ARTICLESPUBLISHED ONLINE: 31 OCTOBER 2010 | DOI: 10.1038/NNANO.2010.214

Magnetoelectric coupling at metal surfaces
L. Gerhard1, T. K. Yamada1,2, T. Balashov1, A. F. Takács3, R. J. H. Wesselink1, M. Däne4,5, M. Fechner4,
S. Ostanin4, A. Ernst4, I. Mertig4,6 and W. Wulfhekel1 *Magnetoelectric coupling allows the magnetic state of a material to be changed by an applied electric ﬁeld. To date, thisphenomenon has mainly been observed in insulating materials such as complex multiferroic oxides. Bulk metallic systems
do not exhibit magnetoelectric coupling, because applied electric ﬁelds are screened by conduction electrons. We
demonstrate strong magnetoelectric coupling at the surface of thin iron ﬁlms using the electric ﬁeld from a scanningtunnelling microscope, and are able to write, store and read information to areas with sides of a few nanometres. Our
work demonstrates that high-density, non-volatile information storage is possible in metals.

M

agnetoelectric coupling (MEC) has the potential to inﬂuence the magnetic state of matter through the applicationof an electric ﬁeld, and is mediated by subtle crystal structure changes induced by the electric ﬁeld affecting the magnetic
properties. Two realizations of MEC in insulators exist. In theﬁrst, single-phase multiferroics combine both electric and magnetic
dipole moments in the same phase, but only display low ordering
temperatures1–3. In the second, ferroelectric and ferromagnetic
phases can be brought into close contact so that electric and magnetic dipoles couple via the interface, driven by elastic4,5 or electronic6,7 effects. In both approaches, the electric polarization (theposition of the ions in the ferroelectric material with respect toone another) can be switched by an applied electric ﬁeld. In
metals, the electric ﬁeld cannot penetrate deeply, prohibiting MEC
in the bulk because the ﬁeld is screened by a free electron charge
near the surface8. This screening surface charge extends into thevacuum, forming a surface barrier, which is reﬂected in the work
function. In the vicinity of the surface, however, the interaction of
the surface barrier with an external electric ﬁeld causes substantial
displacements of free electrons9. Similarly to the electrons, thecores of the surface atoms are also displaced, but in the opposite
direction, as has been observed for non-magnetic palladium10.
In magnetic systems these structural relaxations can in turn inﬂuence the magnetic order. This suggests the possibility of ﬁnding
MEC at the surfaces of magnetic metals. A scanning tunnelling
microscope (STM) is an ideal tool with which to investigate this,as it can image surface structures and it is possible to use the electricﬁeld underneath the STM tip to induce magnetic phase transitions.

Computational design of magnetoelectric coupling
As a model system for surface MEC in metals, we used two atomic
layers of Fe grown on Cu(111). Bulk Fe is known to have a structural
instability between the face-centred cubic (fcc) and body-centredcube (bcc) phases, as well as a strong variation of the magnetic
order following slight changes in the unit cell volume11. The
phase transformation is caused by a diffusionless deformation of
the lattice, termed the martensitic phase transition12,13. In thisphase transition, the atomic volume of Fe is reduced when goingfrom the bcc to the fcc phase, causing a change in the magnetic
ground state. This behaviour is enhanced at the Fe surface and in

