Magnetic phase control by an electric field

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Received 20 February;accepted 17 May 2004;doi:10.1038/nature02673.
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Supplementary Information accompanies this paper on www.nature.com/nature.
Acknowledgements We thank A.Chubukov,P.D.Johnson,S.A.Kivelson,P.A.Lee,D.B.Tanner,
J.J.Tu,Y.Uemura and T.Valla for discussions.Work in Canada was supported by the Natural
Sciences and Engineering Research Council of Canada,and the Canadian Institute for Advanced
Research.The HgBa
2
CuO
4þd
crystal growth work at Stanford University was supported by the
Department of Energy’s Office of Basic Energy Sciences,Division of Materials Sciences and
Engineering.Work at the University of California at San Diego was supported by the National
Science Foundation and the Department of Energy.Work at Brookhaven was supported by the
Department of Energy.
Competing interests statement The authors declare that they have no competing financial
interests.
Correspondence and requests for materials should be addressed to C.C.H.
(homes@bnl.gov).
..............................................................
Magnetic phase control
by an electric field
Thomas Lottermoser
1
,Thomas Lonkai
2,3
,Uwe Amann
2,4
,
Dietmar Hohlwein
2,3
,Jo
¨
rg Ihringer
2
& Manfred Fiebig
1
1
Max-Born-Institut,Max-Born-Straße 2A,12489 Berlin,Germany
2
Institut fu
¨
r Angewandte Physik,Universita
¨
t Tu
¨
bingen,Auf der Morgenstelle 10,
72076 Tu
¨
bingen,Germany
3
Hahn-Meitner-Institut,Glienicker Straße 100,14109 Berlin,Germany
4
Institut Laue-Langevin,6 Rue Jules Horowitz,BP 156 - 38042 Grenoble Cedex 9,
France
.............................................................................................................................................................................
The quest for higher data density in information storage is
motivating investigations into approaches for manipulating
magnetization by means other than magnetic fields.This is
evidenced by the recent boom in magnetoelectronics and ‘spin-
tronics’
1
,where phenomena such as carrier effects in magnetic
semiconductors
2
and high-correlation effects in colossal magneto-
resistive compounds
3
are studied for their device potential.The
linear magnetoelectric effect

the induction of polarization by a
magnetic fieldandof magnetizationby anelectric field—provides
another route for linking magnetic and electric properties.It was
recently discovered that composite materials and magnetic ferro-
electrics exhibit magnetoelectric effects that exceed previously
known effects
4,5
by orders of magnitude
6–10
,with the potential to
trigger magnetic or electric phase transitions.Here we report a
system whose magnetic phase can be controlled by an external
electric field:ferromagnetic ordering in hexagonal HoMnO
3
is
reversibly switched on and off by the applied field via magneto-
electric interactions.We monitor this process using magneto-
optical techniques and reveal its microscopic origin by neutron
and X-ray diffraction.From our results,we identify basic
requirements for other candidate materials to exhibit magneto-
electric phase control.
Hexagonal HoMnO
3
displays ferroelectric ordering at Curie
temperature T
C
¼ 875 K (ref.11),antiferromagnetic Mn

order-
ing at Ne
´
el temperature T
N
¼ 75 K (ref.12),and magnetic Ho

ordering at T
Ho
¼ 4.6 K (ref.13).The ferroelectric phase possesses
P6
3
cm symmetry and a polarization P
z
¼ 5.6mCcm
22
(ref.11)
along the hexagonal z axis.Figure 1 shows that it is made up by three
magnetic sublattices with Mn

