QUANTUM NANOMAGNETISMProceedings of the International Conference Nanomaterials:Applications and Properties September 2012 Javier Tejada, Dept. Física Fonamental Universitat de Barcelona
ContenidosContent Introduction to magnetism Single Domain Particles Quantum relaxation: 1990-96 Resonant spin tunneling: 1996-2010 Quantum magnetic deflagration Superradiance Free rotors Magnetic vortices Quantum effects in type-I superconductors
Introduction to magnetism• Electrostatic interaction + Quantum Mechanics 2 e Overlapping of wave r12 functions 2 e Is different for S 0 and S 1 r12 Heisenberg Term si s In the Hamiltonian j hamiltonian
Introduction to magnetismThe magnetic moment of an atom has e two contributions: p μorbital1. The movement of the electrons around the nucleus. The electric charges generate magnetic fields while moving2. Electron, like the other fundamental particles, has an intrinsic propierty named spin, which generates a magnetic moment even outside the atom: e e μspin S=1/2 S=-1/2 Hence, the magnetic moment of the atom is the sum of both contributions e μtotal = μorbital + μspin p
Título Introduction to magnetism S 0 S 1 Atoms can be found with two or more interacting electrons. Considering two of them in an atom, the energy of the spin interaction can be calculed: e The system always tends to be at e p the lowest energy state:: J ~ TC ˆ ˆ ˆ eff J s1 s 2 The overlapping of the wave Summation over functions decays exponentially. nearest neighbours
Título Introduction to magnetism Existence of metastable states Magnetic Time dependent hysteresis phenomena Slow relaxation towards the free energy minimum. Global Non-linear thermodynamic effects. equilibrium.
Título Single domain particles• Permanent magnets divide themselves in magnetic domains to minimize their magnetic energy.• There are domain walls between these domains: E ex Exchange energy E ex a (nm ) E an Anisotropy energy E an a Lattice constant
Título Single domain particles E ex 3 5 The exchange energy is so high that Tipically 10 10 E an it is difficult to do any non-uniform rotation of the magnetization. If the particle has R then no domain walls can be formed. This is a SDP:The probabilty of the flip E ex exp( ) 0 and E ex Tcof an individual spin is: T Hence, at low T, the magnetic moment is a T Tc S ct vector of constant modulus:
Single domain particlesThe rotation of M as a whole needs certain energy called magnetic anisotropy.• Relativistic origin: p v – Order of magnitude , with p even. c• Classic description: – Energetic barrier of height: U U (H ) U kV e T Anisotropy Volume constant
Single domain particlesQuantum description: Because the spin is a quantum characteristic, it can pass the barrier by tunnel effect. The tunnel effect, that reveals the Easy axis Hard axis quantum reality of the magnetism, allows the chance of finding the magnetic moment of the particle in two different states simultaneously. U + The action of the observer on the particle will determine its final state!!!
Single domain particlesImportant aspects of SDPs:• Volume distribution: f R f V f U• And orientations:• Their magnetic moments tend to align with the applied magnetic field.
Single domain particles• The particles relax toward the equilibrium state: t M M0 1 S ln 0 Magnetic viscosity• Thermal behaviour ( S T) – At high temperatures it is easier to “jump” the barrier.• Quantum behaviour (independent of T) – Relaxation due to tunnel effect.
Magnets: memory and relaxation When removing the applied Magnetic solids (ferromagnets) show field, these materials keephysteresis when an external magnetic field is certain magnetization that applied: slowly decreases with time. M MR ~ Memory MR ~ ln t Hc H Magnetic solids have memory, and they lose it with time!!! t ~ 109 years: Paleomagnets Hc Magnet ~ 5000 Oe t ~ 10 years: credit cards Hc Transformer ~ 1 Oe
Título Quantum relaxation: 1990-96 Magnetic viscosity Magnetic viscosity dependance on T, for low variation with respect T, of a TbFe3 thin film to the magnetic field.
Resonant spin tunneling onmolecular magnets• Identical to single domain particles• Quantum objects[M i , M j ] 2i M B ijk k |M| ~ μB Quantum[M i , M j ] M iM j M jM i B M k |M| » μB Classic Empirically, the magnetic moment is considered in a quantum way if |M| ≤ 1000μB 2 2H A DS z ES x M(H,T) univocally determined by D and E
ResonantTítulo spin tunneling onmolecular magnets • Application of an external field: Zeeman term H S - Longitudinal component of the field (H || easy axis) Moves the levels. - Transverse component of the field (H easy axis) Allows tunnel effect. • The tunnel effect is possible for certain values of the field; resonant fields.
