symmetry and fl t l t i ff tflexomagnetoelectric effects...
TRANSCRIPT
Symmetry and fl t l t i ff tflexomagnetoelectric effects
in multiferroics
A.K. Zvezdin, A.P. Pyatakov, y
A M Prokhorov General Physics InstituteA. M. Prokhorov General Physics InstituteM. V. Lomonosov Moscow State University
MagnetoelectricR i
Technology demandsScientific progress
RenaissanceTechnology demands
- Magnetic Electric
Scientific progress
- Deeper insight into microscopic conversion
- 4-state logic
N l til
mechanisms
- Improved experimental techniques
S lf bl d it - Nonvolatile memory (no transport)
- Microwave signal processing
- Self-assembled nanocomposite
- Thin film deposition technique
BiFeO3 as a trigger for the revival of interest to magnetoelectrics
ContentsContentsI t d ti BiF O t• Introduction: BiFeO3 story
P t 1 S t d t l t i i t ti• Part 1. Symmetry and magnetoelectric interactions in multiferroics. Homogeneous interaction vs. I hInhomogeneous one
P t 2 Fl t l t i ff t• Part 2. Flexomagnetoelectric effect
P t 3 I f l t i h t i d• Part 3 Improper ferroelectrics: what scenario does nature play?
• Part 4 E-field control of micromagnetic structure
BiFeO3 magnetoelectric “holy grail”3 g y g
G.A. Smolenskiy, V.A. Isupov, A.I. Agranovskaya, 1960 Properties : Tc=1083K; TN=643K; (P=0.061 C/m2); dielectric up to ~200К Space group R3c [Kubel, Schmid, Acta Cryst. 1990]p g p [ , , y ]
Theoretical predictions:i
Fe
• linear magnetoelectric effect; • weak ferromagnetism (in basal plane);
c-axis
Fe• weak ferromagnetism (in basal plane); • P,M ME control
t t t !
Fe BiFe
Fe
at room temperatures!1960-1990-ies N i t l fi ti
FeFe
Fe
No experimental confirmation Fe
Cycloid gets the blameCycloid gets the blame
Dubna 1964: G. Bacon, R.P. Ozerov, 1982 reactor at Garching, Dubna 1964: G. Bacon, R.P. Ozerov, И. Sosnowska и E. Sosnowskii:
Discussion on BiFeO3 neutron diffraction results
g,
BiFeO3, TOFD mode,
cycloid period 63nmy p
Spin Cycloid …Spin Cycloid …
…and wagon wheels…and wagon wheels
Spin Cycloid and wagon wheelsSpin Cycloid and wagon wheels
The structure is incommensurate with the lattice period
Hidden within the cycloidy
1
<ME effect>=0<Ms>=0;<Li>=0; dVV
...1VV
Appearance of the effectsAppearance of the effects
Phase transition to homogeneous states:
- High magnetic field induced
- Strain induced (thin films)
- Composition induced (R-earth substituents)
Review: A. M. Kadomtseva, Yu.F. Popov, A.P. Pyatakov, G.P. Vorob’ev, А К Z di d D Vi hl d Ph T iti 79 1019 (2006)А.К. Zvezdin, and D. Viehland, Phase Transitions, v.79 p. 1019 (2006)
Spin cycloid suppression in high magnetic fieldmagnetic field
ME ff t M ti tiME effect Magnetization
H =200kOe
A.M. Kadomtseva et al.
Hc =200кOe
Hc 200kOe
Yu. F. Popov, A. K. Zvezdin, et al., A.M. Kadomtseva et al.JETP Letters, v. 79, p. 571-581 (2004)JETP Lett. 57, 69 (1993).