ultrathin Fe layers, which offers the opportunity to trigger structuraland magnetic transitions by means of an external electric ﬁeld
interacting with the surface charge. Our calculations, performed
for two atomic layers of Fe on Cu(111), predict that the crystal
structure and therefore the magnetic order can be controlled byan electric ﬁeld, allowing magnetic information to be written.
Experimentally, the electric ﬁeld was provided by an STM in thetunnelling regime. In response to the ﬁeld, the Fe islands could beswitched locally on the nanometre scale between the antiferromagnetic fcc and the ferromagnetic bcc conﬁgurations. These properties
allow ultrathin Fe ﬁlms to comprise a simple model system byusing the interactions between magnetism, induced surface chargeand elasticity.
First-principles calculations for the atomic relaxations of thebilayer Fe/Cu(111) surface under an applied electric ﬁeld were
performed with the Vienna Ab Initio Simulation Package(VASP)14 using density functional theory. An applied electric ﬁeldof 1 × 109 V m21 was used. The results of the simulations ofﬁeld-induced vertical relaxations are presented in Fig. 1, showing
the normalized total charge density distribution in the vicinity ofthe surface under the inﬂuence of positive (Fig. 1a) or negative(Fig. 1b) electrodes. As expected, the positively charged electroderepels the atoms towards the bulk, with a substantial reduction in
the interlayer distances (Fig. 1a); however, the electron density at
the surface is increased. With the negatively charged electrode(Fig. 1b), the iron atoms are attracted by the electrode and the electron density at the surface is reduced. Based on a total energy analysis we predict that Fe layers are layerwise antiferromagnetic in
Fig. 1a and ferromagnetic in Fig. 1b. These ﬁndings are related to
the remarkable magnetic phase properties of iron. In Fig. 1a, theinteratomic distances are reduced which favours antiferromagnetic
order, whereas in Fig. 1b, they are expanded, favouring ferromagnetic order in the system11.
Because the electric ﬁeld is perpendicular to the surface, theinduced movements of the electrons and ion cores occur in the vertical direction. Vertical displacement is, however, not the only typeof rearrangement that can take place in this system within a martensitic phase transition. According to a recent STM experiment, fcc
and bcc phases coexist in Fe islands on the Cu(111) surface15.
We therefore investigated possible fcc-to-bcc martensitic transitions

1

Physikalisches Institut, Karlsruher Institut für Technologie (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany, 2 Graduate School of Advanced
Integration Science, Chiba University, Chiba 263-8522, Japan, 3 Faculty of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania, 4 Max-PlanckInstitut für Mikrostrukturphysik, Weinberg 2, 06120 Halle, Germany, 5 Materials Science and Technology Division, Oak Ridge National Laboratory Oak Ridge,
Tennessee 37831, USA, 6 Martin-Luther-Universität Halle-Wittenberg, Institut für Physik, 06099 Halle, Germany. * e-mail: wulf.wulfhekel@kit.edu
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+

+

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−

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ρ
ρmax

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FM

AFM

]

[ 110

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[ 101]a +NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2010.214

[01 −
1]

δ

Fe
0.6

Fe

Relative total energy(eV/unit cell)

c
0.8

d

0.2

Relative total energy(eV/unit cell)

Cu
[110]

−

0.08
0.04

fcc
0.4

Cu

Cu

Fe
Cu

0.00

Fe
Fe

Cu

+
0.12

bcc
−

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Fe
Cu
+

0.08
0.04

0.0

[110]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Displacement, δ (Å)

Figure 1 | Simulations of surface relaxations under the inﬂuence of an electric ﬁeld in Fe/Cu(111). a,b, Normalized electronic charge density in fcc bilayers
Fe and two underlying Cu layers under positive (a) and negative (b) electric ﬁelds. The electric ﬁeld is modelled by a plate capacitor placed 4 Å above thesurface. The electron charge is attracted (repelled) by the positively (negatively) charged electrode, causing the ions to move away from (towards) the
surface. The Fe layers were found to be layerwise antiferromagnetic (AFM) in a and ferromagnetic (FM) in b. c,d, Relative total energy per unit cell as afunction of the lateral displacement d of the top Fe layer due to the martensitic phase transition (red for antiferromagnetic and blue for ferromagnetic states).
When a positive electric ﬁeld is applied, the iron atoms adopt fcc stacking, and the layer magnetizations align in an antiparallel arrangement (c). When theapplied ﬁeld is negative, bcc stacking of magnetic layers aligned in parallel is energetically preferred (d). The ball model illustrates the movement of the top
Fe atoms from their threefold hollow site position of fcc (111) stacking (blue) to the bcc (110) bridge position (orange). Grey and red balls represent Cu andbottom Fe atoms, respectively. Lattice directions in the fcc (111) plane and respective unit cells are indicated.

