BASICS AND MAGNETIC MATERIALS K.-H. Müller Institut für Festkörper- und Werkstoffforschung Dresden, POB 270116, D-01171 Dresden, Germany 1 – INTRODUCTION 2 – MAGNETIC MOMENT AND MAGNETIZATION 3 – LOCALIZED ELECTRON MAGNETISM 4 – ANISOTROPY AND DIMENSIONALITY 5 – PHASE TRANSITIONS AND MAGNETIZATION PROCESSES
History of magnetism • the names magnetism, magnets etc. go back to ancient Greeks: magnetite = loadstone (Fe 3 O 4 ) • The magnetism of magnetite was also known in ancient China - spoon-shaped compass 2000 years ago - long time used for geomancy - open-see navigation since 1100
European traditions in magnetism • A. Neckham (1190): describes the compass • P. Peregrinus (1269): Epistola Petri Peregrini … de Magnete - terrella, poles • E.W. Gilbert (1544 – 1603) • R. Descartes (1569 – 1650) divorced physics from metaphysics de Magnete
Modern developments in the 19th century H.C. Oersted (1777-1851) A.M. Ampère (1755-1836) M. Faraday (1791-1867) • electric currents are magnets • ∇ x H = j • magnetic field & • molecular currents • ∇ x E = - B J.C. Maxwell (1831-1871) H.A. Lorentz (1853-1928) = e + • unification of light, electricity, magnetism • v E v x B ( ) m & & • j → j + ε 0 • Lorentz transformation E • prediction of radio waves
The revolutionary 20th century P. Curie (1859-1906) P. Weiss • the molecular field • paramagnetism and ferromagnetism • domains N. Bohr, W. Heisenberg, W. Pauli P. Dirac • quantum theory • relativistic quantum theory • the need of spin • explains the spin → exchange interaction ←
Magnetism and magnetic materials in our daily life • earth's field • 50 permanent magnets in an average home • natural electromagnetic waves • up to 100 permanent magnets • TV in a modern car • portable phone • soft magnetic materials in power stations and motors and • telecommunication high frequency devices • home devices • traffic • medicine • information technology
Magnetism and magnetic materials in our daily life • earth's field • 50 permanent magnets in an average home • natural electromagnetic waves • up to 100 permanent magnets • TV in a modern car • portable phone • soft magnetic materials in power stations and motors and • telecommunication high frequency devices • home devices • traffic • medicine • information technology
Magnet materials – world market - in the late 20th century - all magnetic materials permanent magnet total 30B$ materials magnetic recording soft magnets others 53% 27% Nd-Fe-B ferrites 55% permanent magnets 30% 20%
Fields in nature, engineering and science in Tesla Brain ; Intergalactic space 10 -13 Heart 10 -10 Galaxy 10 -9 urbanic noise 10 -6 …10 -8 Surface of earth 5·10 -5 near power cable (in home) 10 -4 Surface of sun 10 -2 surface of magnetite simple resistive coil 5·10 -1 10 -1 permanent magnets 1 supercond. permanent magnets 16 superconducting coils 20 high performance resistive coils 26 (stationary) hybrid magnets (resistive + supercond.) 40 long pulse coil (100ms) 60 short pulse coil (10 ms) 80 ≤ 10 2 Anisotropy fields in solids one-winding coil 3·10 2 ≤ 10 3 Exchange fields in solids explosive flux compression 3·10 3 Neutron stars 10 8
2 – Magnetic moment and magnetization 2-1 Magnetization in Maxwell's equations microscopic form of Maxwell's equ. magnetization M and polarization P = ρ − ∇ P r ∇ = ε + h e i x & ∇ h = 0 0 & = + ∇ + i j M P x & ∇ ε 0 = e ∇ x = − µ r e h 0 + ∇ = i r 0 & ⇒ & ∇ ε + = ρ ∇ − = ε + + e P ( ) x ( h M ) e P j & 0 0 ⇒ ≡ µ − ≡ µ H B M h B / / macroscopic fields 0 0 ⇒ e = ≡ ε + E D E P 0 macroscopic form of Maxwell's equ. & ∇ = + ∇ B = H D j x 0 & ∇ x = − µ E H ∇ D = ρ 0 ρ + ∇ = j 0 magnetic moment and magnetization ∫ ∫ ⇒ ∇ = −∇ ⇒ ≡ − τ ∇ = = τ H M m r M d M d K V V ⇒ M is a density of magnetic moments ≡ "magnetization"
2-2 Magnetic moment and angular momentum 1 ∫ ∫ = − τ ∇ = = τ ∇ m r M r M d ( ) d ( ) K x x 2 V V ∫ V e e e ⇒ = τ ρ = = m r v L L d g x m 2 2 2 m m m A. Einstein and W.J. de Haas (1915): g ≈ 2 (instead of 1)