ME effect: 0.06 V(/cm Oe); ~1ps/m
Thin films: great expectationThin films: great expectation
E h d ltif i tiEnhanced multiferroic properties:
large polarization
50 nm
50-500 nm
BiFeO3
Electrode SrRuO
• large polarization
2max 6сmСPspont
BiFeO3 (bulk):
Substrate SrTiO3
50 nmElectrode SrRuO3
J. Wang et al,
2]111[max 100cm
CPP spontspont BiFeO3 (films):
(PbTiO3: )2max 10080 СPspont g ,
Science, v. 299, p. 1719 (2003)• large magnetization
( 3 )2max cm
• giant magnetoelectric effect V/(cm Oe)
Serious doubtsSerious doubts
Cambridge, UK:W. Eerenstein et al, Science v.307, 1203a (2005)
а) SEM image
б) Auger spectrum map R:G:B=Bi:Fe:O
) t i f i iCNRS, IEF France: H. Béa et al, Appl. Phys. Lett., 87, 072508 (2005)
в) atomic force microscopy image
г) resistance mapping
Back to the realityBack to the realityF l t i h t i Magnetic hysteresis
2
/g)1,0
2 )
Ferroelectric hysteresis Magnetic hysteresis
0
1
(111) crystal
(111)c film
ent,
M (e
mu/
0,0
0,5
(111) film
on, P
(C/m
2
-1
(111)c crystal
Long
Mom
e
-1,0
-0,5
(111) crystal
Pol
ariz
ati
-2x104 -1x104 0 1x104 2x104-2
H (Oe)
emuWeak ferromagnetism
l
,
0 25-25-50 50
E, MV/m
L l i ti 100 CPspont
gemuM s 8.0
J. F. Li, D. Viehland, R. Ramesh, A P P t k A K Z di
release:
F. Bai, A. Pyatakov, A.K. Zvezdin, D Vi hl d t l APL 86 032511(2005)
Large polarization 2]111[ 100cm
P p
A.P. Pyatakov, A.K. Zvezdin,APL, 84 (25), 5261 (2004)
D. Viehland et al, APL 86, 032511(2005)
Polarization in bulk BiFeO3Polarization in bulk BiFeO3Theoretical estimates Z.V. Gabasova, A.K. Zvezdin et al, Physics Letter A 158 p 491 (1991)Physics Letter A 158 p.491 (1991)
Ab initio calculations: J B Neaton C Ederer N Spaldin et al
Shifts of Bi3+ and Fe3+ ions: P=63 e c (ε+)/ V; ; 270cm
CPsp caV 2
23
Ab initio calculations: J.B. Neaton, C. Ederer, N. Spaldin et al PRB 71, 014113 (2005):
2100cm
CPsp
Experimental evidence in single crystal
polarizing microscope microphotograph
Up to 60 C/m2
Delphine Lebeugle, Dorothée Colson, Anne Forget, Michel Viret, Pierre Bonville, Jean-FrancisMarucco, Stéphane Fusil, Phys. Rev. B 76, 024116 (2007)
microphotograph
Solid solutions of Bi1 yLayFeO3 -xPbTiO3Solid solutions of Bi1-yLayFeO3 xPbTiO3
Large values of P and release of M
0 25
0,50
Modified Ceramic
m2 )
0 4
0,8
Modified Ceramic
u/g)
Large values of Ps and release of Ms
0,00
0,25
Single Crystal
atio
n, P
(C/m
0,0
0,4
Single Crystal
zatio
n (e
mu
75 50 25 0 25 50 75-0,50
-0,25
(a)Pola
riza
-0,8
-0,4
(b)Mag
neti
-75 -50 -25 0 25 50 75
Electrical Field, E (kV/cm)-8x104 -4x104 0 4x104 8x104
H (Oe)Ms=0.2-0.3 emu/g Ps=30 C/cm2
N. Wang, J. Cheng, A. Pyatakov, A.K. Zvezdin, J.F. Li, L.E. Cross, D. Viehland, Phys. Rev. B, v.72, n.1, p. 104434 (2005)
Bi0.9-xTbxLa0.1FeO3 Ms=9 emu/gV.R. Palkar, Darshan, C. Kundaliya, et al Phys. Rev. B 69, 212102 (2004)
Launch to marketLaunch to marketFujitsu Lab Ltd & Tokyo- Tech & Fujitsu LtdFujitsu Lab Ltd & Tokyo Tech & Fujitsu Ltd
New material for a new generationNew material for a new generation non-volatile FeRAM
difi d i i f i OModified composition of BiFeO3
Element Size 65 nm, 256MbitsShipments 2009
K.Y. Yun, D.Ricinschi, T.Kanashma, M.Noda, M. Okuyama, . . u , . c sc , . a as a, .Noda, . O uya a,Giant Ferroelectric Polarization Beyond 150μC/cm2 in BiFeO3 Thin Film, The Japan Society of Applied Physics, 43, L 647 (2004)
MoralitéMoralité
Growth technique is important
There were predictions:
- Large spontaneous polarizationg p p- Linear ME effect
Polarization induced weak ferromagnetism- Polarization induced weak ferromagnetism
and they do exist!
