PAUL SCHERRER INSTITUTPAUL SCHERRER INSTITUT

Electrical transport and magnetic interactions in 3d and 5d transition

metal oxides

Laboratory for Developments and Methods, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland

kazimierz.conder@psi.ch

Kazimierz Conder

For the past decades, a tremendous amount of effort has been devoted to exploring the nature of 3d transition metal oxides where various exotic states and phenomena have emerged such as:• high-Tc cuprate superconductivity• colossal magnetoresistivity• metal-insulator transitions

Motivation

It has been established that these states and phenomena are caused by strong cooperative interactions of spin, charge, and orbital degrees of freedom.

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Lattice

Chargeorder

Spinorder

Orbitalorder

Spin, charge, orbital and lattice degrees of freedom in strongly correlated electron systems

Higher cation charges:• smaller radius• smaller coord. numbers

Number of (unpaired) electrons:• spin• charge

Occupied and unoccupied orbitalsBond anisotropy

Crystal field splittingJahn-Teller effect

Spin-orbit interaction

Electrical properties of transition metal oxides

• The d-levels in most of the transition metal oxides are partially filled.

• According to band structure calculations half of the known binary compounds should be conducting.

Empty or completely filled

d-band (d0 or d10)

Partly filled

d-band

http://wps.prenhall.com/wps/media/objects/3085/3159106/blb2406.html

Energies of the d orbitals in an octahedral crystal field.

Completely filled

orbitals: d6

Orbital interaction with the lattice

Orbitals are nearby O2-

Orbitals are between O2-

Octahedral crystal field

TiO- rutileTi

O

Ti2+ 3d24s0

metal

NiO- NaCl structure Ni2+ 3d84s0

Is insulator!Why not a metal?

Ni

O

CuO Cu2+ 3d94s0

CoO Co2+ 3d74s0MnO Mn2+ 3d54s0

Cr2O3 Cr3+ 3d34s0

Odd number of d electrons-all this oxides should be metals but are insulators

Whatever is the crystal field splitting the orbitals are not fully occupied!!!

Why not metal?

3d74s23d54s2 3d94s23d44s2 Electron configurations of elements

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Mott-Hubbard insulators(on site repulsive electron force)

Sir Nevill Francis Mot Nobel Prize in Physics 1977

•Most of the oxides show insulating behavior, implying that the d-electrons are localized.•Short-range Coulomb repulsion of electrons can prevent formation of band states, stabilizing localized electron states.

W

W

U

Density of states

Upper Hubbard band

Lower Hubbard band

FL

Density of states

W FL

U

U<W U>W

Ni2+ + Ni2+ → Ni3+ + Ni+ d8 + d8 → d7 + d9

Correlation energy, Hubbard

UBand width=W

small

large Electron transferCoulomb repulsiveforce

e-

9

Mott-Hubbard insulator Charge Transfer insulator

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Electrons have not only charge but also spin!

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Magnetic order in transition metal oxides

DiamagnetismParamagnetismFerromagnetismAntiferromagnetismFerrimagnetism

Magnetit (Fe3O4) inverse spinel.

Ferrimagnet.

Fe2+ 3d6 Fe3+ 3d5

Octahedral coordination

Tetrahedral coordination

Superexchange

Superexchange is a strong (usually) antiferromagnetic coupling between two nearest neighbor cations through a non-magnetic anion. • because of the Pauli Exclusion

Principle both spins on d and p hybridized orbitals have to be oriented antiparallel.

• this results in antiparallel coupling with the neighbouring metal cation as electrons on p-orbital of oxygen are also antiparallel oriented.

Pauli Exclusion Principle

Goodenough–Kanamori–Anderson Rulesdz

2dx2−y

2

dz2

180o – Exchange between half occupied or empty orbitals is strong and

antiferromagnetic

Ferromagnetic superexchange - ferromagnetic when angle 90o

0.0 0.1 0.2 0.310

100

La2-x

SrxCuO

4

Insu

lato

r

Met

al

Ant

iferr

omag

net

Superconductor

TN

TC

Tem

pera

ture

[K]

Sr-content x, (holes per CuO2-layer)

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La, Sr

Cu

O

(LaBa)2CuO4 TC=35K K.A. Müller und G. Bednorz (IBM Rüschlikon 1986, Nobel price 1987)

High Temperature Superconductor: La2-

xSrxCuO4

Undoped superconducting cuprates are antiferromagnetic Mott insulators!

Double-exchange mechanism

Magnetic exchange that may arise between ions on different oxidation states!

• Electron from oxygen orbital jumps to Mn 4+ cation, its vacant orbital can then be filled by an electron from Mn 3+.

