Reversible control of magnetic interactions by electric field in a single-phase material

Abstract

Intrinsic magnetoelectric coupling describes the interaction between magnetic and electric polarization through an inherent microscopic mechanism in a single-phase material. This phenomenon has the potential to control the magnetic state of a material with an electric field, an enticing prospect for device engineering. Here, we demonstrate 'giant' magnetoelectric cross-field control in a tetravalent titanate film. In bulk form, EuTiO(3), is antiferromagnetic. However, both anti and ferromagnetic interactions coexist between different nearest europium neighbours. In thin epitaxial films, strain was used to alter the relative strength of the magnetic exchange constants. We not only show that moderate biaxial compression precipitates local magnetic competition, but also demonstrate that the application of an electric field at this strain condition switches the magnetic ground state. Using first-principles density functional theory, we resolve the underlying microscopic mechanism resulting in G-type magnetic order and illustrate how it is responsible for the 'giant' magnetoelectric effect.

ARTICLE

Received 26 Jun 2012 | Accepted 26 Nov 2012 | Published 8 Jan 2013

P.J. Ryan1, J.-W. Kim1, T. Birol2, P. Thompson3,4, J.-H. Lee1, X. Ke5, P.S. Normile6, E. Karapetrova1,P. Schiffer7,w, S.D. Brown3,4, C.J. Fennie2 & D.G. Schlom8

Intrinsic magnetoelectric coupling describes the interaction between magnetic and electric polarization through an inherent microscopic mechanism in a single-phase material. This phenomenon has the potential to control the magnetic state of a material with an electric eld, an enticing prospect for device engineering. Here, we demonstrate giant magneto-electric cross-eld control in a tetravalent titanate lm. In bulk form, EuTiO3, is anti-ferromagnetic. However, both anti and ferromagnetic interactions coexist between different nearest europium neighbours. In thin epitaxial lms, strain was used to alter the relative strength of the magnetic exchange constants. We not only show that moderate biaxial compression precipitates local magnetic competition, but also demonstrate that the application of an electric eld at this strain condition switches the magnetic ground state. Using rst-principles density functional theory, we resolve the underlying microscopic mechanism resulting in G-type magnetic order and illustrate how it is responsible for the giant magnetoelectric effect.

1 X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA. 2 School of Applied Engineering Physics, Cornell University, Ithaca, New York 14853-1501, USA. 3 University of Liverpool, Department of Physics, Liverpool L69 3BX, UK. 4 XMaS, European Synchrotron Radiation Facility, Grenoble, France. 5 Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA. 6 Instituto Regional de Investigacin Cientca Aplicada (IRICA) and Departamento de Fsica Aplicada, Universidad de Castilla-La Mancha, Ciudad Real 13071, Spain. 7 Department of Physics and Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, USA. 8 Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853-1501, USA. w Present address: Department of Physics, University of Illinois, Urbana-Champaign,

Urbana, Illinois 61801, USA. Correspondence and requests for materials should be addressed to P.J.R. (email: mailto:[email protected]

Web End [email protected] ).

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DOI: 10.1038/ncomms2329

Reversible control of magnetic interactions by electric eld in a single-phase material

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms2329

The magnetoelectric (ME) effect represents the coupling between the electric and magnetic parameters in matter1. Multiferroic (MF) materials with coexisting

ferromagnetism (FM) and ferroelectricity were thought to offer the best prospect of achieving a strong linear ME coupling coefcient owing to the combination of typically higher electric permittivity and magnetic permeability, both of which combine as an upper limit to any potential coupling strength2. Unfortunately, MEMF materials are rare as ferroelectric materials need to be robustly insulating while magnetic materials are typically conducting3. Although uncommon, such compounds have been the subject of intense research over the past decade1,2. The realization of this phenomenon may lead to the development of multistate logic, new memory or advanced sensor technologies2. To integrate such characteristics into a functional device requires strong ME coupling between the ferroic properties, enabling the manipulation of magnetic order with an electric (E) eld or electric polarity with a magnetic eld. The intense search for materials exhibiting such functional ferroic control has centred upon a number of complex oxide systems with a pseudo-cubic perovskite structure25. Within these systems, the electronic band structure of the central B-site cation generally determines the ferroic properties. A completely empty d band is required for ferroelectricity, while partial occupation is essential for the double and superexchange (SE) magnetic interactions, typical of these materials3,6. One approach circumventing this obstacle has been to engineer spatially segregated two-phase systems, which take advantage of electro-or magneto-striction mediated through strain or proximity to generate ME coupling712. However, nding an intrinsic single-phase mechanism would evade the inherent disadvantages and complexities of multiphase environments. In single-phase systems, the d band occupation issue is typically avoided through geometric (magnetic) frustration, where the ferroic properties arise from the DzyaloshinskiMoriya interaction1315. In these cases, the ferroic properties are weak, relegating device application unlikely.

