Spins Dynamics in Nanomagnets. Andrew D. Kent

Transcription

1 Spins Dynamics in Nanomagnets Andrew D. Kent Department of Physics, New York University Lecture 1: Magnetic Interactions and Classical Magnetization Dynamics Lecture 2: Spin Current Induced Magnetization Dynamics Lecture 3: Quantum Spin Dynamics in Molecular Nanomagnets 1

2 Outline I. Introduction Quantum Tunneling of Magnetization Initial Discoveries Single molecule magnets II. Magnetic Interactions in SMMs Energy Scales, Spin Hamiltonians Mn12-acetate III. Resonant Quantum Tunneling of Magnetization Thermally activated, thermally assisted and pure Crossover between regimes Quantum Phase Interference IV. Experimental Techniques Micromagnetometry SQUIDs and Nano-SQUIDs EPR 2

3 Magnetic Nanostructures Image from, W. Wernsdorfer, Advances in Chemical Physics 2001 and ArXiv: Condensed Matter Physics Seminar, Colorado State University, July 22, 2009

4 Quantum Tunneling of Magnetization +m -m U Thermal Quantum T c = U/k B B(0) Thermal relaxation (over the barrier) Quantum Tunneling Magnetic Field Relaxation rate T c Temperature 4 Condensed Matter Physics Seminar, Colorado State University, July 22, 2009 also, Enz and Schilling, van Hemmen and Suto (1986)

5 Magnetic Bistability in a Molecular Magnet Nature 1993, and Sessoli et al., JACS 1993 Magnetic hysteresis at 2.8 K and below (2.2 K) S=10 ground state spin

6 Quantum Tunneling in Single Molecule Magnets Single crystal studies of Mn12: L. Thomas, et al. Nature 383, 145 (1996) Susceptibility studies: J.M. Hernandez, et al. EPL 35, 301 (1996)

7 Single Molecule Magnets Physics Mn 84 S=6 SMM Characteristics Molecules High spin ground state Uniaxial anisotropy Single crystals Synthesized in solution Modified chemically Peripheral ligands Oxidized/reduced Soluble = Bonded to surfaces -Individual molecule can be magnetized and exhibit magnetic hysteresis Quantum Tunneling of Magnetization Quantum Phase Interference Quantum Coherence

8 First SMM: Mn12-acetate [Mn 12 O 12 (O 2 CCH 3 ) 16 (H 2 O) 4 ].2CH 3 COOH.4H 2 O 8 Mn 3+ S=2 4 Mn 4+ S=3/2 Magnetic Core Competing AFM Interactions Ground state S=10 Organic Environment 2 acetic acid molecules 4 water molecules S 4 site symmetry Single Crystal Tetragonal lattice a=1.7 nm, b=1.2 nm Strong uniaxial magnetic anisotropy (~60 K) Weak intermolecular dipole interactions (~0.1 K) Micro-Hall magnetometer 8

9 Intra-molecular Exchange Interactions S=2 J 1 S=3/2 J 2 J 3 J 1 J 2 J 3 J 4 J 1 ~ 215 K J 2,J 3 ~ 85 K J 4 ~ 45 K H = <ij> J 4 J ij S i S j + i S i D i S i +... (2S 1 +1) 8 (2S 2 +1) 4 =10 8 S=10 and 2S+1=21 9

10 Magnetic Anisotropy and Spin Hamiltonian Spin Hamiltonian H = DS z 2 gµ B S H S z m>= m m > E m = Dm 2 (Ising-like) Uniaxial anisotropy 2S+1 spin levels z up x down y U=DS 2 10

11 Resonant Quantum Tunneling of Magnetization Relaxation processes in SMMs Magnetic relaxation at high temperature Thermal activation (over the barrier) z up y U=U 0 (1-H/H o ) 2 x down M/M s Magnetic field µ o H z (T) 11

12 Resonant Quantum Tunneling of Magnetization H = DS z 2 gµ B S z H z S z m>= m m > E m = Dm 2 gµ B H z m with Zeeman term Resonance fields where antiparallel spin projections are coincident, H k =kd/gµ B, levels m and m ; k=m+m z up y U=U 0 (1-H/H o ) 2 x down Magnetic field Anisotropy Field: H A = 2DS gµ B 12