Part 1Magnetic symmetryMagnetic symmetry
and magnetoelectric interactionsand magnetoelectric interactions homogeneous vs inhomogeneoushomogeneous vs. inhomogeneous
Space and time inversion symmetries violation
Spatially modulated
inversion symmetries violation
spin structures M(x)Magnetoelectric effects
P(H); M(E), Ms(Ps)Electromagnetooptical
effects (E)( ) ( ) s( s)
Toroidal moments M-induced Second harmonic generation
I (2)2
P T iP, T- parity
Spin toroidal momentSpin toroidal momentT
rdr 3221 jrrjT
T
rdrc
210
jrrjT
V M D b ik V V T h Ph R 187 145
0BT WV.M. Dubovik, V.V. Tugushev, Phys. Rep. 187, 145
0BT W
MToroidal moment MToroidal momentP-,T- odd vector
Toroidal ordering and ME effectToroidal ordering and ME effect
Ad t d f J G l t l PRL 88 237401 (2002)
HET WAdopted from J. Goulon et al, PRL, v.88, 237401 (2002)
jkijkiT ~ HET W jkijkiT
Space inversion symmetry and SHGp y y
Second Harmonic Generation: Z
EEP )2(Second Harmonic Generation: Z
)2( sE k
k
)(E
kjijki EEP X
Y)(sE
The media should be noncentrosymmetrical, otherwise:X
SHG geometry:E(w) is pump E(2w) is second optical harmonic
ii PIP kjkj EEEIE
0)2()2()2( I The contributions from order parameters:
E(w) is pump E(2w) is second optical harmonic0)()()( ijkijkijk I
...... )()()()()()(ml
ik
ijijklml
ik
ijijkll
ik
ijijkl
Mi MPEEihLEEigPEEfP
Reduction of symmetry due to ordering -> new components in Second Harmonic
SHG in BiFeO3SHG in BiFeO3
Bulk sigle crystals Thin films on STO substrate
x10
Bulk sigle crystals Thin films on STO substrate
x10
Second harmonic generation at Т< Тс Structural contributions prevail Nonlinear growth of SHG atТ< ТN
M.Agaltsov, V.S.Gorelik, A.K.Zvezdin et alLebedev Institute Reports, n.5, pp.48-39 (1989)
Sensible to epitaxial distortion
S. E. Lofland, K. F. McDonald, C. J. Metting et al, Phys Rev B 73 092408 (2006)Phys. Rev.B 73, 092408 (2006)
Structural parameters in BFOp
P l d t A tif di t tic-axisFe
Polar order parameter Antiferrodistortive
Fe
c-axisBi
Fe BiFe
Fe
c-axis
FeFe
Fe
Bi
R3c space group
Magnetic order parameters in BFOMagnetic order parameters in BFO
С-axis [111]c
FeFe
Fe
FeFe
M
Fe
Fe
Fe
LL
Magnetoelectric interaction in multiferroicsin multiferroics
Review 1982:G. A. Smolenskii and I. E. Chupis, Sov. Phys. Usp. 25, 475p , y p ,
Magnetoelectric energy
lkjiijklME MMPPF 1
ss
ssss MMPPF 2
s, s/ - magnetic sublattices number