Sufce to say, a great deal has been accomplished regarding E-eld-controlled magnetism. The popular MF pseudo-perovskite material BiFeO3, which presents both G-AFM and ferroelectric order, has shown intrinsic single-phase ME character. The orientation of the AFM Fe spins are always perpendicular to its rhombohedral long axis, which derives from the ferroelectric distortion. As a result, the magnetic domain structure can be reoriented by E-eld application16. Equally important, the manganite family has had a signicant role in our understanding of ME phenomena. Interest peaked with HoMnO3, when FM, correlated with Ho3 spin ordering, was activated by a static E-eld17. Interestingly, the induced FM order originated from uncompensated magnetization at the AFM domain walls rather than from an intrinsic phenomenon18,19. Similarly, cross-coupling effects were found in another single-crystal ferrite system, GdFeO3, arising from domain wall interactions when weak MFFM domains interfaced with ferroelectric regions12. Designing epitaxial heterostructures have also generated several avenues creating coupled control parameters. Interfacing MF materials BiFeO3 or YMnO3 with a soft FM system provides opportunities for phase coupling to electrically control both magnetic exchange bias and spin reorientation8,10,20,21. In addition, more direct methods have included altering the ferroelectric domain orientation of a BaTiO3 single crystal demonstrating the ability to change the magnetic strength of a FM La0.66Sr0.33MO3 lm7, and active strain tuning

through interfacing the same material to a piezoelectric single crystal presented the ability to change the magnetic transition temperature, TC, with E-eld22.

The rare earth tetravalent titanate, EuTiO3 (ETO), is an emerging multication ferroic prototype, whereby magnetic spins are carried by the half-occupied Eu 4f7 spins, and the unoccupied Ti 3d0 band lends itself to potential ferroelectricity. Moreover, the anomalous response of the dielectric constant to spin alignment indicates an inherent ME coupling mechanism in ETO (ref. 23). It was this effect that impelled Fennie and Rabe to calculate that, through strain engineering, one could create strong multi-ferroicity and additionally predicted the exceptional strain-boundary state, allowing cross-eld control capability24. Indeed, epitaxial lms of tensile-strained ETO showed multiferroicity with a large ferromagnetic moment (7 mB/Eu) alongside spontaneous electric polarization (B10 mCm 2) (ref. 25).

Furthermore, ETO demonstrates a third-order biquadratic ME coupling response (E2H2) allowing for circumvention of the linear ME susceptibility boundary condition26.

In this article, we present E-eld control of the full magnetic moment in the single-phase ETO system. However, our ndings do not match initial predictions. Instead, we nd that the dramatic ME effect does not require the proposed polar instability24. Rather, the combination of tuning the relative strengths of the intrinsic competing magnetic interactions under a moderate compressive strain state with the inherent paraelectric nature of the system is sufcient to generate complete ME control. X-ray resonant magnetic scattering (XRMS) was used to conrm the magnetic structure of the contrasting strained ETO lm series and reveal the emergence of competition between coexisting magnetic interactions in a moderately ( 0.9%) compressed state. First-principles density functional

theory (DFT) calculations identied the third nearest neighbour (NN) Eu interaction central to the G-AFM structure of ETO. Finally, using in situ (E-eld) XRMS, we demonstrate cross-eld ME control by eliminating long-range AFM order and inducing a magnetic state of nanometre-sized FM clusters. The underlying intrinsic mechanism is illustrated through simulations replicating the effect of E-eld application by calculating the energy difference between the AFM and FM spin congurations.

ResultsX-ray resonant magnetic scattering. X-ray scattering is sensitive to both charge and magnetic distributions27. Typically, the magnetic component is about six orders of magnitude lower than conventional charge scattering. However, an enhanced magnetic response is achieved through resonance, in the present case at the Eu LII edge, whereby, mediated by the Eu 4f-5d exchange interaction, the Eu sublattice magnetic structure is probed with E1 (2p1/245d3/2) electronic excitations. In addition, owing to the polarization dependence of magnetic scattering a post-sample analyser can be used to preferentially suppress charge scattering as illustrated in Fig. 1a. Unstrained, compressive and tensile strain states were accomplished with 22 nm of epitaxial cube on cube-layered growth by ozone-assisted molecular beam epitaxy on SrTiO3(STO), (LaAlO3)0.29 (SrAlTaO3)0.71(LSAT) and

DyScO3(DSO) single-crystal substrates, respectively25.

