Multiferroicity due to Charge Ordering
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1 Multiferroicity due to Charge Ordering Jeroen van den Brink ESRF 8/2/2011
2 Multiferroicity due to Charge Ordering Jeroen van den Brink Gianluca Giovannetti & Sanjeev Kumar Sylvia Picozzi & Daniel Khomskii ESRF 8/2/2011
3 Observed multiferroic couplings -- BiFeO 3 and BiMnO 3 T magnetic <<T ferroelectric orderparameters barely couple
4 Observed multiferroic couplings -- BiFeO 3 and BiMnO 3 T magnetic <<T ferroelectric orderparameters barely couple Multiferroics of Type I
5 Observed multiferroic couplings -- BiFeO 3 and BiMnO 3 T magnetic <<T ferroelectric orderparameters barely couple Multiferroics of Type I -- TbMnO 3, DyMnO 3, Ni 3 V 2 O 8 T ferroelectric =T magnetic magnetism induces FE
6 Observed multiferroic couplings -- BiFeO 3 and BiMnO 3 T magnetic <<T ferroelectric orderparameters barely couple Multiferroics of Type I -- TbMnO 3, DyMnO 3, Ni 3 V 2 O 8 T ferroelectric =T magnetic magnetism induces FE Multiferroics of Type II
7 Charge Ordered Multiferroics of Type II Generic idea: in CO material charge can easily be moved over relatively large distances
8 Charge Ordered Multiferroics of Type II Generic idea: in CO material charge can easily be moved over relatively large distances Coupling M to CO large ME effects Allows for large changes of FE polarization
9 Charge Ordered Multiferroics of Type II Generic idea: in CO material charge can easily be moved over relatively large distances Coupling M to CO large ME effects Allows for large changes of FE polarization -- TTF-CA; HoMn 2 O 5 ; RNiO 3 ; Y 2 NiMnO 6 ; LaCaMn 2 O 6 spin-charge order interplay
10 Charge Ordered Multiferroics of Type II Generic idea: in CO material charge can easily be moved over relatively large distances Coupling M to CO large ME effects Allows for large changes of FE polarization -- TTF-CA; HoMn 2 O 5 ; RNiO 3 ; Y 2 NiMnO 6 ; LaCaMn 2 O 6 spin-charge order interplay Generic problem: CO materials tend to have small gaps
11 How is Ferroelectricity induced by Charge Order? 1D cartoon JvdB and Khomskii, J. Phys. Cond. Matt. 20, (2008) FE by longitudinal charge displacements
12 How is Ferroelectricity induced by Charge Order? 1D cartoon JvdB and Khomskii, J. Phys. Cond. Matt. 20, (2008) FE by longitudinal charge displacements
13 How is Ferroelectricity induced by Charge Order? 1D cartoon JvdB and Khomskii, J. Phys. Cond. Matt. 20, (2008) FE by longitudinal charge displacements
14 How is Ferroelectricity induced by Charge Order? 1D cartoon JvdB and Khomskii, J. Phys. Cond. Matt. 20, (2008) FE by longitudinal charge displacements
15 How is Ferroelectricity induced by Charge Order? 1D cartoon JvdB and Khomskii, J. Phys. Cond. Matt. 20, (2008) FE by longitudinal charge displacements
16 How is Ferroelectricity induced by Charge Order? 1D cartoon TTF-CA JvdB and Khomskii, J. Phys. Cond. Matt. 20, (2008) FE by longitudinal charge displacements
17 How is Ferroelectricity induced by Charge Order? 1D cartoon TTF-CA FE by longitudinal charge displacements JvdB and Khomskii, J. Phys. Cond. Matt. 20, (2008) Giovannetti, Kumar, Stroppa, JvdB, Picozzi, PRL 103, (2009)