ME interactions in BiFeOME interactions in BiFeO3R3c space group as a “parent” group
E+ I- 3z+ 2x
+ Ei ; Pi ; Hi ; mi li
Table of irreducible representations
3z
Г11 1 1 1
F 2 +
I-
Bi
Г21 1 1 -1 Hz; mz
Г3R
1001
1001
10
01
x
HH
xm
Fe 2x+
I- Bi
R
Г41 -1 1 1
Г
10
10
10
yH
ym
2x+
Fe
Г51 -1 1 -1
Г6R
xEE
x
x
llxP
P
10
01
1001
1001
zP zzE zl I- Bi
yE
y
ylyP 10 10 10
ME interactions in BiFeO3ME interactions in BiFeO3Homogenous R3c space group as a “parent” group gmagnetoelectric interaction:
E+ I- 3z+ 2x
+ Ei ; Pi ; Hi ; mi li
Table of irreducible representations
lmPMcF zme 0Dzyaloshinskii-Moria-like -> weak ferromagnetismГ1
1 1 1 1
Linear ME effectГ2
1 1 1 -1 Hz; mz
Г3R
1001
1001
10
01
x
HH
xm
1 4 1 2
, 1 4 1 2
3 3 0
x z y y
i j y z x x
y x
a L a L a L a La L a L a L a L
a L a L
Inhomogenous magnetoelectric interaction:
R
Г41 -1 1 1
Г
10
10
10
yH
ym
3 3y x
Г51 -1 1 -1
Г6R
xEE
x
x
llxP
P
10
01
1001
1001
zP zzE zl
The origin of spin cycloid
llll rotdivPF zLifshitz
yE
y
ylyP 10 10 10
I. Sosnovska, A.K. Zvezdin,
JMMM v.140, p.167 (1995)
H-induced magnetic phase transitiontransition
2effuKPAF
Incommensurate phase:
C-phase 2
2 us qPAqF
Homogeneous (commensurate) phase:PT point
effuKF
g ( ) p
2
2HKK ueffu ;
IC-phase
Energy gap:
22
)( AqHKHE u
04 gapEH
42)( AqHEgap
Critical field:
g pcHCritical field:
Energy constantEnergy constant
AqPs 2~
A=3 10-7 erg/cm q=106 cm-1Experimental data:
2/6.0~~ cmergSurface energy of spin cycloid: /6.0 cmerggy p y
2/14 AKD i ll f 2/1~4 cmergAKwall Domain wall surface energy:
Energy minimization problemEnergy minimization problem
4,55,05,56,0
0,5
1,0
2,02,53,03,54,0
0,0 l x
0,00,51,01,5
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6
( )
-1,0
-0,5
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6
x () x, ()
Dependency:harmonic solution domain-like solution
K
mAmK 14
Dependency:
),(sin mxqsn 2
q; ; ;const ;uK
I. Sosnovska, A.K. Zvezdin, JMMM v.140, p.167 (1995)
2
021
cos1
m
dmK
q
Weak ferromagnetism release in BiFeO3g 3
lmPMcF zme 0
Dzyaloshinskii-Moriya-like
weak ferromagnetism
The field orientation: 2 10, ,3 3
H H H
i)(spont PHM
sin)(]001[ zspont PHM
1sin
At phase transitionC
A.M. Kadomtseva, A.K. Zvezdin et al,.JETP Letters, v. 79, p. 571-581 (2004)
Toroidal moment in BiFeOToroidal moment in BiFeO3
ME measurements { , ,0}H HH ME measurements { , , }2 2
333231
232221
131211
ij
H
1331
3223
~
y
x
TTT
HHHPP 2/1