a

c

0.5

bcc

0.3

(dl/dU) / (T)Height (nm)

fcc
0.4

0.2
0.1
0

b

LDOS

5°

−1

5°
δ

−0.5

0

0.5

1

−1

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0

0.5

1

E−EF (eV)Figure 2 | Crystallographic and electronic structure of Fe islands. a, Topographic STM image showing two crystallographic phases in a bilayer Fe island on
Cu(111) (image size, 19 nm × 19 nm). The coexisting phases can be distinguished by a difference in height. b, Atomically resolved image showing the fcc
conﬁguration on the left and the bcc conﬁguration on the right. The top-layer atoms on the left follow the hexagonal fcc (111) structure of the Cu substrate(red grid). The atomic directions on the right (green line) show a slight misalignment of 58 with the fcc directions (red line) and a shift d indicating a bcc(110) stacking (image size 3.7 nm × 3.7 nm). c, Identiﬁcation of the two phases as ferromagnetic bcc and antiferromagnetic fcc by their LDOS: typicalnormalized differential conductance spectrum (continuous lines) on the island rim (orange) and in the island centre (blue), compared to the calculated spinaveraged LDOS of 2 ML Fe/Cu(111) in the ferromagnetic bcc and antiferromagnetic fcc conﬁgurations (dashed lines).
2

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NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2010.214
a

c

b

d
Gap voltage (V)

2
1
0
−1
40
−2
Height (pm)

20

0
0

5

10

15

20

25

30

Time (s)efFigure 3 | Controlled switching with electric ﬁelds. a–c, Switching of antiferromagnetic fcc (blue) and ferromagnetic bcc (orange) areas with electric ﬁeld
pulses. Three STM scans of an island corner were recorded at subcritical electric ﬁelds. By applying a positive ﬁeld pulse after the acquisition of scan a, thebcc region is expanded in b and reduced again by a negative ﬁeld pulse in c. Image sizes in a–c, 6 nm × 6 nm. Positions of the pulses are marked in red.
d, Applied gap voltage (black line) and height (coloured line) recorded as function of time at a ﬁxed tip position. It can be seen that the switching process isdeterministic and reproducible. e,f, Small Fe islands can be completely switched from an antiferromagnetic fcc (e) to a ferromagnetic bcc (f) structure. Image
size in e and f, 11 nm × 9 nm (horizontal × vertical).

by also varying the lateral displacement of the Fe atoms in thepresence of the electric ﬁeld. The layers were relaxed along thevertical direction as a function of the lateral displacement, resulting
in the total energy of the layers for ferromagnetic and antiferromagnetic
conﬁgurations. Our simulations demonstrate that, under a positiveﬁeld, the ferromagnetic bcc stacking is unstable and fcc stacking withlayerwise antiferromagnetic order of the two Fe layers is energeticallymost favourable (Fig. 1c). Additionally, there is an energy barrierof 20 meV at a displacement of 0.25 Å for the transformation to the
fcc state. In the case of a negative applied electric ﬁeld (Fig. 1d), theexpanded fcc stacking is ferromagnetically ordered and unstable,
and can transform to the energetically favoured ferromagnetic
bcc structure (for more details on the energy landscape, see
Supplementary Information).