Both ETO and STO share the same lattice parameter, thus when grown on the (001) surface, the lm is nominally unstrained and exhibits bulk like G-AFM order with the emergence of magnetic scattering intensity at (1/2 1/2 5/2) ETO

below TN at 5.25 K shown in Fig. 1a. A 0.9% compressive strain

is imposed by the LSAT (001) substrate and as shown in Fig. 1b also maintains G-AFM order with the onset of magnetic scattering at TN of 4.96 K. Under 1.1% tensile strain the ETO lm grown on DSO(110) is, however, ferromagnetic, conrmed both by the absence of a resonant magnetic signature at the (1/2

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms2329 ARTICLE

7,000

2.0x103

6,000 5,000

STO

Analyser

Scattering

plane

X-ray

(1/2 1/2 5/2)ETO (1/2 1/2 5/2)ETO

LSAT

Intensity (a. u.)

2,000

[afii9843]

1,500

Intensity (a.u.)

Temperature

1.5 Eu LII

1.0

0.5

7.60 7.62 7.64

Energy (keV)

4,000 3,000 2,000 1,000

[afii9843]

1.5 K

3.0 K

3.5 K

4.0 K

4.5 K

5.0 K

5.5 K

6.0 K

Sample

2.0 K

3.0 K

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4.5 K

5.0 K

5.5 K

2.5 K

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Temperature

2.0 K

1,000

500

0 2.47 2.48 2.49 2.50 2.51

L (STO r.l.u.)

[afii9846]

2.5 K

0 2.42 2.44 2.46 2.48 2.50

L (LSAT r.l.u.)

Figure 1 | XRMS spectra showing G-AFM order in epitaxial ETO lms grown on STO(001) and LSAT (001) substrates. (a) A series of reciprocal L-scans (lm normal) through the (1/2 1/2 5/2)ETO reection of the nominally unstrained ETO on STO(001) through a range of temperatures crossing TN. Also seen is a half-order reection from the STO substrate owing to AFD order. The measurements were taken in vertical scattering geometry with s- to ppolarization selection analysis (inset) used to suppress charge and optimize the magnetic/charge scattering ratio. (b) A similar temperature-dependence data set for the compressively ( 0.9%) strained ETO on LSAT(001). The encumbering substrate charge intensity originates from anti-phase boundary

half-order reections typical of LSAT. The inset shows the resonant response with an energy scan at 1.5 K through the Eu LII edge. The error bars present s.d.

105

Eu LII

10

8

6

4 7.60 7.61 7.62 7.63

(001)ETO

Intensity (a.u.)

12 107

105

103

101

Intrnsity (a.u.)

(105)DSO

Eu LII at (001)ETO

104

103

102

L (DSO r.l.u.)

Energy (keV)

Intensity (a.u.)

Intensity (a.u.)

0.2 0.03

0.02

0.01

Intensity difference (a.u.)

0.90 0.95 1.00 1.05

2 K10 K Difference

0.1

0.0

(1/2 1/2 5/2)ETO

101

100 2.50 2.55 2.60 2.65 7.60 7.62 7.64

0.00

L (DSO r.l.u.) Energy (keV)

Figure 2 | XRMS showing absence of G-AFM order and emergence of FM order in 1.1% tensile-strained ETO on DSO(110) substrate. (a) An L-scan through the (1/2 1/2 5/2)ETO reection at 1.6 K below the TC mark of 4.05 K. Some charge-scattered leakage is detected; however, an energy scan through the Eu LII edge is presented in the inset showing no resonant (magnetic) response. The nding demonstrates absence of long-range G-AFM order of the Eu ions in the FM phase. The leaked charge amplitude derives from the octahedral tilting pattern, (a a c0) (ref. 32). (b) Presents contrasting energy scans through the Eu L II edge above and below TC at the integer (001)ETO reection. Inset plots an L-scan through the same reection. Owing to the overlap of both charge and magnetic scattering at this reection, complete suppression of the former is constrained. The onset of magnetic scattering below TC is

shown with the increase of scattered intensity through the edge and indicates the spontaneous (zero eld) FM long-range order. The magnetic scattering contribution was about 9% of the total intensity. The results of statistical error propagation is presented for the difference signal.

1/2 5/2)ETO reection shown in Fig. 2a and with the emergence of a resonant enhancement of the magnetic scattering at the(001)ETO reection at the Eu LII edge shown in Fig. 2b, with a TC of 4.05 K.

Contrasting with the unstrained (STO) and tensile strain (DSO) conditions, the temperature dependence of the magnetic scattering intensity of the compressive state (LSAT) shows a signicantly dissimilar and suppressed critical behaviour, presented in Fig. 3a. This character is found in systems owing to local competition between FM and AFM interactions exemplied by the mixed-magnetic crystal system GdxEu1 xS

(ref. 28). The temperature-dependent magnetic scattering intensity is t to the critical behaviour /mS2BI I0

(1 T/TC)2b, where /mS is the magnetic moment, I is the

magnetic scattered intensity, T is the sample temperature, TC is

the magnetic transition temperature and b is the the critical order exponent. The AFM order of the ETO on STO lm is best

described by the three-dimensional Heisenberg model owing to the isotropic (rotational degree of freedom) character of half-lled Eu 4f spin states. The measured critical order exponent, b 0.385

of the same lm follows universally within the framework of statistical mechanics. However, a larger exponent, 0.496, is found in the compressively strained ETO lm on LSAT (001). The substantial magnetic suppression demonstrates signicant local magnetic competition. Similar to the unstrained G-AFM state, the tensile-strained ETODSO lm in the FM phase also indicates three-dimensional Heisenberg behaviour where the local FM exchange dominates the AFM interactions without evidence of competing magnetic interactions.