M-field orientationin experiment
2112 zT
kjijkjijsii HHHPP 2/112
2aP H221
2bP H H
912 2
921
(0.029 0.003) 10
(0.032 0.003) 10
Cm Oe
C
21 2(0.032 0.003) 10m Oe
Yu.F. Popov, A.M. Kadomtseva, A.K. Zvezdin et al Low temperature physics, 27, 478, 2001 2112~ zT
Thin films of BiFeO3Thin films of BiFeO3
Cycloid suppressionCycloid suppression
%5.0312 /10 cmergY 39 /105)1( cmergaaY
23K strict
54 1010 a
352
/105~4
K cmergHc
crit
F. Bai, A. Pyatakov, A.K. Zvezdin, D. Viehland et al, APL, v. 86, 032511 (2005)Analysis of the strain influence in BFO films:
BiFeO3
No effect on the Polarization Claude Ederer and Nicola A. Spaldin, PRL 95, 257601 (2005)
Q. Jiang, and J. H. Qiu, J. Appl. Phys. 99, 103901 (2006)The strain effects:
Substrate SrTiO
50 nm
50-500 nm
Electrode SrRuO3
J. X. Zhang,Y. L. Li, Y. Wang, Z. K. Liu, L. Q. Chen; Y. H. Chu, F. Zavaliche, and R. Ramesh, J. of Appl. Phys. 101, 114105 (2007)
Substrate SrTiO3
Magnetization release in thin films of BiFeO3
2
g 3
1
2
(111)c filmmu/
g)g
emuM s 8.0
0
( )cnt
, M (e
m
-1
(111)c crystal
g M
ome
2 104 1 104 0 1 104 2 104-2
Long
-2x104 -1x104 0 1x104 2x104
H (Oe)
F. Bai, A. Pyatakov, A.K. Zvezdin, D. Viehland et al, APL 86, 032511(2005)
Composition induced phase t ititransitions
Rare earth substituents Cycloid suppression Bi1-x LaxFeO3
- Linear ME effect Bi1-x RxFeO3 (R =La, Gd, Dy) [V.A. Murashov, Rakov D.N., Dubenko I.S., Zvezdin A.K., Ionov V.M., Crystallography 33, 445 (1988)]
[A. V. Zaleskii, A.K. Zvezdin et al, Phys. Solid State, 45, 141 (2003)]
(1988)],[Z. V. Gabbasova, M. D. Kuz’min, A. K. Zvezdin,et al, Phys. Lett. A 158, 491 (1991)]
Suppression by substituentsSuppression by substituentsLinear ME effect appearance Bi R FeO (R =La Gd Dy)Linear ME effect appearance Bi1-x RxFeO3 (R =La, Gd, Dy)
(1) Bi L F O T 4 2K(1) Bi0.45La0.55FeO3 T=4.2K (2) Bi0.55Gd0.45FeO3 T=4.2K (3) Bi0.55Dy0.55FeO3 T=4.2K (4) Bi Dy FeO T=77K;
V.A.Murashov, D.N.Rakov, N.A.Ekonomov,A.K.Zvezdin and D.N.Dubenko, Solid State Physics (Leningrad) 32, 2156 (1990)
(4) Bi0.45Dy0.55FeO3 T=77K;
Lessons learned. New horizonsSpatially modulated structure:p y
- obscurs of the ME phenomena related to homogeneous interaction
∆P
- reveals the inhomogenous ME phenomena
Ps
ww
Ps stabilizes cycloid Cycloid gives rise to ∆P
Part 2. FlexoME effectPart 2. FlexoME effect
M t d li id t lMagnets and liquid crystals have much in common.
