Published on: **Mar 3, 2016**

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- 1. Quantum Nanomagnetism and related phenomena Professor Javier Tejada. Dept. Física Fonamental, Universitat de Barcelona. Columbia-Rice Frontier CMP Lecture October 31st, 2013
- 2. Contenidos Content Introduction to magnetism: exchange and anisotropy energies Single Domain Particles Molecular Magnets Resonant spin tunneling on Molecular Magnets Quantum magnetic deflagration Superradiance Conclusions
- 3. Introduction to magnetism • Electrostatic interaction + Quantum Mechanics 2 e r12 e2 r12 Term si s j Overlapping of wave functions Is different for S in the Hamiltonian 0 and S 1 Heisenberg hamiltonian
- 4. Título Exchange interaction Atoms can be found with two or S =0 S =1 more interacting electrons. Considering two of them in an atom, the energy of the spin interaction can be calculated: e e p The system always tends to be at the lowest energy state: J ~ TC ˆ ˆ ˆ = -J s × s Þ Heff 1 2 The overlapping of the wave functions decays exponentially. Summation over nearest neighbours
- 5. Título Magnetic anisotropy • Orbital motion of electrons makes them feel B is the local electric field. v E , where E(r ) • Action of B on the electron spins correlation between the direction of the spin and the orientation of the crystallographic axes. •Quantum description: crystal-field hamiltonian is given by HA where b 1 b 2 v2 O 2 c Sn Sn n and c fourth rank respectively ( , , , 1 c 4 v4 O 4 c Sn Sn Sn Sn n are tensors of second rank and x, y, z )
- 6. Título Macroscopic solid to single domain particles • Domains and domain walls: • Eex Tipically Ean 10 3 10 The exchange energy is so high that it is 5 difficult to do any non-uniform rotation of the magnetization ( • If the particle has then no domain wall can be formed. This is a SDP: • The probabilty of an individual spin flip is: with Hence, at low T, the magnetic moment is a vector of constant modulus: ).
- 7. Single domain particles (SDP) • Classical description: energy barrier of height U=kV Anisotropy constant • Þ e Volume U (V ) / T Microscopic attempt frequency Blocking temperature is defined via the condition 1 / tm which leads to: TB KV / ln tm Analogously, we can also define the Blocking volume: VB T ln K tm U
- 8. Important aspects of SDPs
- 9. SDP: magnetic relaxation • The particles relax toward the equilibrium state: MR t M R 0 1 S ln Initial remanent magnetization • The dependence of S on T shows two different regimes: 1) 2) Thermal regime: at high temperatures it is easier to “jump” the barrier. In this regime, S µ T Quantum regime: at low temperatures, magnetic relaxation is due to tunnel effect. In this regime S is of T. t
- 10. Quantum magnetic entities • Their magnetic moment M is a quantum operator: it verifies the commutation relation which yields Quantum Classical Empirically, the magnetic moment is considered to behave quantumly if |M| ≤ 100μB holds.
- 11. Molecular Magnets (MM): example of Mn12 acetate +2 +2 +2 -3/2 -3/2 -3/2 +2 +2 -3/2 +2 +2 +2 Spin S Η 10 DS z2 H , Sz 0 Quantum counterpart of a SDP. H , Discrete projection of the spin onto the easy axis.
- 12. Magnetic bistability of Mn12 acetate Degenerate ground states for the Mn12 acetate molecule. There exists an anisotropy energy barrier between these two spin orientations. The effect of an external magnetic field applied along the easy axis.
- 13. Resonant Título spin tunneling on MM • Application of an external field: adds a Zeeman term Longitudinal component of the field (H // easy axis) Shifts the levels. Transverse component of the field (H easy axis) Allows tunnel effect. • The tunnel effect is possible for certain values of the field: the resonant fields.