(3d
3
) ions at 6c positions and Ho

(4f
10
) ions at 2a and 4b positions
14
.Anisotropy confines the Mn

spins to the basal x–y plane where frustration leads to four possible
triangular antiferromagnetic structures
12,15
.In contrast,the Ho

sublattices are assumed to order Ising-like along z showing anti-
ferromagnetism or ferri-/ferromagnetism according to Table 1.
Magnetic Mn

ordering was monitored by optical second
harmonic generation (SHG) as detailed elsewhere
12,15
:Light at
frequency q is incident on a crystal,inducing an electromagnetic
polarization at frequency 2q,which acts as source for a SHG light
wave emitted fromthe crystal.The magnetic symmetry determines
the polarization P(2q) of the SHG wave relative to that of the
fundamental wave at q,so that in turn P(2q) reveals the underlying
arrangement of Mn

spins.The relationbetweenSHGpolarization
and Mn

ordering is tabulated elsewhere
12,15
.Magnetic Ho

ordering was monitored by neutron powder diffraction and optical
Faraday rotation,that is,the rotation F/B of the plane of
polarization of linearly polarized light by the magnetic field B in a
transmission measurement.The microscopic mechanisms driving
magnetoelectric phase control were revealed by neutron and X-ray
powder diffraction.
Optical measurements were performed at the MBI on flux-
grown,polished,z-oriented HoMnO
3
platelets (,50mm thick)
using previously described transmission set-ups
15,16
.The static
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541
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electric field E
0
¼ 10
5
Vcm
21
was applied to transparent indium-
tin-oxide electrodes evaporated onto the sample surfaces.E
0
exceeds the saturation value by a factor of.10 in order to acquire
a ferroelectric single-domain state even in strongly pinned samples.
Neutron and X-ray experiments were performed at E ¼ 0 at,
respectively,the E2 beamline of the HMI and the high-resolving
Guinier diffractometer at Tu
¨
bingen.Neutron and X-ray diffraction
data were refined simultaneously for each temperature value,using
the Rietveld programSimRef
17
,the statistical qualifier N
j
(ref.18),
and taking the standard deviation of 2Vinto account
19
.
Figure 2a shows the temperature dependence of SHG intensity
with and without applied electric field.x-polarized fundamental
light is incident along z,and the x- and y-polarized SHG contri-
butions are detected.At E ¼ 0 only x-polarized SHG light is
observed below T
N
,indicating P
6
3
cm as magnetic symmetry
15
.It
is followed at T
R
¼ 37 K by 908 rotation of the Mn

spins and,
thus,of the polarization of the SHG signal,thus changing the
symmetry to P
6
3
c
m (ref.15).At 5 K,the SHG signal is quenched
owing to another 908 rotation of the Mn

spins which leads to
P6
3
cmsymmetry
15
.At E ¼ ^E
0
,the temperature dependence of the
magnetic SHG signal is markedly different.Except from a small
residual surface-induced contribution
20
,the SHG signal is
quenched in the whole temperature range below T
N
.The electric
field forces the HoMnO
3
into a different magnetic state right at T
N
,
thereby controlling the magnetic order of the Mn

sublattice.
Reaction of the Ho

sublattice to the electric field is even more
fundamental.The linear magnetic-field dependence of F(Fig.2b)
confirms the absence of any spontaneous magnetization at E ¼ 0.
However,Fig.2c shows that the electric field ^E
0
induces an
additional contribution to the rotation.This contribution can
only originate in ferromagnetic ordering of the Ho

sublattices:
It is of the same order of magnitude as the rotation induced by
intrinsic ferromagnetic R

ordering in compounds with R [{Er,
Tm,Yb} (refs.13,15),and it is not observed in compounds with
paramagnetic R

sublattices (R [{Sc,Y,In,Lu}).The latter point
excludes additional contributions fromthe Mn

sublattice which
remains antiferromagnetic.The electric field therefore controls the
magnetic order of the Ho

system:para- or antiferromagnetismin
the absence of the electric field is converted into ferromagnetic
ordering with strong macroscopic magnetization (see below) in the
presence of the electric field.The ferromagnetic contribution whose
sign switches with reversal of the electric field is revealed by Fig.2c,
as the difference DF¼ [F(þE
0
) 2F(2E
0
)]/2 suppresses all the
‘background’ contributions from Fig.2b.Figure 2c shows that,in
agreement with Fig.2a,the electric-field-induced ferromagnetism
persists in the whole temperature range below T
N
.
A possible correlation between ferroelectricity and the existence
(or non-existence
21
) of a magnetization was pointed out in experi-
ments on BaMnF
4
(ref.22).Further,manipulation of an existing
‘weak’ magnetization by a ferroelectric polarizationwas reported for
Ni
3
B
7
O
13
I (ref.23).However,only in the present case the electric
field creates a purely ferromagnetic Ho