DFT calculations. Clearly both local AFM and FM interactions coexist within the ETO. In order to describe the underlying mechanism determining the G-AFM Eu spin structure, previous

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L (LSAT r.l.u.)

L (LSAT r.l.u.)

(a0a0c)

1

STO [afii9826] = 0.385 LSAT [afii9826] = 0.496 DSO [afii9826] = 0.332

2.40 2.42 2.44 2.46 2.48 2.50(1/2 1/2 5/2)

(1/2 5/2 1/2)

2.52

11

107

10 109 (002)ETO (002)LSAT

1.0

0.8

0.6

0.4

Log (int.) (a.u.)

2

Intensity (a.u.)

107

3

105

106

103

4

1.8 1.9 2.0 2.1

Intensity (a.u.)

4 3 2 1

Intensity (a.u.)

3rd NN

Log (1T/Tcritical)

Eu

105

ETO film

Ti O

2nd NN

0.2

0.0

104

1st NN

103

0.0

0.2

0.4

0.6

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1.40

1.42

1.44

1.46

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1.50

1.52

Reduced temperature (T/Tcritical)

1.2

L (LSAT r.l.u.)

Figure 3 | Magnetic critical behaviour of the three strain states and XRD of the oxygen octahedral rotations in the ETO on LSAT. (a) The temperature dependence of the XRMS Eu LII amplitudes for all three strain states, STOunstrained, LSAT0.9% compressive and DSO1.1% tensile. The solid lines are ts of the critical behaviour /mS2BI I0(1 T/TC)2b, where /mS is the magnetic moment, I is the magnetic scattered intensity, T is the sample

temperature, TC is the magnetic transition temperature and b is the critical order exponent. Both the G-AFM order in the unstrained (STO) and FM order of tensile (DSO) lms show typical three-dimensional Heisenberg behaviour while the compressively strained (LSAT) lm shows signicant suppression, a classic indicator of local magnetic competition. Insettop, presents a loglog plot showing the near transition region. Inset bottom illustrates the multiple coexisting magnetic interactions between the rst, second and third NN Eu ions. (b) The symmetry response of the ETO lm to the biaxial compressive tetragonal distortion imposed by the LSAT (001) substrate. Both the (1/2 5/2 1/2)ETO and (1/2 1/2 5/2)ETO reections at 300 K are presented. The occurrence of half-order Bragg peaks show the presence of long-range AFD rotations in the lm. The combination of H L allowed and H K forbidden

reections indicate I4/mcm symmetry with the oxygen octahedral pattern (a0a0c ) in Glazer notation32, illustrated in the bottom inset. Again the LSAT

substrate generates substantial background from the anti-phase boundary half-order reections. The top inset indicates the relative position of the(002)ETO reciprocal position with respect to the substrate (002)LSAT.

Table 1 | Calculated magnetic exchange constants.

ETOLSAT J1xy J1z J2xy J2z J3

J/KB(K)bulk 0.075 0.114 0.062 0.083 0.031

# Neighbours 4 2 4 8 8 J/KB(K)LSAT 0.086 0.147 0.06 0.087 0.034

Shown are the exchange constants (J) calculated between the Eu ions within the unconstrained bulk I4/mcm ETO and the ETO lm on LSAT with (a0a0c ) structure under 0.9% compressive strain,

including the rst, second and third NN Eu ions describing both the in-plane (xy) and out-of-plane (z) interactions. Positive indicates FM and negative AFM coupling. The second row indicates the number

of neighbours for each particular interaction. The rst and second NN interactions are mostly FM bar the rst NN out-of-plane J exchange constant. The calculations indicate the importance of J in

determining the G-AFM structure in ETO.