- 14. Resonant spin tunneling on MM -2-10 1 2 -3 3 -4 4 -5 5 -6 6 -7 7 -8 -9 -10 H=0 8 9 10 Magnetic field
- 15. Resonant spin tunneling on MM -2-10 1 2 -3 3 -4 4 -5 5 -6 6 -7 -8 -9 7 8 9 -10 10 H = 0.5HR Magnetic field
- 16. Resonant spin tunneling on MM -3-2 -4 -5 -6 -7 -8 -9 -10 H = HR 12 3 4 5 6 7 8 9 10 Magnetic field
- 17. Resonant spin tunneling on MM -3-2-10 1 -4 2 -5 3 -6 4 -7 5 -8 6 -9 -10 H = 2HR 7 8 9 10 Magnetic field
- 18. Relaxation MM • As we only have a single barrier height, relaxation goes exponential. Mn12 Ac relaxation measurements from the remanent state at different temperatures. Mt M eq T 1 e H t
- 19. Relaxation MM • Peaks of the relaxation rate Γ(H) at the resonant fields Relaxation rates of Mn12 acetate at different fields
- 20. Landau-Zener effect E m m' m' m' W Em Em ' t Transition probability Size of magnetization step E E W P 1 P m m' m m W m 2 2 e m' E 2 / 2
- 21. Resonant Título spin tunneling on MM
- 22. What is a deflagration? Deflagration is a technical term describing subsonic combustion that usually propagates through thermal conductivity Metastable State ∆U Two important characteristic timescales: ∆E τb= τd Energy released ∆E Ignition (barrier overcoming) ∆U Thermal diffusion k Characteristic length of propagation δ • Stable State Thermal diffusion • Burning timescale Deflagration Flame width 22
- 23. From magnetization jumps to magnetic Deflagration (MD) Molecule magnets Field jumps 1999 Deflagration-like description 2005 Intermetallic compounds Field jumps 2002 Deflagration-like description 2010 Manganites Field jumps 1999 Deflagration-like description 2007 23
- 24. First evidences of MD H ΔE Magnetic deflagration: Propagation of a front of reversing spins at constant velocity along the crystal A. Hernández-Mínguez et. al. PRL 95 17205 (2005) Problem: Sweeping H we cannot control the magnetic field at which it occurs. Y. Suzuki et. al. PRL 95, 147201 (2005)
- 25. Quantum magnetic deflagration Avalanche ignition produced by SAW: Surface Acoustic Waves (SAW) are low frequency acoustic phonons (below 1 GHz) Coaxial cable connected to an Agilent microwave signal generator Change in magnetic moment registered in a rf-SQUID magnetometer Hz Coaxial cable IDT Mn12 crystal c-axis Conducting stripes LiNbO3 substrate
- 26. Quantum magnetic deflagration v κ τ0 exp U(H) 2kB Tf This velocity is well fitted: κ = 0.8·10-5 m2/s Tf (H = 4600 Oe) = 6.8 K Tf (H = 9200 Oe) = 10.9 K • The speed of the avalanche increases with the applied magnetic field • At resonant fields the • The ignition time shows peaks at the magnetic fields at which spin velocity of the flame front levels become resonant. presents peaks.
- 27. Quantum Magnetic Deflagration
- 28. Quantum Magnetic Deflagration
- 29. Associated to magnetic avalanches: magnetoresistive avalanches in manganites 29
- 30. Superradiance Proposed by Robert H. Dicke in 1954. This kind of emission (SR) has characteristic properties that make it different from other more common phenomena like luminescence I I N Luminescence τ1 t I L τSR Superradiance L~λ I N2 λ N is the number of dipoles t
- 31. Superradiance All spins decay to the fundamental level coherently, with the emission of photons. -1 -3-2 0 1 2 -4 -5 3 -6 4 -7 5 -8 6 -9 7 -10 B = 2B0 8 9 10
- 32. Superradiance?? Sharp peak shows a signal which is equivalent to the sample being at 20 K (the expected self heating is about 3 K).
- 33. Magnetic deflagration in pulsed fields dB/dt (kT/s) 7.0 6 4.8 3.7 3.2 2.5 1.9 1.6 coil 1 coil 2 Δt dM/dt 4 2 0 200 400 t (s)
- 34. Quantum magnetic detonation t 16 14 12 10 Time-difference between the observation of a magnetisation-reversal in a coil on the left and on the right of a Mn12Ac-sample in function of (high) magnetic field-sweeprates. All observations were done in pulsed fields at a temperature of about 500mK (in liquid 3He). t ( s) 8 6 4 2 0 -2 1000 2000 3000 4000 5000 dHz/dt (T/s) 6000 7000
- 35. Superradiance: indirect evidence 0.30 1066 T/s 1270 T/s 1660 T/s 2050 T/s 2970 T/s 0.20 Mn12-Ac powder in araldite Scaling with fixed HR 1104 T/s 1321 T/s 1725 T/s 2132 T/s 3113 T/s 0.15 0.10 0.10 Scaling 0.05 0.00 1.2 1.4 1.6 0.08 1.8 2.0 r 1/2 dM/dH B(T) dM dH r ~ H r 0.06 0.04 0.02 0.00 -0.010 -0.005 0.000 0.005 0.010 (H - HR) / r 1/2 0.015 0.020 G:scaledFixedHR in G:MolecularMagnetsMn12Pulsed fields (KULeuven)Mn12_B+C(paper) MN12BDN / MN12BGN / MN12BIN / MN12BJN / MN12BMN dM/dB (a.u) 0.25 0.025
- 36. Future • Energy barrier between opposite orientations of the magnetic moment is formed by weak relativistic interactions whether stable molecular magnets can ever break liquid nitrogen temperature of 77K. • Making identical molecules comparable to mesoscopic magnetic particles will be a challenging task for chemists. • Another challenging question would be whether magnetic molecules can ever become ultimate memory units of conventional computers or even elements of quantum computers. • I hope to see answers to these questions in the near future!!
- 37. References [1] E. M. Chudnovsky, J. Tejada, Macroscopic Quantum Tunneling of the Magnetic Moment (Cambridge Univ. Press, 1998). [2] J.R. Friedman, M.P. Sarachik, J. Tejada and R. Ziolo. Phys. Rev. Lett. 76, 3830–3833 (1996). [3] A. Hernández-Mínguez et al. Phys. Rev. Lett. 95, 217205 (2005). [4] Macià et al. Phys. Rev. B 76, 174424 (2007). [5] Macià et al. Phys. Rev. B 77, 012403 (2008). [6] F. Macià et al. Phys. Rev. B 79, 092403 (2009). [7] S. Vélez et al. Phys. Rev. B 81, 064437 (2010). [8] W. Decelle et al. Phys. Rev. Lett. 102, 027203 (2009). [12] P. Subedi et al. Phys. Rev. Lett. 110, 207203 (2013). Physics 6, 55 (2013).