state out of a para- or
antiferromagnetic phase by inducing a change of magnetic
structure.
Figure 3 shows the spatial distribution of Faraday rotation.The
electric-field dependence of Fin Figs 3a and b is obvious.Note that
the spatial distribution of the para- and antiferromagnetic contri-
butions and,thereby,of the sample at E ¼ 0 displays variations by
.108 while the ferromagnetic contribution DF in Fig.3c is
homogeneous within ^18.This corroborates that the two constitu-
ents originate in different magnetic subsystems.
Table 1 reveals that the unusual example of phase control
Table 1 Magnetic structures and correlation in HoMnO
3
Magnetic symmetry Ho (total) Ho(2a) along z Ho(2a) x–y plane Ho(4b) along z Ho(4b) x–y plane Magnetoelectric effect
...................................................................................................................................................................................................................................................................................................................................................................
P
6
3
cm AFM 0 0 FM AFM 0
P
6
3
c
m AFM AFM FM AFM FM 0
P6
3
cm AFM 0 0 AFM AFM a
xy
¼ 2a
yx
P6
3
cm FM FM FM FM FM a
xx
¼a
yy
;a
zz
...................................................................................................................................................................................................................................................................................................................................................................
Magneticspacegroup,allowedHo

ordering,andmagnetoelectriceffect.2aand4brefer tothe Ho

sites with‘x–y plane’ and‘alongz’ referringtocorrelations betweenHo

ions inandperpendicular
to the basal plane respectively,a
ij
denote the non-zero components of the magnetoelectric tensor.(A)FM:(anti)ferromagnetic;0:disordered.
Figure 1 Magnetic structure of hexagonal HoMnO
3
.Mn

and Ho

ordering in the
absence and presence of an electric field E ¼ ^E
0
.Arrows,magnetic moments of Mn

(yellow) and Ho

(red).Open red arrows indicate that the Ho

moments are disordered,
although antiferromagnetic ordering at the 4b site is symmetry allowed.Green lines,unit
cell.Red lines and Y-shaped structures,inter-plane Mn

–Mn

exchange paths with
straight (dashed) lines and black (grey) labels as superior (inferior) path.Cross-wires
denote the frustrated 1/3 positions of Mn

ions (see text).Deflections are enhanced by a
factor of 2.Note that ferromagnetic Ho

ordering is observed exclusively when the
electric field is applied.
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expressed by Figs 2 and 3 originates in the linear magnetoelectric
effect.The magnetoelectric effect is described by the second-rank
axial c tensor ^a (ref.4) and contributes a term H
ME
¼ ^aDB to the
free energy
5,22
(with D ¼ e
0
(E þ P) and B ¼ m
0
(H þ M) repre-
senting the sumof electric field E and induced polarization Pand of
magnetic field Hand induced magnetization M).In comparison to
other compounds
4,5
,the magnetoelectric energy H
ME
of a magnetic
ferroelectric is enhanced by orders of magnitude by the presence of
ferroelectric and/or ferromagnetic ordering.When an external
electric (or magnetic
24
) field maximizes D (or B) towards a
single-domain state,the microscopic processes detailed below
mediate the reorientation of the Mn

spins in the basal plane
and the change in HoMnO
3
from antiferromagnetic to ferromag-
netic interplane coupling between the Ho

spins.According to
Fig.1 and Table 1,this corresponds to a transition into the P6
3
cm
phase where a macroscopic magnetoelectric effect from a
zz
–0 is
active.This transition costs small values of anisotropy and super-
exchange energy,but these are vastly overcompensated by the gain
of magnetoelectric energy froma
zz
M
z
P
z
.
The microscopic processes driving the magnetoelectric effect in
HoMnO
3
are revealed by Fig.4,which shows the temperature
dependence of the ordered magnetic moments of Mn