rst-principles DFT focused on the rst and second NN Eu ion interactions, illustrated in Fig. 3ainset29,30. Without signicant volume (lattice) expansion, the calculations found FM order preferential. However, to investigate the underlying factor leading to the G-AFM magnetic structure, the issue of symmetry needed to be addressed, in order to best know the structure at hand. This was accomplished through a combination of DFT calculations and X-ray diffraction (XRD) measurements. Until recently, bulk EuTiO3 under zero stress boundary conditions was traditionally believed to be in high-symmetry cubic Pm-3m space group. However, our rst-principles calculations indicated that there were strong rotational instabilities as recently discussed by Rushchanskii et al.31 With full ionic relaxation, we show that the lowest energy structure is I4/mcm or (a0a0c ) in Glazer notation with the emergence of antiferrodistortive (AFD) oxygen octahedral rotations32. The energy gained from this distortion is 30 meV f.u. 1(formula unit); however, the energy difference between this state and another metastable state, Imma, (a a c0), is less than an meV f.u. 1 The competition between these two possible rotation patterns becomes evident when we consider the structures under strain. To simulate strain, geometric relaxations were performed keeping the in-plane lattice constant xed and relaxing the out-of-plane lattice length corresponding to

the lms xed biaxial boundary conditions. When we compare energies of different rotation patterns under these conditions, the two aforementioned patterns compete. Consequently the (a a c0) pattern is favoured under tensile strain and (a0a0c )

is preferred under compressive strain. XRD conrmed the I4/ mcm symmetry in the compressed ETO lm on LSAT(001).The combination of the non-zero H L (1/2 5/2 1/2)ETO reection

with the absence of the H K (1/2 1/2 5/2)ETO peak presented in

Fig. 3b indicates the emergence of a pure in-plane AFD rotation nding agreement with the DFT calculations33.

Including the octahedral rotations in our DFT calculations increases the compressive strain required to induce the predicted polar instability24. The competitive coupling between the polar and rotational structural instabilities leads to the calculated suppression of the phonon instability state34. The biaxial compression drives the AFD in-plane rotation in an attempt to maintain the TiO bond lengths, consequently preventing the T01 phonon from freezing out of the lm plane by providing a mechanism to minimize bond length changes. While the previous calculations without rotations (pm-3m) indicated a B 0.9%

strain generating the polar instability, our current calculations, including the AFD rotations, require B 2.5% compressive

strain beyond what is currently achievable.

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms2329 ARTICLE

G-AFM

Eu

Ti

E

2.0x103

1.5

1.0

0.5 Decreasing field

Increasing field

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c

b

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a

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O

X-ray

Amorphous Si

ETO film Au layer

LSAT

Sapphire

Electric field (1x105 V cm1)

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13.0X10312.5

12.0

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0.4

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L (LSAT r.l.u.)

Figure 4 | Electric eld control of the magnetic state. (a) The response of the Ti atom to E-eld is represented pictorially as a displacement along the direction of the eld distorting the EuTiEu third NN bond alignment. (b) Presents a schematic of the experimental sample environment for the in situ XRMS measurement. The sample is mounted on a sapphire block to achieve electrical isolation and maintain good thermal conductivity. (c) A series of L-scans through the G-AFM scattered (1/2 1/2 5/2)ETO reection with incrementally increasing E-eld strength showing the suppressive response of the

AFM signature. (d) Presents a static Q plot of the magnetic scattering intensity (1/2 1/2 5/2)ETO versus E-eld with increasing and decreasing eld strength. The error bars represent the s.d. (e) A plot of the rst-principles DFT calculations of the energy differences between FM and G-AFM spin congurations as a function of polarization modelled upon the ETO on LSATwith a compressive strain state of 0.9% and (a0a0c ) octahedral symmetry.

The calculation replicates the suppression of the AFM state in agreement with the experimental observation.

In Table 1, we present the calculated results of the magnetic exchange interactions (J) for the rst, second and third NN Eu ions for the ETO I4/mcm structure for both bulk (zero boundary conditions) and under 0.9% compressive strain, simulating

epitaxial growth on the LSAT substrate. The exchange constants are broken down further into in-plane (xy) and out-of-plane (z), with positive and negative values indicating FM and AFM, respectively. We nd that both the rst and second NN Eu atoms interact in aggregate, with FM order. The third NN interaction, however, is AFM coupled. This diagonal exchange is most likely facilitated by the central Ti 3d0 band coupled to the Eu 4f7 spins through a 1801 SE mechanism mediated by the intra-atomic-hybridized 4f-5d orbitals, similar to the previously proposed 901 SE mechanism between the rst NN Eu ions29. As a result, the G-AFM structure is dependent upon this third NN interaction. Moreover, the strength of this SE coupling is reliant upon the Eu TiEu bond alignment and the degree of interatomic orbital overlap, thus sufcient angular distortion could signicantly alter the magnetic structure of the entire system35.

Applying electric elds. Upon this premise, the paraelectric nature of the ETO lm becomes central to the feasibility of ME control. In Fig. 4a, the cartoon illustrates how the third NN interaction bond angle alignment is distorted by the Ti displacement from its central position under an applied E-eld, reducing the efcacy of the interaction. Under biaxial compression, the system is expected to have a preferential uniaxial polar anisotropy with the Ti displacement out of the lm plane. Thus in order to examine the capability of ME cross-eld control, we measured the magnetic signature of the strained ETOLSAT lm

where the competition between the magnetic interactions is prevalent and applied an E-eld across the lm to further alter the magnetic balance, as illustrated in the sample schematic in Fig. 4b.

