s-NIO. However, → for
and SHC in the s-NIO suggest that the net Berry curvature effect the cubic r-NIO, A x y vanishes since the integration of Ω [111]( k ) over
can be modulated by the strain. the BZ cancels out. Generally, when twofold rotation symmetries C2
→ → → →
To cross-check, we compared our magnetotransport property values about the x, y, or z axis exist, Ω( k ) →is canceled by Ω(C 2 k ). In the
→
with those of ferromagnets. For example, (Ga, Mn)As (34) and r-NIO, all three C2 exist, so the net Ω( k )contribution becomes hidden
CuCr2Se4–xBrx (35) typically exhibit SHC with A
xy( H = 0 T) ~ 1 to (9). In contrast, for the trigonal s-NIO, the breaking of all C2 sym-
→ →
10 ohms cm and xx(H = 0 T) ~ 1000 ohms cm−1. These ferro-
−1 −1 −1
metries draw out a finite net Ω( k )contribution. Thus, the biaxial
magnets follow a scaling relationship A 1.6
xy ∝ xx that implies the in- strain can promote the net Berry curvature effect originally hidden
A
trinsic nature of the AHE (5). Since xy and xx values for the s-NIO in the bulk, generating the large AHE in the s-NIO films.
film also fall on the same scaling curve (see section S5), we con-
firmed the enhanced AHC and SHC of our fully s-NIO film as the Antihysteresis of AHC
net Berry curvature effect. A
Another notable feature of s-NIO film is that its xy( H) curve shows
Accordingly, we calculated the Berry curvature effect on AHC an intriguing antihysteresis-like behavior, displayed in Fig. 3D.
from the band structure obtained from the mean-field calculations When we sweep the H-field from −9 to +9 T, a sign change occurs
mentioned above (see section→S4). AHC can be obtained by integrat- at an H value of about −1 T (circles in Fig. 3D). Similar behavior is
ing the Berry curvature xy( k )throughout the whole BZ (5): also observed when we reverse the H-field sweep from +9 to −9 T.
This H-dependent sign change of the AHC differs from a typical
A e 2 d 3 k ∑ f(ϵ ( k→) − ) → hysteretic response of most ferroic materials, where the sign change
xy = ─ ∫ ─ [111]( k ) (1)
ℏ BZ (2) 3 n n occurs during the domain switch to the opposite direction.
→ Although a similar antihysteresis-like behavior has been also re-
where f(ϵ n( k ) − )is the Fermi-Dirac distribution function and is ported in an earlier Hall conductivity study of an NIO single crystal
the→ chemical potential. Figure 3E shows the Berry curvature [111] under hydrostatic high pressure (21), its origin has not fully in-
( k )of NIO along its high-symmetry lines with H = 0. Sizable [111] vestigated yet.
Kim et al., Sci. Adv. 2020; 6 : eabb1539 15 July 2020 4 of 7SCIENCE ADVANCES | RESEARCH ARTICLE
To understand our antihysteresis-like xAy (H) curve, we used a and Nd sublattices. In Fig. 4C, the nonhysteretic component (green
phenomenological model (see section S6). The model is composed circles) starts to emerge below TIr N , so it can be attributed to the Ir
of two tangent hyperbolic functions; one is hysteretic (blue line) spin ordering, and we denote the nonhysteretic as Ir
xy . On the other
and the other is nonhysteretic (green line) (see Fig. 4A). Since the hand, the hysteretic component (blue circles) starts to emerge below
experimental data (orange circles) agree with the sum of two tangent TNd
N , so it can be attributed to the Nd spin ordering, and we denote
hyperbolic functions (black solid line), the antihysteretic curve can the hysteretic as Ndxy . The nonhysteretic contribution of Ir is due to
be explained by the two different origins of A
xy. To obtain further the absence of the Ir-AIAO domain switch by the smallness of
A
insight, we measured T-dependent x y( H) curves of s-NIO film below Ir-AIAO coupling to the field. Meanwhile, the hysteretic contribution
40 K. As shown in Fig. 4B, Axy does not exist at 40 K, when the system of Nd is due to the presence of the Ir-AIAO domain switch through
is in a paramagnetic phase. As T decreases, A xy starts to emerge at f-d exchange with either Nd-3O1I or Nd-3I1O, which can be formed
~30 K and becomes stronger thereafter. In 15 K < T < 30 K, A xy ex- by large Nd moments under a [111] magnetic field (see section S6).