and
Ho

,the position of Mn

ions,and the electric dipole moment
in the unit cell as derived fromneutron and X-ray powder diffrac-
tion.Figure 4a shows that even far above T
Ho
¼ 4.6 K,long-range
ordering of Ho

moments is promoted.Ho

–Mn

interaction
therefore leads to an energy contribution H
int
¼
P
S
Ho
^
AS
Mn
with
S
Ho,Mn
as ordered magnetic moments,the summation including all
Ho

and Mn

ions in the unit cell
24,25
.
^
A is the 3 £ 3 interaction
matrix which is made up by symmetric superexchange and asym-
metric Dzyaloshinskii-Moriya
26
contributions.If ferroelectric dis-
tortions are neglected,the sum is H
int
¼ 0 for all types of Mn

ordering in Table 1.Ferroelectric distortions,however,lead to a
correction d
^
A¼d
^
A
0
P
z
for which

in the case of P6
3
cmsymmetry

summation leads to the non-zero contribution H
int
;H
ME
¼
a
zz
P
z
S
Ho
z
with the magnetoelectric susceptibility a
zz
¼6S
Mn
y
ðdA
2a
0
2
dA
4b
0
Þ
zy
:Here superscripts 2a,4b refer to the two Ho

sites (see
Fig.1).
Ho

–Mn

interaction in combination with ferroelectric



Figure 2 Dependence of magneto-optical properties of HoMnO
3
on electric field.
a,Temperature dependence of second harmonic generation (SHG) at 2.42eV in the
absence and presence of an electric field.Filled (open) symbols refer to SHG in the
absence (presence) of a field E
0
¼ 10
5
V cm
21
.Circles (squares) denote the y (x)
polarized components of the SHG signal.Inset,spatial distribution of SHG intensity at
2.46 eV on a sample with semicircular electrode.b,Faraday rotation for E ¼ 0 at 1.55 eV
and 1.4 K with light travelling along z,as a function of the magnetic field H
z
.
Para-/antiferromagnetic behaviour is observed.c,Temperature dependence of
ferromagnetic contribution DFto Faraday rotation for E ¼ ^E
0
at constant absorption
with m
0
H
z
¼ 0.5 T.In DFthe ‘background’ contribution from b has been subtracted.
The line is a guide to the eye.
Figure 3 Spatially resolved Faraday rotation.The rotationFof a homogeneously polarized
sample is shown as a function of the applied electric field E
0
(grey patches:electrodes).
a,F(þE
0
).b,F(2E
0
).c,Contribution DF¼ [F(þE
0
) 2F(2E
0
)]/2 induced by the
applied electric field.





Figure 4 Microscopic manifestation of the magnetoelectric effect.Temperature
dependence of a,ordered Mn

and Ho

moments;b,x position of the Mn

ions in
units of in-plane lattice constant a;c,ferroelectric dipole moment per unit cell.The
transition of the Mn

ions fromx.a/3 to x,a/3 at T
Ho
for E ¼ 0 (or,equivalently,at
T
N
for E –0) reverses the competition between the Mn

–Mn

inter-plane exchange
paths in Fig.1,which leads to a conversion of the
6
3
into a 6
3
axis,thereby allowing the
magnetoelectric effect.
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distortion therefore explains the magnetoelectric coupling.Appli-
cation of the electric field transfers the sample into a single-domain
state with maximum field D for which transition into the P6
3
cm
phase leads to the largest possible energy gain from H
ME
¼ ^aDB:
According to ref.13 and Fig.4a up to 40% (Ho

:3–4m
B
) of the
rare-earth spins are ordered.The increase defining T
Ho
in Figs 2a
and 4 is due to Ho