A series of reciprocal space scans through the G-AFM (1/2 1/2 5/2) ETO magnetic reection at 1.9 K versus E-eld strength is presented in Fig. 4c. The suppression of the XRMS intensity with E-eld is clearly displayed and is ostensibly eliminated by 1.0

105 V cm 1. The transition lacks hysteresis, is continuous and reproducible. In Fig. 4d, the resonant magnetic scattering amplitude at the xed lm Q position is plotted with decreasing E-eld strength and on the return the data are extracted from a series of L scans through the magnetic reection at each eld point. This plot exemplies the reversibility and demonstrates the stability of the transition with each data point separated by 30 min on the return.

To further establish the proposed underlying ME microscopic mechanism, we performed rst-principles DFT calculations to replicate the response of the applied E-eld on the strained lm. In Fig. 4d, the calculated enthalpy difference between the G-AFM and FM spin congurations is plotted against the effective polarization. The simulation calculates the lowest-frequency polar Eigen mode, and forcibly displaces the oxygen ions incrementally further from the face centre in conjunction with the Ti shift to maintain this frequency minimum. The resulting energy differences between both magnetic states are calculated. The system responds by energetically trending from AFM towards FM order with increasing polarization. Crucially, it is the paraelectric ground state that allows for the ability to displace the Ti atom. This shift affects the relative strength of the local magnetic interactions reducing the third NN exchange coupling. This

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(003)ETO

1.2 T 1.2 T

Difference

H-field H-field 0.1 T

No E-field

0.060.050.040.030.020.010.00 0.01

7.58 7.60 7.62 7.64 7.66

Energy (keV)

18x103

16

14

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(i)

(ii)

0.001

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0.0020.003

0.002

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Analyser

[afii9843]

[afii9843]

Scattering plane

Intensity (a.u.)

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[afii9843]

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E-field

H-field

+v

Increasing Decreasing

E-field = 1.0x105V cm1

8 1.0 0.5 0.0 0.5 1.0

H-field (Tesla)

Figure 5 | The response of Eu spin alignment with applied H-eld in the ETO lm on LSAT with and without E-eld. (a) Energy scans through the Eu LII

edge at the (003)ETO reection with 1.2 T showing the maximum interference effect at full saturation between the magnetic and charge scattering amplitudes. The sign of the magnetic amplitude switches with the H-eld direction altering the interference effect. (b) The linear XRIS-H-eld dependence is presented by plotting the scattering amplitude at the line indicated energy in (a). The arrows illustrate the spin reorientation of the Eu ions with H-eld and the inset shows the measurement (pp) geometry. The error bars represent the s.d. (c) The energy dependence of the intensity difference between 0.1 Tacross the resonance edge with and without E-eld application (1 105 Vcm 1). The solid line in the top panel is a scaled version of the 1.2 Tdata

set. The chargemagnetic interference phenomenon is eliminated with E-eld. (cInset) A microscopic cartoon model of the Eu spin arrangement with and without E-eld. Naturally, the G-AFM-ordered Eu spins coherently cant towards the external H-eld direction; however, with applied E-eld, the near magnetic degenerate states likely induce a collinear mixed AFMFM phase devoid of long-range magnetic ordering. While the FM regions produce insufcient coherency themselves, by pining neighbouring AFM spin orientations along the applied H-eld direction they inhibit spin canting and in effect mute the interference effect. S.d. errors are propagated for the difference measurements.

phenomenon is underpinned by the spatial overlap between the Eu 5d and Ti 3d orbitals, and their energetic degeneracy that is intricately balanced so that a small ionic displacement has a signicant effect on the AFM strength. In order to reach a quantitative correlation between experiment and theory, we have estimated the critical E-eld by dividing the energy required to displace the ions by the polarization. To generate a polarization eld of P 18 mC cm 2, where AFM and FM states are degen

erate, would require B5 105 V cm 1. This is comparable to the

experimental eld found to extinguish the AFM state, B1.0 105 V cm 1.

X-ray resonant interference scattering. To explore the ensuing magnetic state by E-eld, we employed X-ray resonant interference scattering (XRIS)36. XRIS is sensitive to the magnetic moment aligned along one direction by either an internal FM interaction or an external magnetic eld. Even in the AFM state, the magnetic moments uniformly canting towards an external magnetic eld direction result in chargemagnetic interference of the scattered intensity illustrated in Fig. 5a. Here, contrasting energy scans through the Eu LII edge at the (003)ETO reection with opposing applied magnetic eld directions ([110]ETO) at

1.2 T in the lm plane demonstrate the interference effect. The measurements were made in horizontal scattering geometry, which provides for additional charge scattering suppression, illustrated in Fig. 5binset. In ETO, the AFM coupling is generally weak and as a result 1 T is sufcient to fully saturate the Eu moments along the magnetic eld direction shown by the magnetic eld dependence of the interference effect in Fig. 5b. This plot shows that the degree of magnetic moment canting by the external H-eld is proportional to the eld strength.

