THE TEAM: Dr. Víctor Pardo Alberto Piñeiro, PhD Student Prof. Daniel Baldomir

1. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo THE TEAM: Dr. Víctor Pardo Alberto Piñeiro, PhD Student Prof. Daniel Baldomir Instituto de Investigacións Tecnolóxicas Universidade Santiago de Compostela, Spain Santiago Blanco-Canosa, PhD Student Dr. Francisco Rivadulla Departamento de Química-Física Universidade Santiago de Compostela, Spain Prof. José Rivas Departamento de Física Aplicada Universidade Santiago de Compostela, Spain Prof. D.I. Khosmkii Prof. M. Abd-Elmeguid II. Physikalisches Institut Universität zu Köln, Germany

2. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo Oxyhalides TiOCl and TiOBr presents spin-Peierls transition at low temperature Low dimensional spin-1/2 compound (Ti3+) Presents 2 consecutive phase transitions Coupling of a one dimensional antiferromagnetic S=1/2 chain with the lattice results in a spin-Peierls transition with a dimerized ground state Commensurate spin-Peierls Temperature (~66K) Incommensurate spin-Peierls Temperature (~91K)

3. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo Methodology • LDA+U method: WIEN2k software: • - All electron, full-potential scheme • U= 0.35 Ry (~5 eV) • Reasonable value for a d1 electron system • Reproduces reasonably the gap of the structure measured al ambient pressure in orthorhombic structure (LDA+U gap proportional to U) • Reproduces very well the commensurate spin-Peierls transition temperature Geometry optimization: GGA (Perdew-Burke-Ernzerhof)

4. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo High pressure Monoclinic structure (P21/m space group) Low pressure Orthorhombic structure (Pmmn space group) S. Blanco-Canosa et al., ArXiv:0806.0230 X-ray diffraction under pressure

5. (a) d d 1 1 (b) d d 2 3 Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo Atomic positions relaxed at every pressure Structural optimization utilizing GGA scheme Monoclinic cell parameters Orthorhombic cell parameters Structure of the TiOCl compound (a) on the ambient pressure orthorhombic phase and (b) on the high-pressure monoclinic phase. Values of the distances are d1=3.36Å, d2=3.25Å and d3=3.39Å.

6. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo Ti3+ (d1) ions have one t2g orbital occupied (dyz) with a large hopping integral along the b direction of the crystal Highly one-dimensional electronic structure. • Interactions along the a-axis are very small • Along the c axis, interactions are negligible due to the large Ti-Ti distance TiOCl is structurally quasi-2-Dimensional, but electronicaly it is quasi-1-Dimensional Electron spin density plot of TiOCl in the orthorhombic structure

7. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo Heissenberg type Hamiltonian 4 inequivalent Ti atoms Ground state We need 3 diferent magnetic configurations to obtain the 3 magnetic couplings constants 1D-mean field approximation J>0 AF coupling J<0 FM coupling In agreement with experimental commensurate TSP J’s in the orthorhombic structure

8. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo crossing with room T expected between 10 and 17 GPa consistent with our theoretical findings S. Blanco-Canosa et al., ArXiv:0806.0230

9. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo Value near experiment Gap evolution Decrease of the gap ~ 30% In orthorhombic structure In concordance with experimental data (resistivity measurements): M.K. Forthaus et al., Phys. Rev. B 77, 165121 (2008) Drastic reduction of the gap: Structural transition In concordance with experiment $ We would need more than 30 GPa to get an insulator-to-metal transition in orthorhombic structure!!

10. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo orthorhombic Drastic reduction of the gap (from 1.5 eV to 0.3 eV) States of d1 electron of Ti are good localized in a ~ 1 eV band near Fermi energy Mot-Hubbard type gap (d-d gap) Increase ~20% of the bandwith monoclinic Oxygen bands are in energies down than -2 eV

11. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo Possible solutions vs. U value P=0 (orthorhombic) : GGA (U= 0) LDA+U (U= 5 eV) - Nonmagnetic solution E> 0 E> 0 metal metal - Magnetic solution E=0 (minimum) E=0 (minimum) metal insulator P=15 GPa (monoclinic): GGA (U= 0) LDA+U (U= 5 eV) - Nonmagnetic solution E=0 (minimum) E> 0 metal metal - Magnetic solution does not converge E= 0 (minimum) insulator

12. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo ‘’dimerized’’ 3% Monoclinic space group: 3.25 Å 3.43 Å 2 types of dimerized structures ‘’long dimerized’’ 11% Ti atom 2.95 Å 3.69 Å b axis Close to metal Ti bond length!!! Limit for electron-itinerancy Spin-Peierls distortion is expected to be supported by a conventional Peierls distortion of the 1D chain

13. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo Energy analysis: long-dimerized expected more stable above 15 GPa. T TSP orthorhombic monoclinic long- dimerized short-dimerized P

14. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo Conclusions: • The quasi-one-dimensional electronic structure of TiOCl was shown and also the one-dimensionality of its magnetic properties • TiOCl presents a double structural transition above 10 GPa and 15 GPa (first one from undimerized phase to dimerized phase and the second one from a short dimerized structure to a long dimerized structure) • Evolution with pressure of TSP is consistent with high pressure dimerization and drastic change in the band gap • The system TiOCl does not present an insulator-to-metal transition, neither from ab initio calculations nor from experimental measurements

15. Ab initio studies at high pressure on TiOCl: electronic structure of the orthorhombic and monoclinic phases V. Pardo Acknowledgments: Project MAT 2006-10027 “Study of phase separation in magnetic oxides combining theory and experiment” Joint Project Spain/Germany HA2006-0119 “Electronic phase separation and Superstructures in transition metal Oxides: a dual theoretical/experimental approach” Ramón y Cajal Program F.P.U. Program Supercomputing Centre of Galicia Project PXIB-20919-PR