–Ho

exchange in the x–y plane which
complements the Ho

–Mn

interaction.
Transition into the magnetoelectric P6
3
cm phase corresponds to
modification of the inter-planar Mn

–Mn

exchange paths
stabilizing the three-dimensional magnetic order.With the Mn

ions at x ¼
1
3
a;the inter-planar Mn

–Mn

exchange is nearly
perfectly frustrated.Frustration is overcome by the,2%movement
of the Mn

ions revealed in Figs 1 and 4b.Depending on the shift
being positive or negative,either the exchange path favouring
formation of the
6
3
axis (above T
Ho
at E ¼ 0) or the exchange
path favouring formation of the 6
3
axis (below T
Ho
at E ¼ 0 and
below T
N
at E ¼ ^E
0
) is strengthened.Figure 4c shows that the
electric dipole moment is modified along with the magnetic
transition which is another manifestation of magnetoelectric inter-
action on the microscopic scale.
Thus we have observed how multifold magnetic ordering in
HoMnO
3
is controlled by a static electric field.Ferromagnetic
Ho

ordering is deliberately activated or deactivated,and
the ferromagnetic component is controlled by the sign of the
electric field.The driving mechanism for phase control are micro-
scopic magnetoelectric interactions originating in the interplay of
Ho

–Mn

interaction and ferroelectric distortion.With their
potential for giant magnetoelectric effects,magnetic ferroelectrics
are most favourable for technological applications of magneto-
electric switching,which is reflected by the current push for novel
compounds and concepts to understand this class of materials
27,28
.
On the basis of the work presented here,promising candidates for
controlled magnetoelectric switching
10
are compounds with elec-
tronic states close to the ground state which are energetically
lowered by magnetoelectric contributions in an applied electric or
magnetic field.Therefore frustrated systems or systems in the
vicinity of phase boundaries or quantum critical points
29
are
prime candidates for magnetic phase control by an electric field
or vice versa.A
Received 19 April;accepted 8 June 2004;doi:10.1038/nature02728.
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Acknowledgements We thank K.Kohn and K.Hagdorn for samples,and the DFGand the BMBF
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Competing interests statement The authors declare that they have no competing financial
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..............................................................
Demixing in simple fluids induced
by electric field gradients
Yoav Tsori,Franc¸ ois Tournilhac & Ludwik Leibler
Laboratoire Matie
`
re Molle &Chimie (UMR167 CNRS-ESPCI),Ecole Supe
´
rieure
de Physique et Chimie Industrielles,10 rue Vauquelin,75231 Paris CEDEX 05,
France
.............................................................................................................................................................................
Phase separation in liquid mixtures is mainly controlled by
temperature and pressure,but can also be influenced by gravita-
tional,magnetic or electric fields.However,the weak coupling
between such fields and concentration fluctuations limits this
effect to extreme conditions
1–3
.For example,mixing induced by
uniformelectric fields is detectable only at temperatures that are
within a few hundredths of degree or less of the phase transition
temperature of the systembeing studied
4–7
.Here we predict and
demonstrate that electric fields can control the phase separation
behaviour of mixtures of simple liquids under more practical
conditions,providedthat the fields are non-uniform.By applying
a voltage of 100 Vacross unevenly spaced electrodes about 50mm
apart,we can reversibly induce the demixing of paraffin and
silicone oil at 1 K above the phase transition temperature of the
mixture;when the field gradients are turned off,the mixture
becomes homogeneous again.This direct control over phase
separation behaviour depends on field intensity,with the elec-
trode geometry determining the length-scale of the effect.
We expect that this phenomenon will find a number of nano-
technological applications,particularly as it benefits from field
gradients near small conducting objects.
The driving force for separation in liquid mixtures is the
preference of constituent molecules to be in contact with their
own species
8
.At high temperatures,however,thermal agitation
dominates over enthalpic interactions,and mixing occurs.Figure 1a
shows the classic phase diagramof a binary mixture of two liquids,
A and B,with phase transition temperature,T
t
(blue curve),as a
function of the concentration of A (f;where 0,f,1).Above T
t
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