O. Janson et al- Volborthite Cu3V2O7(OH)2x2H2O: Orbital ordering on a distorted kagome geometry

Volborthite Cu3V2O7(OH)2·2H2O:Orbital ordering

on a distorted kagome geometry

O. Janson1, J. Richter2, P. Sindzingre3 and H. Rosner1

1Max-Planck-Institut fur Chemische Physik fester Stoffe, Dresden2Institut fur Theoretische Physik, Universitat Magdeburg

3Laboratoire de Physique Theorique de la Matiere Condensee, UniversitePierre et Marie Curie, Paris

J1

Jic

J2

Jic

J1

J2

a

b

27.10.2009

O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome

Motivation

or

magnetic frustration

↓spin-liquid ground state

↗low dimensional geometry

↖√S · (S + 1)� Squantum fluctuations


Motivation

Geometrical frustration

• triangular lattice• honeycomb lattice• pyrochlore lattice• kagome lattice

Frustration due to competinginteractions

• J1—J2 chain• frustrated square lattice• anisotropic (triangular,

pyrochlore etc.) lattices

Quantum fluctuationsCations with localized

spin-1/2: Cu2+, V4+, Cr5+...


Motivation

herbertsmithiteCu3Zn(OH)6Cl2• ideal geometry• Cu/Zn disorder

kapellasite Cu3Zn(OH)6Cl2haydeeite Cu3Mg(OH)6Cl2• ideal geometry• additional coupling Jd

Cu2+

kagomesystems

vs.

volborthiteCu3[V2O7](OH)2·2H2O

• distortedgeometry

• clean samples


Volborthite Cu2+3 [V2O7](OH)2·2H2O

• a candidate for the realization ofa spin-1/2 kagome Heisenberg AFM

• experiments (χ(T ), cp(T ), M(H),51V NMR, µSR)

• no long-range magnetic ordering• frustration (Tmax =21 K, θCW =115 K)• partial spin freezing below 2 K• mysterious “magnetization steps”

• theory: pure and slightly distortedkagome models

• no clear physical picture


Crystal structure

At a first glance looks like a slightly distorted kagome layer...


Crystal structure

Cu(2) “4+2”Cu(1) “2+4”

...but crystal chemistry is different from our expectations:• different types of distortion for Cu(1) and Cu(2)−→ orbital physics?

• coupled edge-sharing chains−→ dimensionality?


Crystal structure

Cu(OH)2

CuO2(OH)2

V2O7

H2O


Method

• DFT calculations (fplo8.00-31)• LDA calculations −→ DOS, band structure• Tight-binding model (fitting the LDA band structure) −→

extended Hubbard model −→ Heisenberg model (JAFM)• Total energy LSDA + U calculations (supercells)

=⇒ orbital patterns −→ orbital GS=⇒ spin patterns −→ J = JAFM + JFM

• Exact diagonalization• full, N=18, 24 −→χ(T )• sparse, N=18, 24, 36 −→ 〈~Si ·~Sj〉, M(H)


LDA: band structure

• Strong hybridization of Cu 3dx2−y2 and 3d3z2−r2

−→ 6 bands at εF instead of 3=⇒ 2 orbitals per Cu atom

• 2D (tiny dispersion along Γ—Z, ⊥ to “kagome” planes)


LDA: orbitals

Cu(1) (2+4):

-2 -1 0energy (eV)

2

4

6

8

DO

S (

stat

es /

eV /

cell)

Cu(1) totalCu(1) 3dxy

Cu(1) 3dxzCu(1) 3d3z

2-r

2

Cu(1) 3dyz

Cu(1) 3dx2-y

2

• strong hybridization of Cu 3dx2−y2

and 3d3z2−r2 orbitals

• 3d3z2−r2 close to half-filling

Cu(2) (4+2):

-2 -1 0energy (eV)

2

4

6

8

DO

S (

stat

es /

eV /

cell)

Cu(2) totalCu(2) 3dxy

Cu(2) 3dxCu(2) 3d3z

2-r

2

Cu(2) 3dyz

Cu(2) 3dx2-y

2

• considerable hybridization of Cu3dx2−y2 and 3d3z2−r2 orbitals

• 3dx2−y2 close to half-filling

What do correlations change?


LSDA+U: magnetic orbitals

GS

standardcupratescenario

0

1

2

3

ener

gy(e

V)

Cu(1) Cu(2)

Cu(1) Cu(2)

Energy cost per Cu atom:Cu(1) ∼0.7 eVCu(2) ∼1.2 eV−→ Orbital order

Exchange integrals?


LSDA+U: exchange integrals

J1

Jic



J1

Jic

FM

AFM

AFM

Where is the frustration?


Possible origin for frustration

volborthite

FMAFM

LiCu2O2Li2ZrCuO4CuCl2

} frustrated chainswith FM J1 andAFM J2



J1

Jic

J2

|J1| ≈ 0.5·JicJ2 ≈ |J1|

2D network with NNN frustration (FM—AFM “chains”)


Phase diagram of the J1—J2—Jic model(ground state)

1 2 3 4 5 6 7Jic/|J1|

0.5

0.75

1

1.25

1.5

1.75

2.0

2.25

J2/

|J1|

singlet GS

GS with S > 0

• AMF • FLL

0−0.5 0.5

0−0.5 0.5

0

R

〈~S0 · ~SR〉

0

−0.5

0.5

0

−0.5

0.5

0R

〈~ S0·~ S

R〉 quantum

classical

〈~S0 · ~SR〉


Ground state of the J1—J2—Jic model

• thermodynamics (N=18) is strongly affected by finite sizeeffects (NNN couplings), work for larger clusters (N=24) is inprogress

• classical GS:−→ singlet GS

• quantum GS:• LSDA + U results are close to the phase transition

↪→ crystal structure data are crucial↪→ accurate choice of parameters forLSDA + U calculations is necessary

• short range order for the spin-spin correlation functionsdoes not contradict to experiments


Summary and outlook• geometrical distortion −→ unique orbital ordering• new microscopic model• frustration originates not from the NN, but from the

NNN couplings• volborthite is far from the original kagome model

Outlook:• results sensitive to O—H distance−→ better structural data (neutron diffraction)

• pressure• NMR in high magnetic field

We acknowledge fruitful discussions with Z. Hiroi, O. Cepas, G. Nielsen,S.-L. Drechsler, D. Kasinathan and A. Tsirlin.

Thank you for your attention!O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome

Picture to take home

Jic

J1

J2

a

b


Documents

O. Janson et al- Volborthite Cu3V2O7(OH)2x2H2O: Orbital ordering on a distorted kagome geometry