Analogy between ME and LCAnalogy between ME and LC
Inhomogeneous ME interaction
Pinteraction
LLLL PF likeLifshitz q
Flexoelectric energy in Liquid Crystals
nnnn EFFlexo
Analogy to FlexoElectricity in Liquid Crystals:Analogy to FlexoElectricity in Liquid Crystals:A. Zvezdin et al, Phys.Rev.B 50, 2953
Flexomagnetoelectric effectFlexomagnetoelectric effect
Additional polarization induced by spin cycloid: ( , ) 2
fmefme EP cmerg /10~ 4 24 /10~ mCP fme ( , )
Phase transition region:
EP g
HPH fme
Theory: A. Zvezdin, A. Pyatakov, arXiv:0811.3677
Flexomagnetoelectric effectFlexomagnetoelectric effect
PP
Yu. F. Popov, A.K. Zvezdin G.P. Vorob’ev et al, JETP Lett. V.57, 69 (1993)
Part 3.Part 3. Improper ferroelectrics:Improper ferroelectrics: What scenario does nature play?p y
Multiferroics: proper and improper ferroelectricsferroelectrics
Proper ferroelectrics Improper ferroelectrics
Electric polarization independent from magnetic ordering: TC>TN
Electric polarization is induced by magnetic ordering: TC<TN
TN TC0 TC T0
FE paraEMF
TN TC0
paraMM
TC TN0
FE
Weak ME coupling: good for Colossal ME coupling: electric
FE paraEMF paraMM FE
Weak ME coupling: good for 4-state logic, bad for ME conversion
Colossal ME coupling: electric field control of magnetism: electric writing, magnetic reading
M-induced FerroelectricityySpiral mechanism [Si×Sj]Exchange Striction (SiSj) p [ i j]1980-ies Inhomogeneous ME effect(Inverse Dzyaloshinskii-Moriya effect)
V Bar’yahtar et al [JETP Lett 37 p 673]
j
1960-ies (Super)exchange strictionJ. Kanamori, [J. Phys. Chem. Solids 10, 87]
V. Bar yahtar et al [JETP Lett. 37, p. 673]
Analogy to FlexoElectricity in LC A. Zvezdin et al [Phys.Rev.B 50, 2953]
( )d
J. B. Goodenough [Magnetism and the Chemical Bond (John Wiley & Sons, New York, 1963)]
+P ( [ ])div rot P L L L L
P2005 Micro-: H. Katsura et al [PRL, 95, 057205]
+P
P
- P
q
ww
2005 Vector triplet:M. Mostovoy [PRL, 96, 067601]
T. Kimura: JPSJ Online-News and Comments[Nov. 10, 2006]
Spiral or exchange-striction h i ?mechanism?
E h t i ti RelativisticExchange striction(Heisenberg)
Relativistic(Dzyaloshinskii-Moria)( g)
P~[L1 x L2]P~(L1 * L2)Tsuyoshi Kimura: Origin of Multiferroicity: Magnetism Induces Ferroelectricity,
JPSJ Online-News and Comments [Nov. 10, 2006]
Electric field control of cycloid chiralitychirality
TbMnO3Y Y ki t l PRL 98 147204 (2007)
DyMnO3E V Mil t l JETP L tt 85 610 (2007)Y. Yamasaki et al, PRL 98, 147204 (2007) E.V. Milov et al, JETP Lett 85, 610 (2007)
Electric field control of magnetism
f fE-field control of spin helicity ... and micromagnetism
TbMnO3: Y. Yamasaki et al [PRL 98, 147204 (2007)]
DyMnO3: E.V. Milov et al [JETP Lett , 85, 610 (2007)] Experiment IG films: A.S. Logginov et al [JETP Lett., 86, 115 (2007)]
Part 4Part 4Magnetoelectricity and micromagnetismMagnetoelectricity and micromagnetism
“ f“Electro-acupuncture” for magnetic domains
Micromagnetic structuresBloch type domain wall Neel type domain wall
z x
Domain Wal Domain
yy
Vertical Bloch line
Micromagnetism in magnetoelectrics
V. Bar’yahtar et al, Inhomogeneous ME effect, JETP Lett. 37, p. 673 (1983)I. Dzyaloshinskii, Magnetoelectricity in ferromagnets, EPL, 83, 013108 (2008)Micromagnetic structure Electric charges
0expatan2 yy 0expatan2 xx
A.S. Logginov, A.K. Zvezdin, A.P. Pyatakov et al, Electric field control of micromagnetic structures, JMMM, v. 310, p. 2569 (2007)