hibits no hysteretic behavior. However, as T decreases further below This hysteretic behavior of Nd xy leads to the finite SHC at zero field
15 K, A
xy starts to show the antihysteresis-like behavior. Figure 4B A
xy( H = 0 T)displayed as the red squares in Fig. 4C. Note that the
shows that all T-dependent xAy curves are well matched with the SHC emerges below T Nd
N .
sum of the nonhysteretic and hysteretic hyperbolic functions. Note that
the bulk NIO has T Nd
~ 15 K and T
N Ir
N ~ 30 K (17), suggesting that the AHE from strain-induced T1-octupoles
hysteretic and nonhysteretic responses are developed because of To reveal the relation of AHE and cluster multipoles under strain, we
the magnetic orderings of Nd and Ir spins, respectively. should compare M and Axy values (see Fig. 1D). The H-dependent M
Figure 4C summarizes the results of the AHC fitting at H = −9 T and xAy hysteresis curves at 3 K are displayed in Fig. 5A, and as-
Downloaded from http://advances.sciencemag.org/ on May 7, 2021
with the TNd N and TN
Ir
values, marked as the dotted lines. Note that, sociated xIry and xNd
y curves are shown in Fig. 5B. Figure 5A
most transport in NIO occurs by Ir d electrons near the Fermi level. demonstrates that the conventional understanding of the SHC (5),
This carrier transport can be affected by the spin ordering at the Ir i.e., xAy (H = 0 T ) ∝ M (0 T), does not hold for the s-NIO film.
Although the s-NIO film has a large SHC signal (orange circles) shown
in Fig. 5A, it has no spontaneous M at 3 K with H = 0 (purple squares)
A B
within the measurement error (± 0.01 B/NdIrO3.5). As shown
in Fig. 1D, the biaxial deformation of pyrochlore lattice can generate
three kinds of multipoles, i.e., a dipole, an A2-octupole, and a T1-
octupole. The dipole is crossed out because of the zero magnetization
of our data, and the A2-octupole is crossed out because of its zero con-
tribution to AHC. Therefore, the strain-induced T1-octupole should
play important roles in generating the AHC without magnetization.
To elucidate how T1-octupole emerges under the strain, we cal-
culated the spin structure from the spin model. Since both Nd and
Ir spins play important roles, we included the Heisenberg,
Dzyaloshinskii-Moriya, anisotropic spin-exchange interactions be-
tween Ir spins (36), the f-d exchange interaction between the Ir and
Nd spins (17), and the Zeeman energy for both the Ir and Nd spins
(for details, see section S7). On the basis of the calculated spin structure,
C we obtained the cluster multipoles (table S1 in section S1). Figure 5C
shows the calculated dipole (M, green circles) and T1-octupole (,
blue circles) as a function of the effective Zeeman energy h in the
r-NIO. According to our calculation, r-NIO does not have a finite
M or value for the Ir sublattice at h = 0. The zero values of M and
can explain the negligible SHC of the r-NIO film (see Fig. 3D).
Figure 5D shows the calculated M and of s-NIO, which are finite
even for h = 0. Particularly, the hysteresis curve of looks similar to
the Nd
x y curve in Fig. 5B. Therefore, we conclude that the large spon-
taneous that generate AHE can be induced by the strain in the
Fig. 4. T-dependent AHC and occurrence of SHC below TNd A
N . (A) AHC xyat T = 3 K. s-NIO film.
