Olivier FRUCHART Univ. Grenoble Alpes / CEA / CNRS, SPINTEC, France
More practicals ahead Hi, I was investigating about magnetism in the human body and I used a speaker with a plug connected to it and then I started touching my body with the plug to hear how it sounds, I realized that when I put the plug in my nipples it made a louder sound which means that the magnetics were bigger in that area, I have asked about this but I get no answer why, there is no coverage about this subject on the internet either, please if you know about this let me know, my theory is that our nipples are our bridge of expulsing magnetics and electric signal to control the energy outside our bodies, hope this helps with some research, thank you... Xxx YYY Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Quizz #1 ℰ = −2 𝜈 0 𝜈 1 𝜈 2 4𝜌𝑠 3 ℰ = + 𝜈 0 𝜈 1 𝜈 2 4𝜌𝑠 3 Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Magnetic domains Numerous and complex shape of domains History: Weiss domains Practical: improve material properties Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Magnetic bits on hard disk drives Underlying microstructure Co-based hard disk media : bits 50nm and below B. C. Stipe, Nature Photon. 4, 484 (2010) Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Motivation Macrospin switching Extended systems Basics Precessional dynamics Statics Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
S pontaneous ≠ S aturation The hysteresis loop Spontaneous magnetization Magnetization reversal under magnetic field The most widespread characterization Remanent magnetization Coercive field Losses 𝑋 = 𝜈 0 ර 𝐈 ⋅ d𝐍 𝐂 = 𝜈 0 𝐈 + 𝐍 Magnetic induction 𝐊 = 𝜈 0 𝐍 Another notation Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Soft magnetic material Hard magnetic material Transformers Magnetic recording Magnetic shielding, flux guides Permanent magnets Magnetic sensors What determines hysteresis loops? Material composition and crystal structure Microstructure Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Mesoscopic scale Bulk material Nanoscopic scale Numerous and Small number of domains, Magnetic single domain complex shape of domains simple shape FeSi soft magnetic sheet Microfabricated elements Nanofabricated dots Kerr microscopy MFM A. Hubert, Magnetic A. Hubert, Magnetic Sample courtesy: domains domains I. Chioar, N.Rougemaille Nanomagnetism ≈ Mesomagnetism Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Motivation Macrospin switching Extended systems Basics Precessional dynamics Statics Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Magnetization 𝑁 𝑦 𝑛 𝑦 Magnetization vector M 𝑁 𝑧 𝑛 𝑧 Continuous function 𝐍(𝐬) = = 𝑁 s 𝑛 𝑨 𝑁 𝑨 May vary over time and space 2 + 𝑛 𝑧 2 + 𝑛 𝑨 2 = 1 Modulus is constant and uniform 𝑛 𝑦 (hypothesis in micromagnetism) 𝑁 s = 𝑁 s 𝑈 Mean field approach is possible: Exchange interaction Atomistic view ℰ = − 𝐾 𝑗,𝑘 𝐓 𝑗 ⋅ 𝐓 𝑘 (total energy, J) 𝑗≠𝑘 2 𝜄 𝑗,𝑘 𝐓 𝑗 ⋅ 𝐓 𝑘 = 𝑇 2 cos(𝜄 𝑗,𝑘 ) ≈ 𝑇 2 1 − Micromagnetic view 2 2 𝜖𝑛 𝑗 𝐹ex = 𝐵 𝛂 ⋅ m 2 = 𝐵 𝜖𝑦 𝑘 𝑗,𝑘 Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Exchange energy Magnetocrystalline anisotropy energy 2 𝜖𝑛 𝑗 𝐹ex = 𝐵 𝛂 ⋅ m 2 = 𝐵 𝜖𝑦 𝑘 𝐹mc = 𝐿 𝑔(𝜄, 𝜒) 𝑗,𝑘 Zeeman energy (→ enthalpy) Magnetostatic energy 𝐹 d = − 1 𝐹 Z = −𝜈 0 𝐍. 