Chapter 8 Nanoscale Magnetism

Transcription

1 Chapter 8 Nanoscale Magnetism 8.1 Characteristic length scales 8.2 Thin films 8.3 Thin film heterostructures 8.4 Wires and needles 8.5 Superparamagnetism 8.6 Bulk nanostructures TCD March

2 One nanoscale dimension: Thin films Two nanoscale dimensions: Nanowires and acicular particles Three nanoscale dimensions: Nanoparticles TCD March

3 Fig 8.1 Magnetostriction in iron thin films TCD March

4 8.1 Characteristic length scales Exchange length Hardness parameter Spin diffusion length sd >> mean free path TCD March

5 8.2 Thin films surface interface Intrinsic magnetic properties M s, T C, K 1, s can be significantly different in thin films and in the bulk. substrate Epitaxial films Oriented films Lattice parameters are influenced by the substrate, when the difference is < 4% Seed and cap layers. TCD March

6 2.1 Magnetization and Curie Point Some metals become ferromagnetic in thin film form (V, Rh) although they are not magnetically ordered in the bulk; Others become ferromagnetic when deposited on a ferromagnetic substrate (Pd on Ni) Magnetism of iron is especially sensitive to structure and lattice parameters. Fe has moment of 4 µ B as an isolated atom; 3.3 µ B in a chain, 3.0 µ B as a plane 2.2 µ B in the bulk bcc iron has a surface layer wth a moment 20% greater than the bulk.. Moment enhancement is due to band narrowing related to reduction in the number of nearest-neighbours TCD March

7 Number of planes Curie temperature of thin films of 3d transition metals on various substrates T C is weakened in ultra-thin films by the reduction in the number of exchange bonds, Also by surface spin waves, structural relaxation. TCD March

8 A uniformly-magnetized thin film produces no stray field. B = µ 0 (H + M )= 0. B is continuous Hence H = 0 outside -N M ; N =1 H = -NM.; N= 0. H is continuous. Hence H = 0 outside TCD March

9 2.2 Anisotropy and domain structure Extra 3s contributions to the anisotropy of a thin film: shape; surface; strain. Shape The demagnetizing factor for a uniformly magnetized film is N = (0, 0, 1) The anisotropic contribution to the self energy in the demagnetizing field is -(1/2)µ 0 MH d E = -K u sin 2 where K shape = -(1/2) µ 0 M 2 s Fe MJ m -3 Co Ni This has to be overcome by some other form of anisotropy if we want to make a true permanent magnet. TCD March

10 Surface Surface anisotropy often leads to perpendicular anisotropy in films about one nm thick. 8.4 Surface anisotropy per unit area cobalt thickness for CoPd multilayers Intercept gives E surface 1 mj m -2 Monolayer thickness is about 0.25 nm; This surface anisotropy corresponds to 4 MJ m -3, as in L1 0 compounds TCD March

11 Strain Fig 8.5 Strain anisotropy induced by epitaxy. The strain in Ni layers on Cu is relaxed beyond 4.5 nm TCD March

12 Magnetic structure of thin films Fig 8.6 Twist of magnetization due to surface anisotropy K s (mj m -2+ ) Euler equation Out of plane with a twist when K v > (1/2)µ 0 M s 2 TCD March

13 Maze domains Bubble domains Fig 8.7 Magnetization and domain structure in a film with perpendicular anisotropy TCD March

14 Magnetization of thin films. Q = -K u /K d where K d = (1/2)µ 0 M s 2 Perpendicular anisotropy for Q > 1; Maze domains In plane when Q < 1 and t < 2 w Fig 8.8 Magnetic structure of a thin film as a function of Q and thickness t TCD March

15 Fig 8.9. Magnetization curves and surface domain structure for a 200 nm film of Ni. Magnetization curves show the magnetization is largely in-plane. The MFM image of stray field at the surface picks up the small perpendicular component. TCD March

16 8.3 Thin film heterostructures A magnetic multilayer is a stack of alternating magnetic and nonmagnetic layers. A bilayer is a pair of layers of different magnetic materials A superlattice is an epitaxial multilayer 3.1 Direct exchange coupling; exchange bias FM2 FM1 FM F1 FM2 AF YCo 2 GdCo 2 Field-controllable domain wall TCD March