Structure and magnetism in iron islands
To conﬁrm these predictions experimentally, we performed STM
measurements at 4.3 K in ultrahigh vacuum on Fe layers depositedby molecular beam epitaxy at 300 K onto clean Cu(111) surfaces.
Fe/Cu(111) is known to nucleate in two atomic-layer high triangular islands15, as illustrated in the STM image in Fig. 2a. The triangular islands, however, display an inhomogeneous structure. Two
different coexisting phases of Fe can be distinguished as different
apparent heights (Fig. 2a). Recently, Biedermann and colleagues
showed in atomically resolved STM studies that the islands consistof fcc Fe in the centre, and the rim has a bcc structure15. In atomically resolved STM images (Fig. 2b), we identiﬁed the same crystallographic phases. In the centre, the atoms show a perfect hexagonalorder with the lattice directions and distances of the fcc Cu substrate

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NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2010.214

a

b

−0.4
Experiment−0.25

E = const.
bcc
Critical voltage, Uc (V)Gap voltage (V)

−0.3
−0.2

−0.15

bcc

I = const.
U = const.
P = const.
d = const.

−0.2

−0.1
fcc

fcc

0

−0.1
0

1

2

3

Position (nm)

0

1

2

3

4

5

Tip sample separation, d (A)Figure 4 | Controlling fcc versus bcc structures with the local electric ﬁeld. a, A single line across the fcc–bcc domain boundary was scanned with the STM,
decreasing the gap voltage scan line by scan line. At a critical gap voltage (0.16 V) a transition from fcc to bcc occurs. This experiment has been carried out
at different tunnelling currents (in a range from 150 pA to 28 nA), that is, with different tip sample separations. b, By plotting the critical gap voltage against
the corresponding tip–sample separation, the boundary (black triangles) in the phase diagram is obtained. The experimental results can be compared withpossible distance dependencies of the critical voltage (coloured lines) resulting from different models (E, constant electric ﬁeld; I, constant current;U, constant voltage; P, constant power; d, constant distance; for details see main text). The curves are all ﬁtted freely to the experimental data.

(red grid). At the rims, however, two directions of the bcc structure(green) deviate by small angles from the fcc substrate direction (red),and the third is aligned with the fcc lattice (red) but with a small
shift to the bridge positions of the bottom Fe layer (d). In agreementwith the work by Biedermann and colleagues15, this indicates a
Kurdjumov–Sachs orientation of the bcc structure.
To verify the predicted magnetic conﬁguration of the two phases,
we performed spin-polarized STM and scanning tunnelling spectroscopy (STS) measurements on the centre and rim of theislands. The spin-polarized STM experiments on the bcc and fcc
regions showed no lateral magnetic superstructures within thephases, excluding rowwise antiferromagnetic, triple-q or 1208 Néelspin structures in both fcc and bcc phases. To distinguish theremaining ferromagnetic and layerwise antiferromagnetic conﬁgurations, STS experiments were performed. The measured differential
conductance dI/dU normalized by the tunnelling matrix element T
is to ﬁrst order proportional to the local density of states (LDOS)
according to an extended Tersoff–Hamann approach16,17 (fordetails see Methods). These experimental spectra were used as electronic ﬁngerprints to identify the magnetic state by comparison with
the LDOS of different magnetic phases of fcc and bcc Fe layers calculated by a ﬁrst-principles Green function method especiallydesigned for layered semi-inﬁnite systems18. The LDOS in the
STM geometry was calculated at a tip height of 4 Å above thesurface layer, mirroring the STM experiment.
The experimental spectrum of the island rim matches well withthe theoretical LDOS of a ferromagnetic bcc structure (Fig. 2c), andthe spectrum of the island centre agrees well with the LDOS of alayerwise antiferromagnetic fcc Fe. The LDOS of other magnetic
conﬁgurations did not match the experimental observations at all(see Supplementary Information). In particular, the peak close to
the Fermi energy in the fcc spectrum can only be explained by an
antiferromagnetic order. Its position depends strongly on the interlayer distance of Fe. The best agreement between experimental andtheoretical data is obtained at an interlayer distance between the two
Fe layers of 2.00 Å for fcc Fe and 2.12 Å for bcc Fe (Fig. 2c). This
height difference is also found in the STM images (cf. Fig. 2a).
The STS measurements, in combination with atomically resolved
images, have conﬁrmed the fcc/bcc structures and revealed themagnetic order of the two coexisting phases. Thus, in the following
we identify them by their apparent height in the topographic STM
4image (blue for antiferromagnetic fcc and orange for ferromagneticbcc). The clear distinction of the two states offers the opportunity toread out the magnetic state.