• Electron has moved between the neighboring metal ions, retaining its spin.

• The electron movement from one cation to another is “easier” when spin direction has not to be changed (Hund's rules).

Mn 3+ d4 Mn 4+ d3

O2- 2p

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FerromagneticMetal

ParamagneticInsulator

La1-xCaxMnO3. Double exchange mechanism. The electron movement

from one cation to another is “easier” when spin direction has not to be changedNote that no oxygen sites are shown!

17A.P. Ramirez, J. Phys.: Condens. Matter., 9 (1997) 8171

CMR (colossal magnetoresistance) La0.75Ca0.25MnO3

Tc

)()()0(

HRHRHRR

Magnetoresistance is defined as the relative change of resistances at different magnetic field

Tc

FerromagneticMetal

ParamagneticInsulator

✓ 4d and 5d orbitals are more extended than 3d’s✓ reduced on-site Coulomb interaction strength✓ sensitive to lattice distortion, magnetic order, etc.✓ spin-orbit (SO) coupling much stronger

5d vs. 3d transition metal oxides

PRB, 74 (2006) 113104

• 4d and 5d orbitals are more extended than 3d’s

• Reduced Coulomb interaction

Heungsik Kim et al., Frontiers in Condensed Matter Physics, KIAS, Seoul, 2009

Insulator

Metal

Insulator

Sr2IrO4Under the octahedral symmetry the 5d states are split into t5

2g and eg orbital states. The system would become a metal with partially filled wide t2g band.

PRL 101, 076402 (2008)

Jeff = |S – L| is an effective total angular momentum defined in the t2g manifold with the spin S and the orbital angular L momenta.

An unrealistically large U>> W could lead to a Mott insulator. However, a reasonable U cannot lead to an insulating state as already 4d Sr2RhO4 is a normal metal. By a strong Spin-Orbit

(SO) coupling the t2g band splits into effective total angular momentum Jeff=1/2 doublet and Jeff=3/2 quartet bands.

The Jeff=1/2 spin-orbit states form a narrow band so that even small U opens a Mott gap, making it a Mott insulator

The formation of the Jeff bands due to the large SO coupling energy explains why Sr2IrO4 is insulating while Sr2RhO4 is metallic.

Opposite directions of electronic orbital motions around a nucleus occur with the same probability, and thereby cancel each other.

Interaction between the electron's spin and the magnetic field generated by the electron's orbit around the nucleus.

Spin and orbital motion have the same directions. The spin-orbit correlation suppresses the transfer of electrons to neighboring atoms making Sr2IrO4 an insulator.

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Na2IrO3 and Li2IrO3 Kitaev-Heisenberg model

Crystal structure of Na2IrO3

monoclinic space group C 2/m

PRB 88, 035107 (2013)

Iridium honeycomb layers stacked along the monoclinic c axis

For both Na2IrO3 and Li2IrO3 a honeycomb structure is observed enabling a realization of the exactly solvable spin model with spin liquid ground state proposed by Kitaev.

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J1=0 J2=0J1=2J2

Heisenberg exchangeKitaev exchange

A Spin Liquid (Figure Credits: Francis Pratt, STFC)

Na2IrO3 and Li2IrO3 Kitaev-Heisenberg model

J>0 ferromagnetic

J<0 antiferromagnetic

PRL 105, 027204 (2010)

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Na2IrO3 and Li2IrO3 Kitaev-Heisenberg model

A Spin Liquid (Figure Credits: Francis Pratt, STFC)

• Na2IrO3 and Li2IrO3 order magnetically at 15K

• I was suggested (PRB 84, 100406 (2011)) that the reduction of the chemical pressure along the c-axis can induce spin glass behavior.

• This can be achieved either by exerting pressure in the ab plane or substituting Na by smaller Li ions.

• Antiferromagnetic transition around 15K for the parent compound Na2IrO3.

• This is suppressed for the doped sample.

K. Rolfs, S. Toth, E. Pomjakushina, D. Sheptyakov, K. Conder, to be published

Na2-xLixIrO3 with x = 0, 0.05, 0.1 and 0.15

Magnetization measurements of Na1.9Li0.1IrO3 in 0.1T. Real and imaginary part of the AC susceptibility measured at different frequencies.

The cusp is frequency dependent which is characteristic for the spin-glass phase

Na1.95Li0.05IrO3

Na2IrO3

Glas

sy

stat

eFor higher doping spin-glass state

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Conclusions Electrical transport properties in transition metals (Mott insulators):• crystal field splitting• Coulomb repulsion

Colossal magnetoresistivity:• crystal field splitting• orbital order

5d iridates:• crystal field splitting• spin-orbit interaction

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