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Spin Tunneling and Inversion Symmetry

Spin Tunneling and Inversion Symmetry. E NRIQUE DEL B ARCO. www.physics.ucf.edu/~delbarco. Department of Physics – UCF Orlando. QCPS II 2009 - Vancouver. E NRIQUE DEL B ARCO , C HRISTOPHER R AMSEY (UCF). Nature Physics 4 , 277-281 (2008). S TEPHEN H ILL

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Spin Tunneling and Inversion Symmetry

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  1. Spin Tunneling and Inversion Symmetry ENRIQUE DEL BARCO www.physics.ucf.edu/~delbarco Department of Physics – UCF Orlando QCPS II 2009 - Vancouver

  2. ENRIQUEDEL BARCO, CHRISTOPHER RAMSEY (UCF) Nature Physics4, 277-281 (2008) STEPHEN HILL (NHMFL andPhysics Department, FSU – Tallahassee) SONALI J. SHAH, CHRISTOPHER C. BEEDLEAND DAVID N. HENDRICKSON (Chemistry Department, UCSD – La Jolla-San Diego) PHILIP C.E.STAMP AND IGOR TUPITSYN (PITP-Physics, UBC, Vancouver) Spin Tunneling and Inversion Symmetry

  3. 5/2 2 2 5/2 2 5/2 5/2 2 5/2 2 2 5/2 THE MOLECULE S=7 [Mn12(Adea)8(CH3COO)14]·7CH3CN Rumberger et al., Inorg. Chem. 43, 6531–6533 (2004).

  4. Tc ~0.3K TB ~0.9K wheel axis S= 7 D = 0.4K 50m HL T= 0.9K MAGNETIZATION - QTM -6 +1 -7 +2 +3 +4 +5 +6 mS = +7 S = 7, D = 0.4 K

  5. Ms=5 Ms=6 Ms=7 HL H HT MAGNETIZATION - QTM ? S = 7, D = 0.4 K

  6. 5/2 2 2 5/2 2 5/2 S=7 5/2 2 5/2 2 2 5/2 [Mn12(Adea)8(CH3COO)14]·7CH3CN Rumberger et al., Inorg. Chem. 43, 6531–6533 (2004). THE MOLECULE

  7. d* d d d d d d d d d d d* THE MOLECULE Foguet-Albiol, D. et al., Angew. Chem. Int. Edn 44, 897–901 (2005) davg~3.17Å J ~2-5 cm-1 d*~3.49Å J* <<J [Mn12(Adea)8(CH3COO)14]·7CH3CN Rumberger et al., Inorg. Chem. 43, 6531–6533 (2004).

  8. 7/2 7/2 THE MOLECULE d* d* [Mn12(Adea)8(CH3COO)14]·7CH3CN Rumberger et al., Inorg. Chem. 43, 6531–6533 (2004).

  9. QUANTUM TUNNELING BTW. STATES OF DIFFERENT SPIN LENGH EXCHANGE-COUPLED SPINS

  10. HARD HL  BERRY PHASE INTERFERENCE OF TWO COUPLED TUNNELING SPINS HT QUANTUM INTERFERENCE

  11. SINGLE SPIN INTERACTING SPINS Classical spin precession Classical coupled-spins precession Sjoqvist, PRA (2000) i.e. Wagh et al., PRL (1998) Pancharatnam (1956) (light interference) Berry (1984) (quantal systems) Aharanov and Anandan (1987) (generalization Hilbert space) . . . Quantum Tunneling Spin Coupled Tunneling Spins THEORY THEORY Loss et al., PRL (1992) Von Delft et al., PRL (1992) Garg, EPL (1993) (??) EXPERIMENT EXPERIMENT Fe8: Wernsdorfer & Sessoli, Science (1999) Mn12: del Barco et al., PRL (2003) Mn12 -tBuAc: da Silva Neto et al., (2008) Mn12 wheel: Ramsey et al., Nature Physics (2008) NEW TOPOLOGICAL EFFECT

  12. Dzyaloshinskii–Moriya interaction SYMMETRY RULES ANTI-SYMMETRIC TERM NEEDED NOT ALLOWED ON A DIMER MODEL with INVERSION SYMMETRY

  13. 7/2 7/2 Wernsdorfer, PRB (2008) Wernsdorfer, PRL (2008) a - Dimer model identically usedin a Mn6 wheel (CI) b - DM interaction used to explain results a - Dimer model used in an “identical” Mn12 wheel b – DM interaction used to explain results SYMMETRY RULES Wernsdorfer, arXiv:0804.1246v1,v2,v3 a - Dimer model not valid Rejected by NP: See our response in arXiv:0806.1922