Figure 5ci presents the XRIS spectroscopic difference applying0.1 T showing that the magnetic moments cant towards the eld direction with B10% of the full Eu moment. Once the electric eld (1 105 V cm 1) is applied, the interference effect is

quenched Fig. 5cii. This was a surprising result because an

enhanced XRIS effect owing to long-range FM order would be expected. Alternatively, if the electric eld induced a true AFM FM degenerate state, such magnetically frustrated moments would nevertheless align along the applied magnetic eld direction resulting in an interference effect. Similarly, if the E-eld caused a paramagnetic state, 0.1 T is sufcient to align the magnetic moments producing an interference effect owing to small thermal uctuations at this temperature, 1.9 K. Consequently, the magnetic state induced by the E-eld is neither frustrated nor paramagnetic. However, to adequately explain both the XRIS and AFM order suppression would require the emergence of short-range-ordered nanometre-sized FM clustering. This model disrupts the long-range spin coherence of the AFM order while the emergence of FM interactions in short-range cluster formation remains insufciently large to signicantly contribute to the chargemagnetic interference.

DiscussionOur ndings present conclusive evidence for direct single-phase cross-eld ME control in a compressively strained EuTiO3 lm.

Employing in situ X-ray scattering measurements, we present reversible electric switching of magnetic order using a strong intrinsic coupling phenomenon. We have directly measured the microscopic magnetic structure of EuTiO3 as G-AFM under low-strain states (0.0 and 0.9%) and FM under 1.1% tensile strain. The magnetic critical parameters show 0.9% compressive strain

that alters the relative strengths of coexisting AFM and FM magnetic interactions bringing them into competition. First-principles DFT calculations indicate that the third NN Eu ion SE interaction, mediated through the central Ti ion, ultimately determines the G-AFM spin periodicity along the /111S direction. Moreover, by calculating the energy of the simulated ETOLSAT lm, we have replicated our experimental ndings by modelling the eld-induced polarization effect with controlled Ti displacements. As such, the energetic stability of the AFM order dissipates leading to the emergence of FM interactions.

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Table 2 | TC and TN from rst-principles for bulk ETO in space group Pm3m and with varying U for I4/mcm.

U 5.7 eV(Pm3m) 5.7 eV(I4/mcm) 6.0 eV 6.2 eV 6.5 eV 7.0 eV Exp. TN (K) 12.0 17.9 13.9 11.4 8.8 4.0 5.5

TC 10.5 5.6 7.0 7.7 8.3 9.4 3.8 TN/TC 1.14 3.2 1.99 1.48 1.06 0.43 1.45

Exp., Experimental measurements.

The last column extracts the T from the positive magnetic susceptibility parameter in ref. 38 in order to use the T /T ratio to estimate a best guess of an appropriate value of U.

The underlying mechanism relies on bond alignment distortion suppressing the efcacy of the third NN EuTiEu interaction. This novel giant ME coupling phenomenon will likely offer intriguing prospects to explore new types of ME functionality.

Methods

X-ray resonant magnetic scattering. XRMS measurements were performed on the 6-ID-B beamline at the Advanced Photon Source and the XMaS beamline at European Synchrotron Radiation Facility. The sample was mounted on the cold nger of a JouleThomson stage closed cycle helium displex refrigerator. The incident X-ray energy at 6-ID was tuned to the Eu LII edge by a liquid nitrogen-cooled double-crystal Si(111) monochromator source with a 3.3-cm period undulator. The XMaS beamline is a bending magnet source, and the energy selection performed with a water-cooled double-crystal Si(111) monochromator. All samples were oriented with respect to the substrate crystallographic axis. The lms are epitaxial to their substrates so that the lm diffraction peaks are easily found with respect to the substrate reciprocal matrix. The incident X-ray is linearly polarized perpendicular to the scattering plane (s polarization). The resonant magnetic scattering, arising from electric dipole transitions from the 2p-to-5d states, rotates the polarization resulting in p-polarized photons (parallel to the scattering plane). A post-sample pyrolytic graphite analyser at the (0 0 6)PG

reection was used to select p-polarized radiation and suppress the background from charge scattering (s-polarized light).