13 Resonant Quantum Tunneling of Magnetization H L = kh R kh R < H L < (k+1)h R H L = (k+1)h R on-resonance off-resonance on-resonance 10 on-resonance off-resonance on-resonance QT on (fast relaxation) QT off (slow relaxation) H L (T ) 13

14 Resonant Quantum Tunneling of Magnetization Relaxation processes in SMMs Magnetic relaxation at intermediate temperature Thermally assisted tunneling z up U=U 0 (1-H/H o ) 2 x down y U Γ TAT = f (T) k=6 k=7 k=8 Magnetic field H z 14

15 Resonant Quantum Tunneling of Magnetization Relaxation processes in SMMs Magnetic relaxation at low temperature Pure quantum tunneling z up y U=U 0 (1-H/H o ) 2 x Magnetic field down M/M s Magnetic hysteresis Field sweep rate 0.4 T/min 0.2 T/min 0.1 T/min 0.05 T/min 0.02 T/min k=7 k=8-0.5 k= Applied Field (Tesla)

16 Thermal to Quantum Crossover in Magnetization Relaxation ln Γ Quantum Tunneling Thermal activation crossover ln Γ Top E T 0 1/S T ln Γ E T 0 1/S T T 0 T Bottom T 0 T T 0 T Second order crossover Larkin and Ovchinnikov '83 First order crossover Chudnovsky '92 16 U(x) = x 2 + x 4 x 2 ± x 3 U(x) = x 2 x 4 ± x 5 Chudnovsky and Garanin '97 Uniaxial nanomagnets for small transverse magnetic fields!!!

17 Energy/(DS 2 ) D=0.548(3) K g z =1.94(1) H0= D/gzµB = 0.42 T B=1.17(2) 10-3 K (EPR: Barra et al., PRB 97) Energy relative to the lowest level in the metastable well m =6 m =7 m =8 m =9 m =10 n = ChudnovkyFest! Spin Physics and Nanomagnetism, March 13, 2009 H z /H o K. Mertes et al. PRB 2001

18 Experiments on the Crossover to Pure QTM in Mn12-acetate dm/dh versus Hz Schematic: dominant levels as a function of temperature 1.0 m =6 Energy/(DS 2 ) m =7 m =8 m =9 m =10 n = Thermal ~1 K ~0.1 K Quantum H z /H o 18 ADK et al. EPL 2000 L. Bokacheva, PRL 2001 K. Mertes et al. PRB 2001 W. Wernsdorfer et al. PRL 2006

19 Tunneling Selection Rules H = DS 2 z gµ B S z H z + H A Form of H A determined by the site symmetry of the molecule Fe 8 Mn 12 -acetate 180 o 90 o C 2 -site symmetry (rhombic) S 4 -site symmetry (tetragonal) H A = E(S 2 x S 2 y) H A = C(S S 4 ) 19

20 Hysteresis Loops as a Function of Transverse Magnetic Field Landau-Zener Transitions P = e ɛ ɛ = π 2 /(2 v) v =2Sgµ B db z /dt 20

21 Oscillations and Parity Effect in the Tunnel Splitting Spin-parity effects in QTM: Loss et al., 1992 von Delft & Henley, 1992 Predicted for a biaxial system by Garg 1992! 21

22 Quantum Phase Interference in Fe8 H = DS 2 z + E(S 2 x S 2 y) gµ B S x H x H T H T 22

23 Micromagnetometry µ-hall Effect B sample µ-squid B sample 1 µm Hall bars 1 to 10 µm Josephson Junctions Based on Lorentz Force Measures magnetic field Large applied in-plane magnetic fields (>20 T) Broad temperature range Single magnetic particles Based on flux quantization Measures magnetic flux Applied fields below the upper critical field (~1 T) Low temperature (below T c ) Single magnetic particles Ultimate sensitivity ~1 µ B Ultimate sensitivity ~10 2 µ B see, A. D. Kent et al., Journal of Applied Physics 1994 W. Wernsdorfer, JMMM

24 Nano-SQUID 24 NYU-Poly Physics Seminar, February 9, 2009

25 Summary I. Introduction Quantum Tunneling of Magnetization Initial Discoveries Single molecule magnets II. Magnetic Interactions in SMMs Energy Scales, Spin Hamiltonians Mn12-acetate III. Resonant Quantum Tunneling of Magnetization Thermally activated, thermally assisted and pure Crossover between regimes Quantum Phase Interference IV. Experimental Techniques Micromagnetometry SQUIDs and Nano-SQUIDs EPR 25