  14. 7/2 7/2 Wernsdorfer, PRB (2008) Wernsdorfer, PRL (2008) a - Dimer model identically usedin a Mn6 wheel (CI) b - DM interaction used to explain results a - Dimer model used in an “identical” Mn12 wheel b – DM interaction used to explain results SYMMETRY RULES Wernsdorfer, arXiv:0804.1246v1,v2,v3 a - Dimer model not valid Rejected by NP: See our response in arXiv:0806.1922 • Wernsdorfer-justification: • Disorder • Local DM interactions are not forbidden • del Barco et al., PRL (2009) • Disorder • Local DM interactions are not forbidden

  15. 7/2 2 5/2 5/2 2 center of inversion d1 5/2 2 center of inversion middle point 5/2 2 middle point 7/2 2 5/2 2 5/2 D = 0 SYMMETRY RULES

  16. The Hamiltonian of the coupled half-wheels: 7/2 Each half-wheel: center of inversion middle point Exchange coupling: 7/2 Symmetric exchange: D  0 parallel to z-axis (Ramsey, Nature Physics) D  0 tilted (Wernsdorfer, PRL) Antisymmetric exchange (DM interaction): SYMMETRY RULES

  17. z y  2 5/2 5/2  x 2 d1 5/2 2 center of inversion  * 5/2 2 middle point 2  * 5/2 2 5/2 D D SYMMETRY RULES

  18. z z y y   2 5/2 5/2   x x 2 d1 5/2 2 center of inversion 5/2 2 middle point 2 5/2 2 5/2 D D SYMMETRY RULES

  19. SYMMETRY RULES H H Center of Inversion

  20. z z z z z z y y y y y y ’ ’       ’   ’ x x x x x x D D’ D D’ D D SYMMETRY RULES 2 5/2 5/2 2 d1 5/2 2 center of inversion middle point 5/2 2 2 5/2 2 5/2 (d,J) 2 3/2 center of inversion 3/2 middle point (d’<d,J’>>J) 2

  21. z z z z The Hamiltonian of 4 coupled quarter-wheels: y y y y ’  ’  Each quarter-wheel: ’ ’   x x x x Exchange coupling: Symmetric exchange: D D’ D’ D Center of inversion symmetry imposes: Antisymmetric exchange (DM interaction): SYMMETRY RULES (d,J) 2 k = 1(A) is degenerate 3/2 center of inversion 3/2 middle point (d’<d,J’>>J) 2

  22. SYMMETRY RULES  

  23. SYMMETRY RULES In a centro-symmetric molecule local DM-interactions MUST BE related by inversion symmetry and DO NOT BREAK THE DEGENERACY BETWEEN LEVELS OF OPPOSITIVE PARITY independently of how complex the Hamiltonian is because PARITY (good quantum number) MUST BE CONSERVED

  24. SYMMETRY RULES when inversion symmetry is not present BOTH SYMMETRIC and ANTISYMMETRIC INTERACTIONS CAN BREAK DEGENERACIES DM-interactions are important in S = 1/2 systems ONLY SOURCE OF DEGENERACY BREAKING (Kagome lattice – weak ferromagnetism) but never mix states of opposite parity in a system with inversion symmetry E. del Barco, S. Hill and D. N. Hendrickson, Phys. Rev. Lett. in press (2009) E. del Barco et al., In preparation

  25. z z y y   2 5/2 5/2   x x 2 d1 5/2 2 center of inversion 5/2 2 middle point 2 5/2 2 5/2 D D Dipolar fields? (Philip?) 

  26. Quantum superposition of states with different spin length in a SMM New topological effect: Quantum phase interference of two coupled tunneling spins CONCLUSIONS Local DM interactions in a centro-symmetric SMM do not break the degeneracy between states of opposite parity

  27. Physics collaborations Stephen Hill (NHMFL-FSU) MasaIshigami, Robert Peale, Lee Chow (UCF) Agustin Camon, Fernando Luis (UZ-Spain) Javier Tejada (UB-Spain) Oliver Waldmann (U.Freiburg-Germany) Andrew Kent (NYU) XiXiang Zhang (KAUST) Eduardo Mucciolo, Michael Leuenberger (UCF) Philip Stamp, Igor Tupitsyn (UBC-Canada) Chemistry collaborations David Hendrickson (UCSD) George Christou (UF) Eugenio Coronado (UV-Spain) Florenzio Hernandez (UCF) Joel Miller (UU) Del Barco Lab Low temperature nanomagnetism Single-molecule magnets FM thin films and nanowires Nanoparticles Low temperature nanotransport Molecular spintronics Single-electron transistors Low-dimensional systems i.e. graphene, nanowires, nanoparticles, molecules,…

  28. [Mn12(Edea)8(CH3CH2COO)14] [Mn12(Adea)8(CH3COO)14].7CH3CN [Mn12(Edea)8(CH3COO)2(CH3CH2COO)12] d d d d* d* d* d* d* d* d d d < >> > << d*/davg= 1.093 J*/Javg d*/davg= 1.100 J*/Javg d*/davg= 1.091 J*/Javg S = 7 S = 7/2 + 7/2 S = 7 SISTER MOLECULES

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