𝐈 2 𝜈 0 𝐍 ⋅ 𝐈 d Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Usefull expressions Analogy with electrostatics ℰ d = − 1 𝛂 ⋅ 𝐈 d = −𝛂 ⋅ 𝐍 Maxwell equation → 2 𝜈 0 ම 𝐍 ⋅ 𝐈 d d𝒲 𝒲 𝛂 ⋅ 𝐧 𝐬 ′ (𝐬 − 𝐬 ′ ) ℰ d = 1 𝐈 d 𝐬 = −𝑁 s ම d𝒲′ 𝟑 d𝒲 2 𝜈 0 ම 𝐈 d 4𝜌 𝐬 − 𝐬 ′ 3 𝒲 ′ 𝒲 Always positive To lift the singularity that may arise at boundaries, a volume integration around the boundaries yields: Zero means minimum 𝐈 d 𝐬 = ම 𝜍 𝐬 ′ 4𝜌 𝐬 − 𝐬 ′ 3 d𝒲 ′ + 𝜏 𝐬 ′ 𝐬 − 𝐬 ′ 𝐬 − 𝐬 ′ 4𝜌 𝐬 − 𝐬 ′ 3 d𝒯 ′ Hd depends on shape, not size Magnetic charges Synonym: dipolar, 𝜍(r)= − 𝑁 s 𝛂 ⋅ 𝐧(𝐬) magnetostatic 𝜏(r)=𝑁 s 𝐧 𝐬 ⋅ 𝐨(𝐬) Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Examples of magnetic charges Note for infinite cylinder: no charge ℰ = 0 Charges on side surfaces Surface and volume charges Take-away message Dipolar energy favors alignement of magnetization with longest direction of sample Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Vocabulary Generic names Magnetostatic field Dipolar field Inside material Demagnetizing field Oustide material Stray field Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Films with easy axis out-of-the-plane: Kittel domains Principle: compromise between gain in dipolar energy, and cost in wall energy C. Kittel, Physical theory of ferromagnetic domains, Rev. Mod. Phys. 21, 541 (1949) Nanostructures with in-plane magnetization – Van den Berg theorem Principle: Reduce dipolar energy to zero H. A. M. van den Berg, J. Magn. Magn. Mater. 44, 207 (1984) Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
The dipolar exchange length The anisotropy exchange length When: anisotropy and exchange compete When: anisotropy and exchange compete 2 2 𝐹 = 𝐵 𝜖𝑛 𝑗 𝐹 = 𝐵 𝜖𝑛 𝑗 + 𝐿 d sin 2 𝜄 + 𝐿 sin 2 𝜄 𝜖𝑦 𝑘 𝜖𝑦 𝑘 Dipolar Anisotropy Exchange Exchange 𝐿 d = 1 2 2 𝜈 0 𝑁 s J/m 3 J/m 3 J/m J/m Δ u ≃ 1 nm → 100 nm Δ u = 𝐵/𝐿 2 Δd = 𝐵/𝐿 d = 2𝐵/𝜈 0 𝑁 s Hard Soft Δ d ≃ 3 − 10 nm Critical single-domain size, relevant for small particles made of soft magnetic materials Sometimes called: Bloch Often called: exchange length parameter, or wall width Note: Other length scales can be defined, e.g. with magnetic field Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Bloch wall in the bulk (2D) Domain walls in thin films (towards 1D) Bloch wall 𝑢 ≳ 𝑥 No magnetostatic energy Néel wall 𝑢 ≲ 𝑥 Δu = 𝐵/𝐿 Width Implies magnetostatic energy 𝛿w = 4 𝐵𝐿 Energy No exact analytic solution Other angles & L. Néel, C. R. Acad. Sciences 241, 533 (1956) anisotropy Vortex (1D → 0D) Bloch point (0D) F. Bloch, Z. Phys. 74, 295 (1932) Point with vanishing Constrained walls (eg in strips) magnetization Permalloy (15nm) Strip width 500nm W. Döring, T. Shinjo et al., JAP 39, 1006 (1968) Science 289, 930 (2000) Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
What is a Bloch point? A magnetization texture with local cancellation of the magnetization vector R. Feldkeller, Z. Angew. Physik 19, 530 (1965) W. Döring, J. Appl. Phys. 39, 1006 (1968) 2 Bloch-point wall, theory 𝐸 ≳ 7𝛦 d Bloch-point wall, experiments Experiment Simulation WIRE SHADOW Shadow XMCD-PEEM H. Forster et al., J. Appl. Phys. 91, 6914 (2002) A. Thiaville, Y Nakatani, Spin dynamics in confined S. Da-Col et al., PRB (R) 89, 180405, (2014) magnetic structures III, 101, 161-206 (2006) Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
The Dzyaloshinskii-Moriya interaction Magnetic skyrmions Usual magnetic exchange ℰ 𝑗,𝑘 = −𝐾 𝑗,𝑘 𝐓 𝑗 ⋅ 𝐓 𝑘 Promotes ferromagnetism (or antiferromagnetism) Bulk FeCoSi 90 nm Lorentz microscopy The DM interaction Claims and facts ℰ DMI = −𝐞 𝑗,𝑘 ⋅ 𝐓 𝑗 × 𝐓 𝑘 Requires: loss of inversion symmetry Promotes spirals and cycloids I. Dzyaloshiinsky, J. of Phys. Chem. Solids 4, 241 (1958) O. Boulle et al., T. Moriya, Phys. Rev. 120, 91 (1960) Nat. Nanotech., A.Fert and P.M.Levy, PRL 44, 1538 (1980) 11, 449 (2016) Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Motivation Macrospin switching Extended systems Basics Precessional dynamics Statics Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
Quizz #2 Olivier FRUCHART – Magnetization textures and processes ESM2019, Brno, Czech Republic
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