Switching the magnetic order by local electric ﬁelds
Following the theoretical predictions, we applied electric ﬁeld pulses
in the tunnelling junction with the tip positioned close to thedomain boundary between the fcc and bcc areas. An enlarged
view of an Fe island is shown in Fig. 3a, with fcc and bcc areas
recorded at low electric ﬁelds. A ﬁeld pulse of þ5.5 × 109 V m21
and of 50 ms duration was applied with the STM, leading to
an expansion of the bcc area laterally by about 1 nm (Fig. 3b).
This conﬁguration was stable at 4.3 K until a second pulse of
25.5 × 109 V m21 was applied, switching the area back to an fcc
structure (Fig. 3c). This phase transition is mainly observed near the
fcc–bcc domain boundary. However, islands smaller than 10 nm
could be completely switched from a dominantly antiferromagnetic
fcc (Fig. 3e) to a fully ferromagnetic bcc structure (Fig. 3f). We experimentally ruled out that the switching was driven by adsorptioninduced effects such as structural modiﬁcations because of hydrogencontamination (see Supplementary Information), and have conﬁrmed
using STS that when the crystal structure is switched, the electronic
structure also switches accordingly. This experimentally veriﬁed thecapability to induce a crystallographic and magnetic transition.
Furthermore, the stability of both phases at a low electric ﬁeld conﬁrms the above predicted barrier between fcc and bcc conﬁgurations.
This switching process is deterministic and reproducible, as can beseen in Fig. 3d. By applying alternating ﬁeld pulses (black line), themagnetic phase could be switched back and forth (coloured line).
Switching could be achieved by pulses as short as 60 ms, the time
limit of our STM set-up (see Supplementary Information). Theseexperiments illustrate that, with an STM, information can be
written, stored and read out on the nanometre scale.
In the calculations only electric ﬁelds were applied. In our experiments, however, tunnelling currents were also present, and an
overlap of the wavefunctions of tip and sample is signiﬁcant. To
verify MEC as the switching mechanism we carried out a systematic
study of the phase transition. The basic experiment comprised scanning along a single line across the domain boundary many times,
varying the tunnelling parameters. First, the gap voltage U was
decreased line by line from 20.10 V to 20.25 V with the tunnelling

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NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2010.214
current I kept constant. Figure 4a shows the arrangement of fcc andbcc as function of the gap voltage plotted in the y direction. It was
found that at a critical value of the gap voltage Uc (0.16 V in Fig. 4a),a transition from fcc to bcc occurs, shifting the domain boundary to
the left. This gives us a value of Uc for a chosen I. Determination of
the critical voltage was then repeated at different tip sample distances d, scanning exactly the same line on the sample. This wasachieved by varying the tunnelling current. Finally, we obtained aset of points describing the relation between critical voltage Uc
and distance d. As the distance was a priori unknown, it was determined from the experimental current distance relation (for details
see Supplementary Information). The electric ﬁeld in the STM junction was given by the gap voltage over d. Figure 4b plots the criticalvoltage Uc against distance d. In other words, this ﬁgure provides thephase diagram. Above the critical voltage the bcc phase is preferredand below it, the fcc phase is favoured. In the interval from 3 to 6 Å alinear distance dependence of the critical voltage was found; in particular, a freely ﬁtted straight line passes through the origin. Thus,
the boundary in the phase diagram corresponds to a constant electric ﬁeld, in agreement with a magnetic phase transition by means of
MEC, verifying the theoretical predictions. A series of experimentswith different tips and Fe islands revealed critical electric ﬁelds inthe range between 3 × 108 and 9 × 108 V m21, in good agreementwith calculations. These ﬁelds are close to those used in recent
experiments on MEC19.
To test further for mechanisms not related to MEC, the experimental data were compared with relations resulting from different
scenarios (Fig. 4b). The transition could be directly caused by thecurrent, for example, due to spin torque20, spin accumulation21 orelectromigration. This would lead to a switching that only
depends on the tunnelling current (I ¼ const., green line). This,
however, disagrees with the observed dependence. Similarly, mechanisms that relate to the energy of the tunnelling electrons (such as
inelastic excitation of speciﬁc lattice vibrations or electronic excitations; Uc ¼ const., yellow line) or local heating (population of acontinuum of excited vibronic or electronic states, P ¼ I . Uc ¼
const., red line) do not ﬁt the experimental data. Mechanicalforces between the tip and the sample due to the overlap of theirwavefunctions22 (d ¼ const., blue line) also fail to explain the data.
Indeed, this excludes these other switching mechanisms.

