MSE 7025 Magnetic Materials (and Spintronics) Lecture 2: Magnetic Units and Basic E&M Chi-Feng Pai [email protected] Course Outline • Time Table Week Date Lecture 1 Feb 24 Introduction 2 March 2 Magnetic units and basic E&M 3 March 9 Magnetization: From classical to quantum 4 March 16 No class (APS March Meeting, Baltimore) 5 March 23 Category of magnetism 6 March 30 From atom to atoms: Interactions I (oxides) 7 April 6 From atom to atoms: Interactions II (metals) 8 April 13 Magnetic anisotropy 9 April 20 Mid-term exam 10 April 27 Domain and domain walls Course Outline • Time Table Week Date Lecture 11 May 4 Magnetization process (SW or Kondorsky) 12 May 11 Characterization: VSM, MOKE 13 May 18 Characterization: FMR 14 May 25 Transport measurements in materials I: Hall effect 15 June 1 Transport measurements in materials II: MR 16 June 8 MRAM: TMR and spin transfer torque 17 June 15 Guest lecture by Prof. S.Y. Huang (physics) 18 June 22 Final exam Magnetic Field • Magnetic field… what is it, anyway? Magnetic Field • Magnetic field… what is it, anyway? Magnetic Field • Magnetic field… what is it, anyway? http://hyperphysics.phy-astr.gsu.edu/ Magnetic Field • Magnetic field… what is it, anyway? – Exist in some certain metals – Can be induced by current Magnetic Field • Magnetic field… what is it, anyway? Magnetic Field • Magnetic field… what is it, anyway? Magnetic Field • Magnetic field… what is it, anyway? Magnetic Field • Magnetic field… what is it, anyway? – Something that can be measured and quantified. – A physical quantity that has a value for each point in space and time (definition of “field”). – The notation is “B” in this case. – And the unit of it is “G” (gauss) in this case. Magnetic Field • And when you read more papers, you will find… Magnetic Field • And when you read more papers, you will find… Growth and study of magnetostrictive FeSiBC thin films, for device applications, Mannan Ali (1999) Magnetic Field • And when you read more papers, you will find… Magnetic Field • And when you read more papers, you will find… Magnetic Field • And when you read more papers, you will find… Magnetic Field • And when you read more papers, you will find… Magnetic Field • And when you read more papers, you will find… Magnetic Field • And when you read more papers, you will find… Notation Unit H kG = 1000 G = 1000 gauss H Oe = oersted H A/m = ampere/meter B mT = 0.001 T = 0.001 tesla B G = gauss μ0H T = tesla Magnetic Field • And when you read more papers, you will find… Notation Unit H gauss (G) H oersted (Oe) H ampere/meter (A/m) B tesla (T) B gauss (G) μ0H tesla (T) What you gonna do first when you report to a new magnetism lab? Print out the units table! Units Table Units of B-field and H-field • “Magnetic flux density” and “magnetic field strength” Vacuum permeability (真空磁導率) Units of B-field and H-field • “Magnetic flux density” and “magnetic field strength” • In cgs (Gaussian) units • In SI units Units of B-field and H-field • “Magnetic flux density” and “magnetic field strength” • In cgs (Gaussian) units • In SI units (From wikipedia) Units of B-field and H-field • “Magnetic flux density” and “magnetic field strength” • In materials (SI units) Magnetization – With “magnetization” term – If linearly magnetized Magnetic susceptibility (磁化率) BHH0 r permeability Relative permeability Units of B-field and H-field • “Magnetic flux density” and “magnetic field strength” Units of B-field and H-field • “Magnetic flux density” and “magnetic field strength” Units of B-field and H-field • “Magnetic flux density” and “magnetic field strength” • In SI (MKS) units BHMHHHHH0 0 01 0 r • In Gaussian (cgs) units BHMHHH 4 4 1 4 Units of B-field and H-field • “Magnetic flux density” and “magnetic field strength” Notation Unit SI or cgs? H (B) kG = 1000 G = 1000 gauss cgs (symbol misused) H Oe = oersted cgs H A/m = ampere/meter SI B G = gauss cgs B mT = 0.001 T = 0.001 tesla SI μ0H T = tesla SI Units of B-field and H-field • “Magnetic flux density” and “magnetic field strength” Notation Unit SI or cgs? H (B) kG = 1000 G = 1000 gauss cgs (symbol misused) H oersted (Oe) cgs H ampere/meter (A/m) SI B gauss (G) cgs B tesla (T) SI μ0H tesla (T) SI Strength of magnetic fields • In terms of tesla Strength of magnetic fields • Levitation of a frog using a 16T-magnetic-field Levitating frog from the Nijmegen High Field Magnet Laboratory, which won the Ig Nobel Prize in 2000. But why frog? http://www.ru.nl/hfml/research/levit ation/diamagnetic/ Andre Geim 2000 Ig Nobel Prize 2010 Nobel Prize in Physics Strength of magnetic fields • Fractional Quantum Hall Effect, discovered using a 23T- magnetic field (Bitter magnet) The Physics Nobel Prize 1998 was given for the discovery and theory of the Fractional Quantum Hall Effect to Daniel Tsui, Horst Stormer and Bob Laughlin Strength of magnetic fields • NdFeB (Neo, NIB) magnets (B ~ 1 Tesla) – Nd2Fe14B https://www.youtube.com/watch?v=Y1MDOerruDU Interesting experiment using Neodymium-Iron-Boron magnets More on B-field • Lorentz force equation – The force on a charged particle by EM fields – Dimension analysis More on B-field • The Biot-Savart law – The magnetic field B generated by an electric current I Magnetization “M” and magnetic susceptibility “χ” • Magnetization (per unit volume) Magnetization “M” and magnetic susceptibility “χ” • Magnetic susceptibility Magnetization “M” and magnetic susceptibility “χ” • Magnetic susceptibility Ferromagnetism 0 0 0 Magnetization “M” and magnetic susceptibility “χ” • Magnetic susceptibility (T-dependence) Diamagnetism Maxwell’s Equations • Gauss’s law • Gauss’s law for magnetism • Faraday’s law of induction • Ampere’s circuit law Maxwell’s Equations • Gauss’s law • Gauss’s law for magnetism • Faraday’s law of induction • Ampere’s circuit law Maxwell’s Equations • Ampere’s circuit law Maxwell’s Equations • Typically, within the scope of magnetic materials – Magneto-quasi-static – Simplified Maxwell’s equations (differential form) Maxwell’s Equations • Typically, within the scope of magnetic materials – Magneto-quasi-static – Simplified Maxwell’s equations (integral form) Maxwell’s Equations in materials • Have to consider “bound charges” and “bound currents” Maxwell’s Equations in materials • Have to consider “bound charges” and “bound currents” BKM00b B 0 nI Magnetic dipole moment • Similar to the concept of electrical dipole moment, but... • Magnetism comes from moving charges Magnetic dipole moment • A heuristic approach – Ampere’s current loop concept (Unit) ~ Magnetic dipole moment • Magnetic moment unit conversion • Magnetization unit conversion emu/cm3 = 103 A/m Torque, energy, and force • Dipole moment in a magnetic field • Magnetic potential energy Torque, energy, and force • Force experienced by the moment • Since the moment is typically independent of position • Dimension analysis .