17 Exchange Bias. Discovered by Mieklejohn and Bean; 1956 A new type of magnetic anisotropy has been discovered, which is best described as exchange anisotropy. This anisotropy is a result of an interaction between an antiferromagnetic material and a ferromagnetic material Co CoO Fig 8.11 Rotational hysteresis of the same particles Fig 8.10 Shifted hysteresis loop of Co particles measured on field cooling in 1 T to 77 K TCD March

18 Exchange bias of thin films. Néel 1964 AFM FM Fig 8.13 TCD March

19 It is as if an effective field H eff = H + H ex is acting on the film; H ex 4 ka/m; µ 0 H ex 50 mt H z y M H ex = K ex /µ 0 M 2 x The energies are better written per unit area of film as exchange bias scales with the area. K ex = /t p The energy per unit area is: The corresponding field is E A /µ 0 M p t p Minimize E A Switching occurs when = /2; H = H ex = - /M p t p Perpendicular anisotropy field H a = ( +2K u t p )/µ 0 M p t p TCD March

20 Dependence on layer thickness There is a threshold t af necessary for exchange bias to become effective; t crit K as ; t crot = 10 nm, K af = 20 kj m mj m -2 H ex 1/t p Fig 8.14 TCD March

21 Table 8.2. Antiferromagnetic Materials for Exchange Bias Exchange bias only becomes effective below a blocking temperature T b which is considerably lower than T N TCD March

22 Models for exchange bias *Atomically flat antiferomagnetic surface. A) could be spin compensated; = 0; B) could present one ferromagnetic plane; = A/d 200 mj m -2 *Only about 1/1000 of the spins seem to participate in the exchange coupling. Surface is inevitably rough. Regions of dimension L contain (L/a) 2 atoms. Uncompensated moment is that of (L/a) 2 atoms. Hence L 1000a 200 nm. OK But these regions will themselves add randomly. * Exchange bias may arise from defects of grain boundaries where there are frustrated spins TCD March

23 Models for exchange bias Fig 8.16 * Interfacial coupling leads to perpendicular fm and afm axes. Coupling energy will be similar to that in a 90 degree domain wall; (1/2) (KA af ) 0.4 mj m -2 TCD March

24 Fig Fig TCD March

25 3.2 Indirect exchange coupling Fig 8.21 Oscillations of the exchange coupling between ferromagnetic layers as a function of the ruthenium spacer thickness Fig TCD March

26 Best for af coupling is 0.8 nm Ru FM FM Ru Artificial Antiferromagnet Fig 8.20 The aliasing effect FM FM Ru Artificial Ferrimagnet TCD March

27 TCD March

28 3.3 Dipolar coupling A perfectly smooth film creates no stray field. Correlated roughness leads to orange-peel coupling With t n,the spacer thickness - 5nm, roughness = 1 nm, period l = 20 nm, the coupling is 0.03 mj m -2 TCD March

29 3.4 Giant magnetoresistance The GMR effect was discovered by Fert et al in 1988 Magnetoresistance in an Fe/Cr multilayer was as high as 80 % at low temperature and in high fields Much greater than AMR - hence the name. Fig 8.23 GMR of an Fe/Cr multilayer First understanding in terms of the Mott two-current model. The and channels conduct in parallel, with no spin-flip scattering. and are the resistivities of the two channels. = / Fig 8.22 Derivation of GMR in the two-current model TCD March

30 Fig 8.24 TCD March

31 3.5 Spin valves FM FM Cu (pseudo) Spin valve TCD March

32 TCD March

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34 3.6 Magnetic tunnel junctions I FM FM AlO x V I = GV + V 3 E Magnetic tunnel junction V Nonlinear I:V Current decreases exponentially with thickness w Little temperature dependence w TCD March

35 Juliere formula for TMR I Parallel magnetic tunnel junction Julière formula: MR = 2P 1 P 2 /(1 - P 1 P 2 ) Antiparallel If P 1 = P 2 MR = 2P 2 /(1 - P 2 ) Taking P = 45%, MR = 51% TCD March