Conclusions
Because the studied phase transition in Fe is of ﬁrst order (activated)
and is reversible, it conﬁrms a prototype for writing, storing andreading information on the nanometre scale. The dream of storing
information magnetically and switching it electrically is thus not
restricted to the class of insulating materials, but has been provento be valid at metallic surfaces as well. The observed effect is not apeculiarity of Fe, because the underlying structural and magnetic
phase transition occurs in a whole variety of transition metals.

Methods
Relaxations with an applied electric ﬁeld. To simulate atomic relaxations in
Fe/Cu(111), the Vienna Ab initio Simulation Package (VASP)14,23,24 was used within
the generalized gradient approximation (GGA-PBE) approximation25 for exchange
and correlation effects. Electron–ion interactions were described by the projectoraugmented wave (PAW) pseudopotential26, and the electronic wavefunctions wererepresented by plane waves with a cutoff energy of 600 eV. To model the (111)
surface of Cu, we constructed a 7 ML (monolayer) thick (1.5-nm) supercell, with avacuum spacer of 2 nm. The in-plane fcc lattice parameter was set to theexperimental value of 2.5561 Å. The two top Cu monolayers and two Fe adlayers inthis asymmetric slab were relaxed. For ionic relaxations the 12 × 12 × 4 k-point
Monkhorst–Pack27 mesh was used. Ionic relaxation was performed within the spinpolarized mode, starting from the ferromagnetic or, alternatively, from theantiferromagnetic conﬁguration in the Fe layers, until the forces were less than 7 ×
1023 eV/Å. To calculate the electronic charge density as well as the local magnetic
moments, we used the tetrahedron method with a k-mesh of 32 × 32 × 16 points foreach completely relaxed atomic conﬁguration. To imitate the presence of an external
electric ﬁeld in our numerical simulations we used a plate capacitor placed in