The orange circles are the measured values. The blue (green) line indicates a fitting
curve for the Nd (Ir) spin contribution, i.e., xNd Ir
y ( xy), obtained from the pheno
menological model (see main text). The black line is the sum of Nd Ir
xy and xy. AOAI, DISCUSSION
all-out-all-in. (B) T-dependent A xy. The orange circles (black solid lines) depict the
Our work demonstrates that the strain-engineering of an antiferro-
experimental results (fitting curves). Near T ~ TNIr (~ 30 K), AHC starts to emerge,
magnet can generate the net Berry curvature effects by modulating
which indicates the Ir spin ordering effect. Below T ~ TNd N (~ 15 K), AHC starts to ex-
hibit hysteretic behavior, indicating that Nd spin ordering plays an important role
its cluster multipoles. In particular, our findings highlight that the
via the f-d exchange interaction. (C) T-dependent contributions of Ir and Nd spins strain-induced T1-octupole is closely connected with the topological
to AHC, i.e., Irxy (H = − 9 T) (green circles) and Nd
xy (H = −9 T) (blue circles). The red
properties of NIO. We can further extend this strain-engineering
squares indicate the SHC values, i.e., AHC without magnetic field |A xy( H = 0 T)|. Note approach to search for the other novel topological phenomena in
that SHC develops below TNd N ~ 15 K. correlated magnets. For example, the strain engineering approach
Kim et al., Sci. Adv. 2020; 6 : eabb1539 15 July 2020 5 of 7SCIENCE ADVANCES | RESEARCH ARTICLE
A B pattern was monitored and the intensity of the oscillation was re-
corded. After growth, NIO films were characterized by an x-ray dif-
fractometer (Bruker Corp.) and an atomic-resolution high-angle
annular dark-field scanning transmission electron microscope
(JEM-ARM200F; JEOL) equipped with an energy-dispersive x-ray
spectrometer.
Transport and magnetic properties
Magnetotransport properties were measured via a standard four-
point probe method using a commercial physical property measure-
C D ment system (PPMS, Quantum Design), which has a base T of 2 K
and a maximum magnetic field of 9 T. During the measurements,
the current was applied along the [1-10] direction, and H was
applied along the [111] direction. Magnetization data were obtained
using a commercial superconducting quantum interference device
magnetometer (MPMS, Quantum Design) with the magnetic field
applied normal to the film.
The AHC value A
xy can be obtained from the resistivity values,
xAy ( H)
namely, xAy ( H ) = ___________ A
Downloaded from http://advances.sciencemag.org/ on May 7, 2021
2 A 2 where xy is anomalous Hall resist
xx (H) + xy (H)
Fig. 5. Emergence of strain-induced magnetic multipoles and their relation to ivity and xx is longitudinal resistivity. To exclude the longitudinal
AHC in NIO. (A) The M/H curve (purple squares) of s-NIO film at 3 K, overlaid with contribution from the raw Hall resistivity data xr y , we used the
the experimental AHC (orange circles). Note that M = 0 but A xy≠ 0without H. The antisymmetrization procedure (8, 9, 13). We separated the positive
nonzero value of A
xy at H = 0 and M = 0 indicates an alternative origin of the AHE. and negative field sweep branches andr− thenr+antisymmetrized xy
(B) The AHC of s-NIO film at 3 K. The orange circles are experimental data. The green r+ r−
x y( H ) − x y( −H) x y( H ) − x y( −H)
using +x y (H)
= _ and −xy (H)
= _ . Note that r+
xy( H)
line is the contribution of Ir spins, i.e., xIry, based on our model calculation (see r−
2 2
Fig. 4A). The blue solid and dashed lines are the contributions of Nd spins, i.e., Nd
xy,
and x y (H)denote positive field sweep (+9 T to −9 T) and negative
during decreasing and increasing h-sweeps, respectively. Calculated magnetic field sweep (−9 T to +9 T) branches, respectively. From +xy( H) and
multipoles in NIO under the effective Zeeman energy, h, (C) without and (D) with x−y (H)
, we took out the linear part (ordinary Hall resistivity) to
1% strain are shown. The green and blue circles indicate dipole M and T1-octupole , determine A x y.
respectively. The strain-induced becomes the origin of the SHC in our s-NIO film.
Self-consistent mean-field Hubbard model
We developed the Hubbard model for the s-NIO thin film under
on numerous series of R2Ir2O7 can realize novel correlated topological
the magnetic field and acquired the ground state and electronic
phases, such as Weyl semimetal, axion insulator (16), a strong topo-
structure by the self-consistent mean-field method. We adopted
logical insulator (18), and line-node semimetal (19, 21) by properly
24 × 24 × 24 and 32 × 32 × 32 k-point mesh and found that the re-
modifying their magnetic structure. In this perspective, we believe
sults are consistent. We calculated the AHC by integrating the Berry
that our strain study on NIO could provide a cornerstone to discov-
curvature, adopting a 48 × 48 × 48 k-point mesh of the entire BZ.
er strain-engineered novel topological phenomena in oxides and to
Details of the calculation are provided in section S4.
understand their fundamental mechanisms.
