Spin Tunneling and Inversion Symmetry ENRIQUE DEL BARCO

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

Spin Tunneling and Inversion Symmetry ENRIQUE DEL BARCO, CHRISTOPHER RAMSEY (UCF) Nature Physics 4, 277 -281 (2008) STEPHEN HILL SONALI J. (NHMFL and Physics Department, FSU – Tallahassee) SHAH, CHRISTOPHER C. BEEDLE AND DAVID N. (Chemistry Department, UCSD – La Jolla-San Diego) PHILIP C. E. STAMP AND IGOR TUPITSYN (PITP-Physics, UBC, Vancouver) HENDRICKSON

THE MOLECULE 5/2 2 2 5/2 2 S=7 5/2 2 [Mn 12(Adea)8(CH 3 COO)14]· 7 CH 3 CN Rumberger et al. , Inorg. Chem. 43, 6531– 6533 (2004).

MAGNETIZATION - QTM Tc ~0. 3 K -6 -7 +1 TB ~0. 9 K +2 +3 wheel axis +4 +5 S= 7 D = 0. 4 K +6 m. S = +7 50 m HL T = 0. 9 K S = 7, D = 0. 4 K

MAGNETIZATION - QTM Ms = 5 ? Ms = 6 Ms = 7 HL H HT S = 7, D = 0. 4 K

THE MOLECULE 5/2 2 2 5/2 2 S=7 5/2 2 [Mn 12(Adea)8(CH 3 COO)14]· 7 CH 3 CN Rumberger et al. , Inorg. Chem. 43, 6531– 6533 (2004).

d d* d d [Mn 12(Adea)8(CH 3 COO)14]· 7 CH 3 CN Rumberger et al. , Inorg. Chem. 43, 6531– 6533 (2004). davg~3. 17Å J ~2 -5 cm-1 d*~3. 49Å J* <<J Foguet-Albiol, D. et al. , Angew. Chem. Int. Edn 44, 897– 901 (2005) THE MOLECULE

THE MOLECULE d* 7/2 d* [Mn 12(Adea)8(CH 3 COO)14]· 7 CH 3 CN Rumberger et al. , Inorg. Chem. 43, 6531– 6533 (2004).

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

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

NEW TOPOLOGICAL EFFECT 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) Quantum Tunneling Spin Berry (1984) (quantal systems) Coupled Tunneling Spins THEORY Aharanov and Anandan (1987) (generalization Hilbert space) THEORY Loss et al. , PRL (1992) Von Delft et al. , PRL (1992) Garg, EPL (1993) EXPERIMENT Fe 8: Wernsdorfer & Sessoli, Science (1999) Mn 12: del Barco et al. , PRL (2003) Mn 12 -t. Bu. Ac: da Silva Neto et al. , (2008) . . . (? ? ) EXPERIMENT Mn 12 wheel: Ramsey et al. , Nature Physics (2008)

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

SYMMETRY RULES Wernsdorfer, ar. Xiv: 0804. 1246 v 1, v 2, v 3 a - Dimer model not valid Rejected by NP: See our response in ar. Xiv: 0806. 1922 7/2 Wernsdorfer, PRB (2008) a - Dimer model identically used in a Mn 6 wheel (CI) b - DM interaction used to explain results 7/2 Wernsdorfer, PRL (2008) a - Dimer model used in an “identical” Mn 12 wheel b – DM interaction used to explain results

SYMMETRY RULES Wernsdorfer, ar. Xiv: 0804. 1246 v 1, v 2, v 3 a - Dimer model not valid Rejected by NP: See our response in ar. Xiv: 0806. 1922 7/2 Wernsdorfer, PRB (2008) a - Dimer model identically used in a Mn 6 wheel (CI) b - DM interaction used to explain results 7/2 Wernsdorfer, PRL (2008) a - Dimer model used in an “identical” Mn 12 wheel b – DM interaction used to explain results Wernsdorfer-justification: 1) Disorder 2) Local DM interactions are not forbidden del Barco et al. , PRL (2009) 1) Disorder 2) Local DM interactions are not forbidden

SYMMETRY RULES 2 5/2 7/2 2 5/2 D=0 d 1 center of inversion 5/2 middle point 2 2 center of inversion middle point 5/2 2 2 5/2 7/2

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

SYMMETRY RULES z 5/2 2 5/2 D 2 d 1 5/2 * D 2 center of inversion * 2 5/2 middle point 5/2 y 2 2 5/2 x

SYMMETRY RULES z 5/2 2 5/2 D 2 d 1 5/2 2 center of inversion z D 2 5/2 y middle point 2 5/2 y x 2 5/2 x

SYMMETRY RULES H H Center of Inversion

SYMMETRY RULES z z ’ D’ 5/2 2 22 z d 1 ’ D’ D middle point y ’ 2 middle point x 2 2 y center ofx inversion z 5/2 ’ 3/2 5/2 2 y (d , J) D 5/2 2 y 5/2 3/2 x (d’<d , J’>>J) x

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

SYMMETRY RULES

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

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

Dipolar fields? (Philip? ) z 5/2 2 5/2 D 2 d 1 5/2 2 center of inversion z D 2 5/2 y middle point 2 5/2 y x 2 5/2 x

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

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, … Physics collaborations Stephen Hill (NHMFL-FSU) Masa Ishigami, Robert Peale, Lee Chow (UCF) Agustin Camon, Fernando Luis (UZ-Spain) Javier Tejada (UB-Spain) Oliver Waldmann (U. Freiburg-Germany) Andrew Kent (NYU) Xi. Xiang 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)

SISTER MOLECULES [Mn 12(Edea)8(CH 3 CH 2 COO)14] [Mn 12(Adea)8(CH 3 COO)14]. 7 CH 3 CN [Mn 12(Edea)8(CH 3 COO)2(CH 3 CH 2 COO)12] d d d* d* d* d d*/davg = 1. 093 J*/Javg S=7 d* d < >> d*/davg = 1. 100 J*/Javg S = 7/2 + 7/2 > << d* d d*/davg = 1. 091 J*/Javg S=7