ARTICLES

vacuum at a distance 4–5 Å above the surface28. The plates of the capacitor wereseparated by a vacuum spacer to avoid interaction and charge transfer between them.
Thus, one plate of the capacitor placed above the Fe adlayers simulates either anegatively or positively charged tip. The strength of the electric ﬁeld was chosen to be
109 V m21. Non-equilibrium effects were not taken into account in the model.
Simulations of STM spectra. To simulate scanning tunnelling spectra we used the
Tersoff–Hamann treatment for the tunnelling current16. In this approximation, thetunnelling current is proportional to the LDOS of the surface at the tip position. In
the present work the LDOS was calculated from ﬁrst principles using a Greenfunction multiple-scattering approach29 within density functional theory in the local
spin density approximation (LSDA). The method was specially designed for layered
systems by treating adequately semi-inﬁnite boundary conditions30. The LDOS for
the Fe/Cu(111) system was calculated from non-spherical potentials determined
self-consistently for bulk, surface and vacuum regions.
Experimental set-up. The STM tips were chemically etched from a tungsten wireand cleaned in a vacuum chamber by melting the end of the tip. The Cu(111)substrate was prepared by sputtering with 3 keV Arþ ions followed by annealing to
450 8C to obtain a clean and ﬂat surface. About 0.2 ML of pure Fe were deposited bymolecular beam epitaxy at a substrate temperature of 300 K. Both this preparationand our studies in the STM were carried out in ultrahigh vacuum ( p , 1 ×10210 mbar). The differential conductance dI/dU was obtained with a lock-in
technique using a sinusoidal modulation of 5 mV and a frequency of 16.4 kHz.
When ramping the voltage, the feedback loop was open. As the experimental dI/dU
spectra not only depend on the LDOS but also on the tunnelling probability T, theycannot be compared directly with a calculated LDOS. We therefore normalized ourspectra using the tunnelling probability T: LDOS / dI/dU . 1/T. As shown by
Ukraintsev17 this allows a deconvolution of density of states and tunnellingprobability within a WKB (Wentzel Kramers Brillouin) approach. The applied gap
voltage is deﬁned as the potential of the tip with respect to the sample.

Received 4 June 2010; accepted 7 October 2010;
published online 31 October 2010

References
1. Smolenskii, G. A. & Chups, I. E. Ferroelectromagnetism. Soviet Physics Uspekhi
25, 475–493 (1982).
2. Lottermoser, T. et al. Magnetic phase control by an electric ﬁeld. Nature 430,
541–544 (2004).
3. Spaldin, N. A. & Fiebig, M. The renaissance of magnetoelectric multiferroics.
Science 309, 391–392 (2005).
4. Zheng, H. et al. Multiferroic BaTiO3–CoFe2O4 nanostructures. Science 303,
661–663 (2004).
5. Zavaliche, F. et al. Electric ﬁeld-induced magnetization switching in epitaxial
columnar nanostructures. Nano Lett. 5, 1793–1796 (2005).
6. Duan, C.-G., Jaswal, S. S. & Tsymbal, E. Y. Predicted magnetoelectric effect in
Fe/BaTiO3 multilayers: ferroelectric control of magnetism. Phys. Rev. Lett. 97,
047201 (2006).
7. Fechner, M. et al. Magnetic phase transition in two-phase multiferroics
predicted from ﬁrst principles. Phys. Rev. B 78, 212406 (2008).
8. Lang, N. D. & Kohn, W. Theory of metal surfaces: charge density and surface
energy. Phys. Rev. B 1, 4555–4568 (1970).
9. Weisheit, M. et al. Electric ﬁeld-induced modiﬁcation of magnetism in thin-ﬁlm
ferromagnets. Science 315, 349–351 (2007).
10. Weissmüller, J. et al. Charge-induced reversible strain in a metal. Science 300,
312–315 (2003).
11. Moruzzi, V. L., Marcus, P. M., Schwarz, K. & Mohn, P. Ferromagnetic phases ofbcc and fcc Fe, Co, and Ni. Phys. Rev. B 34, 1784–1791 (1986).
12. Bain, E. C. The nature of martensite. Trans. Am. Inst. Min. Metall. Pet. Eng. 70,
25–46 (1924).
13. Sandoval, L., Urbassek, H. M. & Entel, P. The Bain versus Nishiyama–
Wassermann path in the martensitic transformation of Fe. New J. Phys. 11,103027 (2009).
14. Kresse, G. & Furthmüller, J. Efﬁciency of ab-initio total energy calculations formetals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6,
15–50 (1996).
15. Biedermann, A., Rupp, W., Schmid, M. & Varga, P. Coexistence of fcc- and bcclike crystal structures in ultrathin Fe ﬁlms grown on Cu(111). Phys. Rev. B 73,
165418 (2006).
16. Tersoff, J. & Hamann, D. R. Theory and application for the scanning tunnelingmicroscope. Phys. Rev. Lett. 50, 1998–2001 (1983).
17. Ukraintsev, V. A. Data evaluation technique for electron-tunneling spectroscopy.
Phys. Rev. B 53, 11176–11185 (1996).
18. Lüders, M., Ernst, A., Temmerman, W. M., Szotek, Z. & Durham, P. J. Ab initio
angle-resolved photoemission in multiple-scattering formulation. J. Phys.
Condens. Matter 13, 8587–8606 (2001).
19. Maruyama, T. et al. Large voltage-induced magnetic anisotropy change in a few
atomic layers of iron. Nature Nanotech. 4, 158–161 (2009).