Spin model calculation
We developed the spin model including Heisenberg exchange,
MATERIALS AND METHODS
Dzyaloshinskii-Moriya interaction, anisotropic exchange, the f-d
Film growth and structural characterization
exchange between Nd and Ir electrons, and the Zeeman effect by
Fully s-NIO films were in situ grown on insulating YSZ substrates
applying second-order perturbation theory to the Hubbard model
using the RRHSE method. This film growth method is a modi-
and referring to previous works. We calculated the ground state by
fied form of pulsed laser deposition, based on repeated short-term
the iterative minimization method, which repeatedly aligns spins to
thermal annealing processes using an infrared laser. RRHSE con-
the effective field direction until each spin is fixed. Details of the
sists of two key steps in one thermal cycle. During the first step,
calculation are provided in section S7.
amorphous stoichiometric NIO and IrO2 layers were deposited by a
KrF excimer laser ( = 248 nm, 5 Hz) at T ~ 600°C with PO2 ~ 50
SUPPLEMENTARY MATERIALS
mtorr. The additional IrO2 layer was deposited to compensate for Supplementary material for this article is available at http://advances.sciencemag.org/cgi/
the Ir loss that would unavoidably occur later during the synthesis content/full/6/29/eabb1539/DC1
process. During the second step, the pyrochlore phase is formed by
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Structural control of magnetic anisotropy in a strain-driven multiferroic EuTiO3 thin film. interests: The authors declare that they have no competing interests. Data and materials
Phys. Rev. B 88, 094434 (2013). availability: All data needed to evaluate the conclusions in the paper are present in the
24. K.-Y. Yang, Y.-M. Lu, Y. Ran, Quantum Hall effects in a Weyl semimetal: Possible paper and/or the Supplementary Materials. Additional data related to this paper may be
application in pyrochlore iridates. Phys. Rev. B 84, 075129 (2011). requested from the authors.
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26. W. C. Yang, Y. T. Xie, W. K. Zhu, K. Park, A. P. Chen, Y. Losovyj, Z. Li, H. M. Liu, M. Starr, Accepted 29 May 2020
J. A. Acosta, C. G. Tao, N. Li, Q. X. Jia, J. J. Heremans, S. X. Zhang, Epitaxial thin films Published 15 July 2020
of pyrochlore iridate Bi2+xIr2-yO7-: Structure, defects and transport properties. Sci. Rep. 7, 10.1126/sciadv.abb1539
7740 (2017).
27. T. C. Fujita, Y. Kozuka, M. Uchida, A. Tsukazaki, T. Arima, M. Kawasaki, Odd-parity Citation: W. J. Kim, T. Oh, J. Song, E. K. Ko, Y. Li, J. Mun, B. Kim, J. Son, Z. Yang, Y. Kohama, M. Kim,
magnetoresistance in pyrochlore iridate thin films with broken time-reversal symmetry. B.-J. Yang, T. W. Noh, Strain engineering of the magnetic multipole moments and anomalous
Sci. Rep. 5, 9711 (2015). Hall effect in pyrochlore iridate thin films. Sci. Adv. 6, eabb1539 (2020).
Kim et al., Sci. Adv. 2020; 6 : eabb1539 15 July 2020 7 of 7Strain engineering of the magnetic multipole moments and anomalous Hall effect in
pyrochlore iridate thin films
Woo Jin Kim, Taekoo Oh, Jeongkeun Song, Eun Kyo Ko, Yangyang Li, Junsik Mun, Bongju Kim, Jaeseok Son, Zhuo Yang,
Yoshimitsu Kohama, Miyoung Kim, Bohm-Jung Yang and Tae Won Noh
Sci Adv 6 (29), eabb1539.
DOI: 10.1126/sciadv.abb1539
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