Quantum Phase Transitions

1
Quantum Phase Transitions
Condensed Matter Physics 29 Sept. 13-17,
2005 IIAS, Kizu

• Kazuo UEDA
• Institute for Solid State Physics
• University of Tokyo
• In collaboration with
• Yasufumi YAMASHITA
• Institute for Molecular Science

2
Why Quantum Phase Transitions

• Interesting in itself
• Superconductivity in strongly correlated electron
  systems
• examples
• (i) high-Tc cuprates
• superconductivity close to the AF
  instability
• (ii) heavy Fermion superconductors

3
Phase diagram for the alloy system CeRh1-xIrxIn5
Schematic phase diagrams for hole- and
electron-doped high-Tc cuprates La2-xSrxCuO4 and
Nd2-xCexCuO4-d
4
(No Transcript)
5
Tc 52K µS 1.4µB

• discovery of co-existence of superconductivity
  and ferromagnetism under high pressure
  10GPa16GPa
• S. S. Saxena et al., Nature 406 (2000) 587

Tsc 0.8K
N. Tateiwa et al., J. Phys. Soc. Jpn. 70 (2001)
2876
6
Routes to quantum phase transitions in magnetic
insulators

• dimer spin ladder
• plaquette CaV4O9
• depletion
• (i) 1/5 depleted square lattice CaV4O9
• (ii) triangular lattice ? Kagomé lattice
• frustration

7
pyrochlore lattice3D network of corner-sharing
tetrahedra

• Important symmetry Td

8
examples

• (1) spinel compounds (AB2O4) B-sites
• ZnV2O4 V3 (S1)
• ZnCr2O4 Cr3 (S3/2)
• (2) pyrochlore compounds (A2B2O7) A, B-sites
• Ho2Ti2O7, Dy2Ti2O7 spin ice
• (3) C15 Laves phase AMn2 Mn-sites

9
LiTi2O4 1 Ti3.5 t2g0.5 superconductivity Tc13.7K
LiV2O4 2 V3.5 t2g1.5 heavy Fermion behaviors
ZnV2O4 3 V3 t2g2 Two transitions Ts50K, TN40K
ZnCr2O4 4 Cr3 t2g3 Single transition Tc12K
1 D. C. Johnston, J. Low. Temp. Phys. 25 (1976)
145 2 S. Kondo et al., PRL 78 (1997) 1052 3
Y. Ueda et al., JPSJ 66 (1997) 778 4 S. H. Lee
et al., PRL 84 (2000) 3718
10
Lifting of degeneracy in Mott insulatorsSpin-lat
tice coupling and orbital degeneracy.

• 1 S1 Heisenberg model with spin-lattice
  coupling
• Y. Yamashita and K. U. PRL 85 (2000)4960
• Spin-driven Jahn-Teller distortion based on the
  Valence Bond Solid picture
• 2 Classical Heisenberg model with spin-lattice
  coupling
• O. Tchernyshyov, R. Moessner and S. L. Sondhi
• PRL 88 (2002) 067203
• 3 Spin-orbital model
• H. Tsunetsugu and Y. Motome PRB 68 (2003)
  060405(R)
• t2g Kugel-Khomskii model

11
Spin-driven Jahn-Teller mechanism

• ZnV2O4 spinel, S1 AF Insulator (TN40K, J53K)

• Susceptibility (Y. Ueda et al. JPSJ 66 ,778)

• Lattice structure

• Schematic energy level

• Aim of the present study
• Origin of the structural phase transition

12
AF Heisenberg model on the pyrochlore lattice
13
Magneto-elastic couplings
14
Summary The structural phase transition of AF
insulating spinel, ZnV2O4 1) S1 AF Heisenberg
model on the pyrochlore lattice is investigated
by introducing the tetrahedron-unit VBS wave
function. 2) Twofold degeneracy of tetrahedron
singlets is lifted by the spin-lattice
coupling 3)The structural phase transition can be
explained by the spin-driven Jahn-Teller
effect. (the low-temperature behaviors of
magnetic susceptibility and electronic entropy
are consistent, at least qualitatively.)