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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
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
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+...
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
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
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
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
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
Crystal structure
At a first glance looks like a slightly distorted kagome layer...
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
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?
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
Crystal structure
Cu(OH)2
CuO2(OH)2
V2O7
H2O
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
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)
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
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)
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
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?
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
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?
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
LSDA+U: exchange integrals
J1
Jic
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
LSDA+U: exchange integrals
J1
Jic
FM
AFM
AFM
Where is the frustration?
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
Possible origin for frustration
volborthite
FMAFM
LiCu2O2Li2ZrCuO4CuCl2
} frustrated chainswith FM J1 andAFM J2
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
LSDA+U: exchange integrals
J1
Jic
J2
|J1| ≈ 0.5·JicJ2 ≈ |J1|
2D network with NNN frustration (FM—AFM “chains”)
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
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〉
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
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
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome
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
O. Janson, J. Richter, P. Sindzingre, H. Rosner volborthite Cu3V2O7(OH)2·2H2O distorted spin-1/2 kagome