36 500 % TMR Fig 8.25 TCD March

37 Calculation of tunelling through a an Fe/MgO/Fe crystalline tunnel barrier Exchange-biased MgO magnetic tunnel junction R/R % Majority channel tunneling is dominated by the transmission through a 1 (sp) state 1 state decays rapidly in anti-parallel configuration µ 0 H (mt) TCD March

38 Spin filter A thin layer of ferromagnetic insulator can act as a spin filter, producing a spinpolarized tunnel current. An N/F/N structure. F = EuO, NiFe 2 O 4, CoFe 2 O 4 I E vac ex The spin-split barrier favours electron tunneling. w 1 w 2 E F t TCD March

39 Metal/Insulator/Superconductor junctions Tederov-Meservey experiment Fig 8.27 TCD March

40 TCD March

41 8.4 Wires and needles Acicular particles 30x30x300 nm are used in magnetic recording. N < 0.1 Shape anisotropy K shapa = [(1-3N)/4]µ 0 M s 2 For a long wire K shapa = (1/4]µ 0 M s 2 Maximum anisotropy field 2K shape /µ 0 M s = M s /2 The coercivity cannot exceed M s /2 not enough for a permanent magnet. TCD March

42 Alnico Sophisticated nanostructures with spinodal nanostructure of oriented acicular Fe-Co in a nonmagnetic Al-Ni matrix, developed mainly in the 1930s. NiAl Shape anisotropy: E a = (1/4)µ 0 (1-3N)M s2 sin 2 = 1 sin 2 Anisotropy field: H a = 2K 1 /µ 0 M s = (1/2)(1-3N)M S FeCo H C < -H A Coercivity due to shape anisotropy < M s /2 Insufficient for a permanent magnet! TCD March

43 8.5 Superparamagnetism 1/ 0 1 GHz Energy landscape of a superparamagnetic particle TCD March

44 T 0 blocked T b superparamagnetic T C paramagnetic Blocking is not a phase transition, but an exponential variation of fluctuation tims Superparamagnetic behaviour of cobalt nanoparticles TCD March

45 When an ensemble of superparamagnetic particles is cooled through T b in a magnetic field, it acquires a thermoremanent magnetization. Igneous rocks (basalts) contain superparamagnetic magnetite particles. They acquire a TRM as they cool in the Earth s magnetic field. TCD March

46 5.1 Magnetic viscosity The entire hysteresis loop reflects metastable states. The magnetization at any point evolves with time spontaneous magnetization remanence coercivity virgin curve initial susceptibility major loop M M(t) = M(0) - S ln t Ln t Viscosity coefficient TCD March

47 8.6 Bulk nanostructures Fig 8.29 TCD March

48 6.1 Single-phase nanostructures In single-phase nanostructures the bulk anisotropy can be greatly reduced by exchange coupling of nanocrystallites with different anisotropy axes. Exchange-averaging occurs when 1. Crystallites are single-domain with D << w and 2. There is exchange coupling across grain boundaries. TCD March

49 Fig 8.30 Coercivity vs. grain size for a range of soft magnetic materials. TCD March

50 Remanence enhancement: TCD March

51 6.2 Two-phase nanostructures Two-phase nanostructures can be produced by partial recrystallization of an amorphous material If v c is the volume fraction of the crystalline phase, which has anisotropy K 1, and the amorphous phase has no anisotropy. TCD March

52 Recrystallization of amorphous Fe-Cu-Nb- Si-B to obtain a two-phase crystalline/ amorphous soft nanocomposite Finemet is a near-ideal soft magnetic material with high polarization 1.6 T zero magnetostriction Minimal anisotropy TCD March

53 TCD March

54 Hard/soft nanocomposite; Nd 2 Fe 14 B/Fe SmCo 5 /Co 35 Fe 65 w is too short to average away anisotropy, When the size of the soft region is < 2 w the soft and hard phases are exchange coupled. and behave in an averaged way, In this way it is possible to obtain a hard material with a magnetization greater than any single-phase hard magnet. Fig 8.33 TCD March

55 Fig TCD March

56 Fig 8.35 TCD March