NATURE NANOTECHNOLOGY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturenanotechnology© 2010 Macmillan Publishers Limited. All rights reserved.

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ARTICLES

NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2010.214

20. Slonczewski, J. C. Conductance and exchange coupling of two ferromagnets
separated by a tunneling barrier. Phys. Rev. B 39, 6995–7002 (1989).
21. Jedema, F. J., Filip, A. T. & van Wees, B. J. Electrical spin injection andaccumulation at room temperature in an all-metal mesoscopic spin valve. Nature
410, 345–348 (2001).
22. Hofer, W. A., Fisher, A. J., Wolkow, R. A. & Grütter, P. Surface relaxations,current enhancements, and absolute distances in high resolution scanningtunneling microscopy. Phys. Rev. Lett. 87, 236104 (2001).
23. Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid–
metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 49,
14251–14269 (1994).
24. Hafner, J. Ab-initio simulations of materials using VASP: density-functional
theory and beyond. J. Comput. Chem. 29, 2044–2078 (2008).
25. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation
made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
26. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector
augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).
27. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations.
Phys. Rev. B 13, 5188–5192 (1976).
28. Neugebauer, J. & Schefﬂer, M. Adsorbate–substrate and adsorbate–adsorbateinteractions of Na and K adlayers on Al(111). Phys. Rev. B 46,
16067–16080 (1992).
29. Lüders, M., Ernst, A., Temmerman, W. M., Szotek, Z. & Durham, P. J. Ab initio
angle-resolved photoemission in multiple-scattering formulation. J. Physics
Condens. Matter 13, 8587–8606 (2001).

6

30. Szunyogh, L., Újfalussy, B., Weinberger, P. & Kollár, J. Self-consistent localized
KKR scheme for surfaces and interfaces. Phys. Rev. B 49, 2721–2729 (1994).

Acknowledgements
This work was supported by the Alexander von Humboldt Foundation, the CNCSISUEFISCSU and the Sonderforschungsbereich SFB 762, ‘Functionality of Oxidic Interfaces’.
The authors thank P.J. Kelly for careful reading of the manuscript, and H.L. Meyerheim,
Z. Szotek and W.M. Temmerman for many stimulating discussions. A.E. thanks V.M.
Kuznetsov and T.A. Shabunina for their help and support during his stay at the Tomsk State
University. Calculations were performed at the John von Neumann Institute in Jülich andRechenzentrum Garching of the Max Planck Society (Germany).

Author contributions
L.G., T.K.Y. and W.W. conceived and designed the experiments. L.G., T.B., A.F.T. and
R.J.H.W. performed the experiments. L.G., R.J.H.W. and T.K.Y. analysed the data. A.E., I.M.
and S.O. designed the calculations. A.E., S.O. and M.D. performed the calculations. M.F.
and M.D. contributed analysis tools. A.E., L.G., I.M. and W.W. co-wrote the paper. All
authors discussed the results and commented on the manuscript.

Additional information
The authors declare no competing ﬁnancial interests. Supplementary informationaccompanies this paper at www.nature.com/naturenanotechnology. Reprints andpermission information is available online at http://npg.nature.com/reprintsandpermissions/.
Correspondence and requests for materials should be addressed to W.W.

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