Jeroen van den Brink

Bond- versus site-centred ordering and possible ferroelectricity in manganites Jeroen van den Brink Leiden 12/08/2005

Coupling of orbital degrees of freedom to: Orbital induced ferroelectricity in manganites -- Lattice Dima Efremov, JvdB, Daniel Khomskii, Nature Materials 3, 853 (2004) -- Spins -- Charge Outline

Magnetic Ferroelectrics Why study them? Magnetic ferroelectrics are very rare! Possible application: switching of magnetic bits by electric field Fundamental interest: why rare? How to get around? Lottermoser et al., Nature 430, 541 (2004). Van Aken et al., Nature Mat. 3, 164 (2004). Kimura et al., Nature 426, 55 (2003). Hur et al., Nature 429, 392 (2004). Zheng et al., Science 303, 661 (2004). Fiebig et al., Nature 419, 818 (2002). Wang et al., Science 299, 1719 (2003). Spaladin, Physics World, April 2004.

dipole disorder ferroelectric What is a ferroelectric? Breaking of inversion symmetry

a R >>a R a R >> a conventional metals, semiconductors Ra correlated electron systems Do atomic physics first, include translation symmetry later What is special about manganites? Valence electrons are in localized 3d orbitals

Large Atomic Hund’s rule exchange Electron Spins Parallel 3d orbitals of a Mn- ion Large Coulomb interaction between electrons on the ion • eg orbitals • t2g orbitals

Possible Multiferroic behavior Orbitals are extra degree of freedom Impact on physical properties Ferro-electricity • Order-disorder • Thermodynamics • Magnetism • Lattice distortions Orbitals behave like electron spins Compare orbitals and spins....

Orbitals and spins Similarities Localized moment emergent from electron-electron interactions Angular momentum SU(2) algebra: [Sx,Sy]=iSz Possibility of long range ordering Spin-spin and orbital-orbital interaction due to superexchange

Spins Orbitals Orbitals and spins Differences Weak coupling to lattice Strong High Symmetry of Hamiltionian Low Gapless Excitations Gaped Sometimes Frustration of order Always

Perovskite crystal structure of La1-xCaxMnO3 La3+/Ca2+ Oxygen2- Mn4+ / Mn3+

– – – – – – – – – – – – Mn (3+) =3d4 eg 5x t2g Local considerations Cubic Crystal field splitting • eg orbitals Mn4+ / Mn3+ • t2g orbitals Mn (4+) =3d3 eg 5x t2g

Mn (3+) =3d4 eg1 Mn (4+) =3d3 eg0 Orbital induced ferroelectricity in manganites with doping near x=1/2 Ferro zig-zag chains Magnetic CE-type order Charge ordering E.O. Wollan and W.C. Koeler, Phys. Rev. 100, 545 (1955)

JAF eg eg t2g t2g Site center Antiferro JvdB, Khomskii, PRL 82, 1016 (1999) Interplay orbital, spin and charge t Bond center Ferro Formally: DDEX model

DDEX model

eg t2g Near x=0.4 : Bond-centered charge ordering Dimer A.Daoud-Aladine et al., PRL 89 97205 (2002)

Near x=0.5 : Site-centered charge ordering E.O. Wollan and W.C. Koeler, Phys. Rev. 100, 545 (1955)

x=0.4 x=0.5 0.4 < x < 0.5 Bond centered CO Site centered CO intermediate Ferro-electric groundstate It is allowed by symmetry: Can happen Will happen Ferroelectric?

Magnetic structure of Zener polaron? CE type ? Or: Jaffet-Kittel structure “orthogonal”structure

0.4 < x < 0.5 intermediate Magnetic Structure x=0.4 x=0.5 JvdB, Khaliullin, Khomskii, PRL 83, 5118 (1999)

Continous transition from Site centered CO to Bond centered CO “In between” centered CO Breaking of inversion symmetry in the intermediate phase Ferro-electricity Magnetism Calculated phase diagram Dima Efremov, JvdB, Daniel Khomskii, Nature Mat. (2004)

Conclusions Between bond- and site-centered charge order: ferroelectric phase Prediction for manganites: Multiferroic phase appears close to x=1/2

From: To: Calculated magnetic structure We find a continous transition as function of doping x=0.4 x=0.5

2x 2x eg eg 5x 5x 3x 3x t2g t2g Lifting of degeneracy: lattice Crystal field splitting of eg levels Jahn-Teller distortion

x=0.5 : Site-centered charge ordering JvdB, Khaliullin, Khomskii, PRL 83, 5118 (1999);PRL 82, 1016 (1999)

Goodenough (1963) Orbital order in plane Orbital order LaMnO3 Order by disorder

Jeroen van den Brink