18 Ferroelectricity induced by Charge Order A. Longitudinal charge displacements TTF-CA HoMn 2 O 5 PrCaMn 2 O 6
19 Ferroelectricity induced by Charge Order A. Longitudinal charge displacements TTF-CA HoMn 2 O 5 PrCaMn 2 O 6 B. Transversal charge displacements HoMnO 3 Y 2 NiMnO 6
20 Ferroelectricity induced by Charge Order A. Longitudinal charge displacements TTF-CA HoMn 2 O 5 PrCaMn 2 O 6 B. Transversal charge displacements HoMnO 3 Y 2 NiMnO 6 A. & B. RNiO 3
21 multiferroic HoMn 2 O 5 ( Ho ) 3+ ( Mn 2 ) 7+ ( O 5 ) 10- (Mn) 3+ (Mn) 4+
22 charge order/magnetic structure HoMn2O5
23 charge order/magnetic structure HoMn 2 O 5 Mn 3+ Mn 4+ chains with ferro and antiferro bonds Cheong and Mostovoy, Nature Materials (2007)
24 ferroelectricity in HoMn 2 O 5 conceptual picture: ferro bonds win Mn 3+ Mn 4+ Betouras, Giovannetti, JvdB, PRL 98, (2007)
25 ferroelectricity in HoMn 2 O 5 conceptual picture: ferro bonds win Mn 3+ Mn Betouras, Giovannetti, JvdB, PRL 98, (2007)
26 ferroelectricity in HoMn 2 O 5 conceptual picture: ferro bonds win Mn 3+ Mn electronic and ionic displacements ferroelectric polarization Betouras, Giovannetti, JvdB, PRL 98, (2007)
27 ferroelectricity in YMn 2 O 5 ICM CM: commensurate ICM CM ICM: incommensurate magnetic ordering indeed commensurate magnetic phase is ferroelectric! Chapon, Radaelli, Blake, Park, Cheong Phys. Rev. Lett. 96, (2006)
28 Ab initio bandstructure computations: P ~1200 nc/cm 2 experimental polarization ~80 nc/cm 2 ferroelectric domains? Incorporating electron correlation effects with LDA+U fixes the problem Giovannetti and JvdB, PRL 100, (2008)
29 Ab initio bandstructure computations: P ~1200 nc/cm 2 Incorporating electron correlation effects with LDA+U fixes the problem Giovannetti and JvdB, PRL 100, (2008)
30 multiferroic La 1/2 Ca 1/2 MnO 3 ( LaCa ) 2.5+ ( Mn) 3.5+ ( O 3 ) 6- (Mn) 3+ (Mn) 4+
31 Perovskite crystal structure of La 1-x Ca x MnO 3 Oxygen 2- La 3+ /Ca 2+ Mn 4+ / Mn 3+ 12
32 Near x=0.5 : Site-centered charge/spin ordering E.O. Wollan and W.C. Koeler, Phys. Rev. 100, 545 (1955)
33 Near x=0.4 : Bond-centered charge/spin ordering e g t 2g Dimer A. Daoud-Aladine et al., PRL (2002)
34 Ferroelectric? x=0.4 Bond centered spin/co x=0.5 Site centered spin/co Θ=90 Θ=0 Efremov, JvdB, Khomskii, Nature Mat. (2004)
35 x=0.4 Bond centered spin/co Ferroelectric? x=0.5 Site centered spin/co 0 < Θ < 90 intermediate Θ=90 Θ=0 Efremov, JvdB, Khomskii, Nature Mat. (2004) Ferro-electric groundstate
36 x=0.4 Bond centered spin/co Ferroelectric? x=0.5 Site centered spin/co 0 < Θ < 90 intermediate Θ=90 Θ=0 Efremov, JvdB, Khomskii, Nature Mat. (2004) Ferro-electric groundstate It is allowed by symmetry: can happen
37 x=0.4 Bond centered spin/co Ferroelectric? x=0.5 Site centered spin/co 0 < Θ < 90 intermediate Θ=90 Θ=0 Efremov, JvdB, Khomskii, Nature Mat. (2004) Ferro-electric groundstate It is allowed by symmetry: can happen will happen
38 x=0.4 Bond centered spin/co Ferroelectric? x=0.5 Site centered spin/co 0 < Θ < 90 intermediate Θ=90 Θ=0 Efremov, JvdB, Khomskii, Nature Mat. (2004) Ferro-electric groundstate It is allowed by symmetry: can happen will happen observed to happen Jooss et al., PNAS 104, (2007)