Magnetic scattering is not frequently used to measure FM with zero magnetic eld because the magnetic reection occurs at the same position in reciprocal space as the larger charge scattered intensity. In the rare-earth compound, however, the magnetic scattering intensity can be comparable to the nal charge scattering by coupling the large resonant enhancement and suppression of the charge scattering by polarization analysis37. It is expedient to choose the optimum reection to maximize the magnetic to charge scattering ratio as the chemical structure factor is different from the magnetic structure factor. The (0 0 Odd)ETO charge reection is about 40 times smaller than the (0 0 Even)ETO reection, where the diffracted X-rays are in-phase enhancing the scattering amplitude owing to the structure factor of the ETO lm. The magnetic structure factor, on the other hand, is the same for both (0 0 Even)ETO and (0 0 Odd)ETO reections. Hence, we obtained the clear resonant behaviour from the difference between the intensity of the (001)ETO

reection above and below TC presented in Fig. 2b.

X-ray resonant interference scattering. Measurement of ferromagnetic order can also be achieved from the interference between magnetic and charge scattering at the resonant edge36. Nominally in the XRMS process, the electric dipole resonance is dominant. The magnetic scattering (E1 transition) from the moments out of the scattering plane produce the same polarization as the charge scattering when the incoming polarization is parallel to the scattering plane (p polarization). Thus, the charge scattering and magnetic scattering can interfere, and consequently the interference effect is dependent on the magnetic moment direction. X-rays from synchrotron radiation are linearly polarized (in the plane of the synchrotron itself) so by using horizontal scattering geometry with the magnetic eld applied in the vertical direction orthogonal to both the beam direction and beam polarization one may measure the interference change by alternating the H-eld direction.

First-principles DFT. We performed DFT calculations with projector-augmented wave potentials in the GGA U (refs 39,40) framework, using VASP41,42 code. We

used a 8 8 8 k-point grid for Brillouin zone integrals and a 500 eV plane-wave

energy cutoff. This cutoff has been increased to 600 eV in certain parts of the calculations for greater accuracy. Geometric relaxations are done by keeping the in-plane lattice parameter a xed and relaxing the out-of-plane lattice parameter c. Residual force threshold was decreased to 0.5 eV 1 where necessary in order to resolve differences between states close in energy. An external stress has been applied along the c axis in order to compensate for the overestimation of cell volume. Exchange parameters for an Ising model are tted to total energy calculations done in a 2 2 2 perovskite supercell that consists of 40 atoms and

10 different magnetic congurations. S.d.s of these exchange parameters are not reported as they are small and of no qualitative signicance.

EuTiO3 is predicted to be near a magnetic phase transition as a function of the on-site Hubbard repulsion parameter U (ref. 30). In order to pick a best initial

estimateof U, we calculate the CurieWeiss constant and Neel temperature for bulk (under xed stress boundary conditions) ETO, the results are presented in Table 2. It is not possible to reproduce the exact transition temperatures from rst principles owing to limitations of the simple mean eld theory we used, and also because of the very small energy differences under consideration. However, if we pick a U that gives a TN:TC ratio close to experiment (TC is extracted from susceptibility measurements38), then we can get a good sense of the competition between FM and AFM states. We see that U 5.7 eV, which is the value that was

used in previous studies works well when oxygen rotations were not taken into account24. However, once the rotations are taken into account and calculations are repeated in the relevant structure (I4/mcm), a U 5.7 eV overestimates the TN:TC

ratio. To better x the deciencies in DFT, we instead use U 6.2 eV as standard.

Also, an intra-atomic exchange parameter J 1.0 eV is kept xed.

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Acknowledgements

Work at Argonne and use of beamline 6-ID-B at the Advanced Photon Source at Argonne was supported by the US Department of Energy, Ofce of Science, Ofce of Basic Energy Sciences under Contract No. DE-AC02-06CH11357. The EPSRC-funded XMaS beamline at the ESRF is directed by M.J. Cooper, C.A. Lucas and T.P.A. Hase. P.S.,X.K., J.-H.L. and D.G.S were funded through PSU MRSEC, Grant DMR-0820404. T.B. and C.J.F. were supported by the DOE-BES under Grant No. DE-SCOO02334. P.J.R. is grateful for fruitful discussions with Jonathon Lang, Steve May, John W. Freeland, Andreas Kreyssig and Yusuke Wakabayashi. Additional thanks to Michael Wieczorek, Chian Liu, and Michael McDowell, David Gagliano for sample processing and sample environment engineering, respectively. We are grateful to O. Bikondoa, D. Wermeille and L. Bouchenoire for their invaluable assistance, and to S. Beaufoy and J. Kervin for additional XMaS support.

Author contributions

X-ray measurements were performed by J.-W.K., S.D.B., P.T., P.S.N. and P.J.R. DFT calculations were accomplished by T.B. and C.J.F. Samples were prepared by J.-H.L. and D.G.S. Project was designed and supervised by P.J.R. Manuscript was written by J.-W.K., T.B. and P.J.R. with contributions by all authors.

Additional information

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How to cite this article: Ryan, P. J. et al. Reversible control of magnetic interactions by electric eld in a single-phase material. Nat. Commun. 4:1334 doi: 10.1038/ncomms2329 (2013).

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