0
ME phenomena in iron garnet filmsME phenomena in iron garnet films
• 1967 Quadratic ME effect in YIG T.H. O’Dell, Philos. Mag. 16, 487• 1985 Electro-M-optical effect in YIG B. B. Krichevtsov et al JETP Lett., 41, 317• 1989 Linear ME effect in garnet films B. B. Krichevtsov et al JETP Lett., 49, 466g , ,
Advantages:
• Magneto-optical material
• Room temperature magnetoelectricity
• Considerable magnetization (ferrimagnetic)
D i b d
• Considerable magnetization (ferrimagnetic)
• Single phase material (thin films)Domain structure observed by magnetooptical method
g p ( )
Experimentp
1. Copper wire
2. Ground contact
3. Ferrite garnet film
(thickness ~ 10μ)
4. Substrate (0.5mm)
5. Objective lens
DW — Domain wall
A.S. Logginov, G.A. Meshkov, A.V. Nikolaev, E.P. Nikolaeva, A.P. Pyatakov, A.K. Zvezdin,
APL, v.93, p.182510 (2008)
Electric field driven domain wall motionElectric field driven domain wall motion
A.S. Logginov, G.A. Meshkov, A.V. Nikolaev, E.P. Nikolaeva, A.P. Pyatakov, A.K. Zvezdin,
APL, v.93, p.182510 (2008), , p ( )
DiscussionDiscussionCharacteristic Features of the effect:
• Does not depend on magnetic polarity (M-even)• Change sign with electric polarity (E-odd)
Parasitic effects exclusion:
• Change sign with electric polarity (E-odd)• Depend on crystal orientation of the substrateParasitic effects exclusion:
• Current leakage I
2R• no current detected in mA-meter
• contradicts M-evenness of the effect
2R
•Mechanical pressure of the tipF
• contradicts E – oddness of the effect
Resume: The effect is of ME nature
Summary tableSummary tableN b t t f l h 4 M G μ Eff t?N substrate formula h, μ 4πMs, Gs p, μ Effect?
1 (111) (BiTm)3(FeGa)5O12 10 144 8,7 NO
2 (111) (BiLu)3(FeGa)5O12 19 78 39 NO
3 (110) (BiLu)3(FeGa)5O12 4 162 9,2 YES
4 (110) (BiLu)3(FeGa)5O12 6 76 14,4 YES
5 (210) (BiLu)3(FeGa)5O12 10 53.5 34 YES
6 (210) (BiLu)3(FeGa)5O12 10 62 28 YES
7 (210) (BiLu)3(FeGa)5O12 8.6 55 27 YES
The role of anisotropypy
MMMMP )(FInhomogenous ME energy:
MMMMP )(LifshitzF(111) films: Bloch type domain walls z
x (111) films: Bloch type domain walls
0, 0 M M M
(111) films: Neel type domain walls
y 0, 0 M M M
( ) ypz
x
0 M 0 M My
Domain wall dynamics measurementsDomain wall dynamics measurements
A.S. Logginov, G.A. Meshkov, A.V. Nikolaev, E.P. Nikolaeva, A.P. Pyatakov, A.K. Zvezdin,
APL, v.93, p.182510 (2008)
Facts and figuresFacts and figures
Static displacement of domain wall ~35
Characteristic time interval ~10ns (velocity ( y~100m/s)
The voltage 500V corresponds to the effective magnetic field ~50 Oee ec e ag e c e d 50 Oe
Control voltages ~ 100V (tip size r~10m Control voltages ~ 100V (tip size r~10m, E=100 kV/cm)
Reversible DW displacement
Exchanged coupled
Reversible DW displacement
Exchanged coupled structures
Magnetic nanobriges
Iron garnetg
Gateelectrode
magneticnanobridgeA.V. Khvalkovskii,
K.A. Zvezdin, JMMM,300 270 (2006)300, e270 (2006)
Reversible DW displacementReversible DW displacementCrossed polarizers
EMO сellА
Crossed polarizers
Р
Slightly uncrossed polarizersSlightly uncrossed polarizers
А
α
Р
Conclusion
Spatially modulated structures
Magnetoelectric anomalies at IC-C phase transitions
Magnetically induced polarization in improper g y p p pferroelectrics
Electric field control of micromagnetism
Thank you for attention!y f