39 What about intermediate phase in La 1/2 Ca 1/2 MnO 3?
40 What about intermediate phase in La 1/2 Ca 1/2 MnO 3? DDEX model spin dimer CE Giovannetti, Kumar, JvdB, Picozzi, PRL (2009)
41 What about intermediate phase in La 1/2 Ca 1/2 MnO 3? DDEX model spin dimer finite Hubbard U finite electronphonon coupling λ Θ ~45 o CE Giovannetti, Kumar, JvdB, Picozzi, PRL (2009)
42 What about intermediate phase in La 1/2 Ca 1/2 MnO 3? DDEX model spin dimer finite Hubbard U finite electronphonon coupling λ Θ ~45 o CE Giovannetti, Kumar, JvdB, Picozzi, PRL (2009)
43 B. Transversal charge displacements
44 Ferroelectricity induced by Charge Order 1D cartoon oxygens at inequivalent spin bonds JvdB and Khomskii, J. Phys. Cond. Matt. 20, (2008)
45 Ferroelectricity induced by Charge Order 1D cartoon oxygens at inequivalent spin bonds transversal charge displacements JvdB and Khomskii, J. Phys. Cond. Matt. 20, (2008)
46 Perovskite HoMnO 3 with GdFeO 3 distortion Magnetic E-phase S. Picozzi et al., Phys. Rev. Lett. 99, (2007)
47 Perovskite HoMnO 3 with GdFeO 3 distortion Magnetic E-phase S. Picozzi et al., Phys. Rev. Lett. 99, (2007)
48 Double Perovskite Y 2 NiMnO 6 Magnetic E-phase stabelized by longer range magnetic interactions Kumar, Giovannetti, JvdB, Picozzi, PRB 82, (2010)
49 Double Perovskite Y 2 NiMnO 6 Magnetic E-phase stabelized by longer range magnetic interactions P of few µc/cm 2 Kumar, Giovannetti, JvdB, Picozzi, PRB 82, (2010)
50 Double Perovskite Y 2 NiMnO 6 Magnetic E-phase stabelized by longer range magnetic interactions P of few µc/cm 2 B field of ~14 T transition from E-type to FM transition finite P to zero P Kumar, Giovannetti, JvdB, Picozzi, PRB 82, (2010)
51 A. & B. Longitudinal & Transversal charge displacement
52 Perovskite RNiO 3 (R = Ho, Lu, Nd, Pr..) Charge and Magnetic order JvdB and Khomskii, J. Phys. Cond. Matt. 20, (2008)
53 E-phase in RNiO3
54 E-phase in RNiO 3 Giovannetti, Kumar, Khomskii, Picozzi, JvdB, PRL 103, (2009)
55 Conclusions
56 Conclusions Interplay of charge and spin order gives rise to
57 Conclusions Interplay of charge and spin order gives rise to Type I & Type II multiferroics
58 Conclusions Interplay of charge and spin order gives rise to Type I & Type II multiferroics Potential large MF effects in charge ordered magnets
59 Conclusions Interplay of charge and spin order gives rise to Type I & Type II multiferroics Potential large MF effects in charge ordered magnets Longitudinal Transversal charge displacements
60 Conclusions Interplay of charge and spin order gives rise to Type I & Type II multiferroics Potential large MF effects in charge ordered magnets Longitudinal charge displacements TTF-FA, HoMn 2 O 5, RNiO 3, La 1/2 Ca 1/2 MnO 3, R 2 MnNiO 3... Transversal
61 E-phase in RNiO3
62 E-phase S and T in RNiO3
63 small polarization due to near cancellation of P ion and P elec
64 Interplay orbital, spin and charge e g t t 2g Bond center Ferro
65 Interplay orbital, spin and charge e g t e g t 2g t 2g J AF Bond center Ferro Site center Antiferro JvdB, Khomskii, PRL 82, 1016 (1999)
66 Interplay orbital, spin and charge e g t e g t 2g t 2g J AF Bond center Ferro Site center Antiferro Formally: DDEX model JvdB, Khomskii, PRL 82, 1016 (1999)
67 Orbital Order and Magnetic Order x=0.5 x= < x < 0.5 JvdB, Khaliullin, Khomskii, PRL 83, 5118 (1999)
68 Orbital Order and Magnetic Order x=0.5 x= < x < 0.5 CE-phase ZP-phase Θ-phase JvdB, Khaliullin, Khomskii, PRL 83, 5118 (1999) rotation of every second dimer with angle ±Θ
69 Computed phase diagram of Pr1-xCaxMnO3
70 Computed phase diagram of Pr 1-x Ca x MnO 3 Continous transition from Site centered CO to Bond centered CO in between order
71 Computed phase diagram of Pr 1-x Ca x MnO 3 Continous transition from Site centered CO to Bond centered CO in between order Breaking of inversion symmetry in the intermediate phase Ferro-electricity Magnetism Interplay of charge & orbital and spin ordering
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