The spin of the electron and its g-factor A. Einstein and W.J. de Haas (1915) W. Gerlach and O. Stern (1922) Ag atoms scale ∂ B / ∂ z ≠ 0 z mirror iron bar G. Uhlenbeck and S. Goudsmit (1925) : atomic spectra at B ≠ 0 (Zeeman effect) S → ± ħ /2 g = 2 spin of the electron:
2-3 Quantization and relativity; diamagnetism = e + v E v x B ( ) m & H.A. Lorentz 2 B 2 e e = − + + + − λ ( 2 2 Dirac 's Hamiltonian ( L S ) B ( ) L S ) 2 x y H H 0 2 2 4 m m ⇒ m = < µ > = – ∂ < H >/ ∂ B M = N < µ > χ ij = µ 0 ∂ M i / ∂ B j = – µ 0 N ∂ 2 < H >/ ∂ B i ∂ B j diamagnetic susceptibility ( in 10 -6 ): H 2 O: –9, alcohol: –7.2
Omnipresence of diamagnetism 0.9 0.8 Magnetization (a.u.) Brillouin function 0.7 0.6 0.5 0.4 0.3 Ho 2 @C 84 in a glass ampoule 0.2 T = 1.8 K 0.1 0.0 0 1 2 3 4 5 6 7 8 Magnetic field (T)
Levitation of a diamagnetic body levitated glass cube melted by a laser beam • µ 0 H ≈ 23 Tesla • F ∼ χ ·H·(dH/dz) • stable only for χ < 0 M. Kitamura et al., Jpn. J. Appl. Phys. 39 (2000) L324
Stable position of a superconducting permanent magnet Levitation Suspension Cross stiffness YBCO NdFeB • by varying the spatial distribution of the external field the position of the superconducting magnet may have different degrees of freedom : 0 D – as in the examples above 1 D – as a train on a rail • the same holds for rotational degrees of freedom
2-4 Magnetization in thermodynamics problems: (i) thermodynamically metastable states (ii) the field generated by the samples own magnetization (iii) how to define a correct expression for magnetic work • Quantum statistical thermodynamics with the Hamiltonian H ∫ τ < > = δ − µ = δ − µ m H M H d H Q d Q d d 0 0 V • alternative definition of internal energy U = < H > + µ 0 Hm (a Legendre transformation) ∫ τ = δ + µ = δ + µ H m H M dU Q d Q d d ⇒ 0 0 V ⇒ both expressions are correct: work done on different systems ! (iv) magnetostatic interaction is long range
Magnetism in atoms and condensed matter Periodic System of Elements 1 2 H He 3 4 5 6 7 8 9 10 Li Be B C N O F Ne 11 12 13 14 15 16 17 18 Na Mg Al Si P S Cl Ar 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 55 56 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 Cs Ba Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
Magnetism in atoms and condensed matter Periodic System of Elements 1 2 H He 3 4 5 6 7 8 9 10 Li Be B C N O F Ne 11 12 13 14 15 16 17 18 Na Mg Al Si P S Cl Ar 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 55 56 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 Cs Ba Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
2-5 Localized vs. itinerant electron magnetism in solids • isolated atoms or ions with incompletely filled electron shells • magnetization: M ∼ B J (H/T) ⇒ Curie 's law M = χ H χ = C/T with • Two main types of solids – large electron density ⇒ delocalized (itinerant) electrons – e.g. in Li- or Na-metal ⇒ Hund's rule magnetic moment disappears ⇒ a small, (nearly) temperature independent susceptibility – small electron densities ⇒ strongly correlated electrons ⇒ they can be localized and carry a magnetic moment ⇒ examples: MnO, FeO, CoO, CuO (antiferromagnets); EuO, CrCl 3 (ferromagnets ) • In 4f materials localized and itinerant electrons coexist
2-6 Itinerant electron magnetism • weakly interacting Landau quasiparticles 2 1 | | m h e χ = µ µ − 2 ( ) ( ) 2 E 1 µ = N with 0 B F 2 3 * B 2 m m ⇒ metals with large or moderate m * (e.g. Na: m / m * ≈ 1) are Pauli paramagnets, χ > 0 ⇒ those with small m * (e.g. Bi m / m * ≈ 10 2 ) are Landau diamagnets, χ < 0
Susceptibility vs . temperature after M. Bozort 1951 10 -3 10 -4 MOLECULAR SUSCEPTIBILITY 10 -5 10 -6 -10 -6 -10 -5 -10 -4 -10 -3 -200 0 200 400 600 800 TEMPERATURE [°C]
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