Resonant spin tunneling onmolecular magnetsThe spin energy levels are moved by an applied magnetic fieldFor multples of the resonant field (HR, 2HR, 3HR, …) the energy oftwo levels is the same, producing quantum superposition, allowingthe tunneling. This is known as magnetic resonance
Resonant spin tunneling onmolecular magnets -3-2 12 -4 3 -5 4 -6 5 -7 6 -8 7 -9 8 -10 9 B = B0 10 Magnetic field
Resonant spin tunneling onmolecular magnets -3-2-10 1 -4 2 -5 3 -6 4 -7 5 -8 6 -9 7 -10 8 9 B = 2B0 Magnetic field 10
ResonantTítulo spin tunneling onmolecular magnets• After a certain time, the relaxation becomes exponential: M t M eq t 1 exp H t• Peaks on the relaxation rate Γ(H) at the resonances:
Quantum magnetic deflagration Avalanche ignition produced by SAW:Surface Acustic Waves (SAW) are low frequency acoustic phonons(below 1 GHz)Coaxial cable connected to an Agilent microwave signal generatorChange in magnetic moment registered in a rf-SQUID magnetometer Hz Coaxial cable LiNbO3 IDT Mn12 crystal substrate c-axis Conducting stripes
Quantum magnetic deflagration κ U(H) v exp τ0 2k B T f This velocity is well fitted: κ = 0.8·10-5 m2/s• The speed of the avalanche Tf (H = 4600 Oe) = 6.8 Kincreases with the applied Tf (H = 9200 Oe) = 10.9 Kmagnetic field• At resonant fields the • The ignition time shows peaks atvelocity of the flame front the magnetic fields at which spinpresents peaks. levels become resonant.
Magnetic Vortices (MV): IntroductionVortex State• The spin field splits into two well-differentiated structures: 1) the vortex core consisting of a uniform out-of-plane spin component (spatial extension about the exchange length) and 2) the curling magnetization field (in-plane spin component), characterized by a non-zero vorticity value.• The application of an in-plane magnetic field yields the displacement of the vortex core perpendicularly to the field direction.• The vortex shows a special vibrational mode (called gyrotropic mode) consisting of the displacement of the vortex core as a whole, following a precessional movement around the vortex centre. Its characteristic frequency belongs to the subGHz range.Experimental set-upWe have studied several arrays of permalloy (Fe19Ni81) disks with diameter 2R = 1.5 μm and differentthickness (L = 60, 95 nm) under the application of an in-plane magnetic field up to 0.1 T in the range oftemperatures 2-300 K. Samples were prepared stacking four 5x5 mm2 arrays with parallel sides.
MV: Magnetic Characterization Hysteresis loop of a sample with thickness L = 95 nm.The vortex linear regime in the ascending branchshould extend from H=-300 Oe to 500 Oe (at least)in the L = 95 nm sample. Analogous behaviour has a) ZFC-FC curves for an applied magnetic field H = 300 Oe (L =been observed in the other sample. 95 nm). b) Isothermal magnetic measurements along the descending branch, Mdes(H), from the SD state (H = 0.1 T) to H = 300 Oe (L = 95 nm).
MV: Relaxation ExperimentsRelaxation mesurements of magnetic vortices from the metastable states of the descendingbranch at H = 0 to the equilibrium state (which corresponds to M=0) for both samples. Normalized relaxation measurements for samples L = 60 nm (left) and L = 95 nm (right). M0 corresponds to the initial point of the relaxation.
MV: Viscosity and conclusions Conclusions: • Logarithmic time dependence of the magnetization broad distribution of energy barriers in our system. • Thermal activation of energy barriers dies out in the limit T 0. Observation that magnetic viscosity S(T) tends to a finite value different from zero as T 0 indicates that relaxations are non- thermal in this regime. • The presence of structural defects in the disks could be a feasible origin of the energy barriers. We consider them to be capable of pinning the vortex core, when the applied magnetic is swept, in a non-equilibrium position. Magnetic viscosity S versus temperature T for both samples.Below T = 6 K, magnetic viscosity reaches a plateau withnon-zero value.
Type I SC: Topological hysteresis Flux penetration: bubbles Flux expulsion: lamellae Different flux structures appear in the Intermediate state depending on the magnetic history:There is a GEOMETRICAL BARRIER controlling both the Tubes/bubbles are formed during magnetic fieldpenetration and the expulsion of magnetic flux in the penetration and laberinthic patterns appear uponintermediate state. It is the responsible for both the expulsionintrinsic irreversibility of a pure defect-free samples andthe formation of different flux patterns.
Type I SC: Magnetic relaxation Relaxation mesurements of a Pb sample from the metastable states of the descending branch for different reduced fields h in steps of 0.027 at T=2 K (a) and at different T for the fixed reduced field h=0.10 (b). We observe a perfect logarithmic time dependence of m(t) for several T and h: This law holds for any system having a broad distribution of energy barriers as the source of its metastability
Quantum tunneling of N-SC interfaces Left figure: Temperature dependence of the magnetic viscosity for different reduced fields (a) and reduced magnetic field dependence of S at different T (b). Right figure: Reduced magnetic field vs. T phase diagram showing the different dynamical regimes.