Magnetic Properties of Materials 𝐹 … force in 𝑥 direction 𝑉 … sample volume 𝜒… magnetic susceptibility 𝐻 … magnetic field 𝑑𝐻/𝑑𝑥 … gradient of the magnetic field The magnetic susceptibility 𝜒 characterizes the magnetic properties of materials

Other Parameters … force acting on a material … permeability (similar to permittivity:  = 1 + P/[0E]) … magnetic induction … magnetization … magnetic flux (B… magnetic flux density) … magnetization and magnetic moment

Magnetic Properties of Materials … plus antiferromagnetic and ferrimagnetic

Interaction with an External Magnetic Field Material Interaction Diamagnetic Is repelled by the applied magnetic field Paramagnetic Are attracted by the applied magnetic field with different forces Ferromagnetic Antiferromagnetic Ferrimagnetic

Diamagnetism Change of the inner or atomic “electrical” current within an external magnetic field: Change in angular velocity of strongly bound electrons Rotation (circular movement) of free (metallic) electrons

Diamagnetism Diamagnetic materials create an induced magnetic field (magnetization 𝑀) in a direction opposite to the external magnetic field, therefore the magnetic induction 𝐵 is small in the material. Ideal diamagnetic materials are superconductors in the superconducting state (Meissner effect) … negative in diamagnetic materials

Paramagnetism Without an external magnetic field (𝐻 = 0), there is no magnetization of the material (𝑀 = 0), because the magnetic moments of single atoms (electrons) are oriented randomly. In an external magnetic field (H > 0), the magnetic moments of single atoms (electrons) are oriented in the direction of the external magnetic field  M > 0. Temperature vibrations disturb the orientation of magnetic moments  susceptibility depends on temperature. 𝐻

Paramagnetism 𝑀 (a) … Curie’s law (b), (c) … Curie-Weiss law for paramagnetic materials (d) … diamagnetic material 𝐻 … Curie … Curie-Weiss

Molecular field theory* Paramagnetism Meaning of constants 𝐶 and 𝜃 in Curie’s law and the Curie-Weiss law Magnetism of electrons in an atom (orbital electrons) Molecular field theory* (Weiss 1907) 𝑛 … number of magnetic moments (atoms) * Belongs to the mean field theory

Additional effect to the orbital magnetism Spin Paramagnetism Additional effect to the orbital magnetism Elements with 3d electrons (occupation of orbitals is described by Hund’s rules): Fe: 3s2, 3p6, 3d6 Spin magnetic Co: 3s2, 3p6, 3d7 Spin magnetic Ni: 3s2, 3p6, 3d8 Spin magnetic Cu: 3s2, 3p6, 3d10 Not spin magnetic Zn: 3s2, 3p6, 3d10 Not spin magnetic

Elements with 3d Electrons

Ferromagnetism The major characteristics of ferromagnetic materials Ordering of magnetic moments below 𝑇 c Saturation of magnetization Transition ferromagnetic  paramagnetic at 𝑇 c Temperature dependency of 𝑀 s

Magnetic Properties of Ferromagnetic Materials – Examples

Influence of Real Structure (Residual Stress) on magnetic properties of ferromagnetic materials Nickel (fcc) Iron (bcc)

Influence of Real Structure (Crystallite Orientation) on magnetic properties of ferromagnetic materials Example: iron single crystal Crystal anisotropy of magnetic properties (magnetization) The average of physical properties is measured

Permanent Magnets Wide hysteresis curve is needed

Materials for Permanent Magnets

Magnetoelastic Effects Magnetostriction Change in length (in the lattice parameters) of magnetic crystals within a magnetic field Spontaneous magnetostriction Change in length (lattice parameters) of magnetic crystals in the own magnetic field Observed in some materials below 𝑇c – at the ordering of magnetic moments

Spontaneous Magnetostriction ErCo2 RT: Fd-3m LT: R-3m  = 90°    90°

Spontaneous Magnetostriction Separation of crystallographically non-equivalent diffraction lines

Coefficients of magnetostriction in Er(Co,Ge)2 and Er(Co,Si)2

Er(Co1-xSix)2 Increase of lattice parameters (volume of unit cell) at low temperatures Ordering of magnetic moments  magnetic interactions between single atoms  Change of the crystal structure

Ordering of magnetic moments below 𝑇 c ( 𝑇 N … Néel temperature) Antiferromagnetism Ordering of magnetic moments below 𝑇 c ( 𝑇 N … Néel temperature) Example: MnO, UN (fcc, Fm3m, NaCl structure), MnF2 Antiparallel ordering of magnetic moments Negative critical temperature: Susceptibility in paramagnetic state

Experimental Methods to Investigate the Orientation of Magnetic Moments Neutron diffraction Elastic scattering of neutrons on atomic nuclei  Information about the crystal structure (similar to x-ray diffraction) Interaction between the magnetic moments of the neutrons and the magnetic moments of atoms  information about the magnetic structure

Magnetic Properties of Antiferromagnetic Materials – Examples UN 𝑇N = 53 K −𝜃 = 247 K CrN 𝑇N = 273-286 K

Influence of Real Structure on magnetic properties of antiferromagnetic materials Thin layers of UN Different temperature of coating  different residual stress, crystallite sizes and density of defects Formation of an apparent ferromagnetic component at low temperatures  unbalanced magnetic moments UN 𝑇N = 53 K −𝜃 = 247 K

Ferrimagnetism Spontaneous ordering of magnetic moments and hysteresis below the Curie temperature as in ferromagnetic materials A ferrimagnetic compound is typically a ceramic material (ferrite – FeO.Fe2O3, NiO.Fe2O3, CuO.Fe2O3, …) with spinel structure.

Susceptibility and Magnetization of Ferrimagnetic Materials NiO.Fe2O3

GMR Effect Giant Magnetoresistance in Multilayers Diamagnetic material: Cu, Ag, Au Ferromagnetic material: Fe, Co, Ni dia dia ferro ferro I  I  dia dia ferro ferro H = 0 H > 0

Physical Principle of GMR Scattering depends on the relative orientations of the electron spins and the magnetic moments of atoms. Parallel: weakest scattering Antiparallel: strongest scattering Antiferromagnetic coupling of two ferromagnetic layers above a diamagnetic layer

Nobel prize in physics 2007 For discovery of the giant magneto-resistance effect Peter Andreas Grünberg Albert Louis François Fert

Change of the Electrical Resistance in an External Magnetic Field Definition of GMR:

Change of Electrical Resistance in an External Magnetic Field System: Co/Cu

Important Parameters of Magnetic Multilayers Selection of materials (diamagnetic, ferromagnetic) Thickness of layers Roughness and morphology of the interfaces Methods for investigation Measurement of the resistance within a variable magnetic field XRD, neutron diffraction TEM Applications Magnetic field sensors (reading heads for hard disks) Solenoid valves (Spin valves) 10 nm

Influence of Thickness of “Spacers” on magnetic properties of multilayers Co Cu . 50x

Reading Head in a Hard Disk Pros: Very small dimensions [(Co 11Å/ Cu 22 Å) x 50] = = 1650 Å = 165 nm = 0.165 m

Storage capacity

Storage capacity Reading heads with GMR effect Magneto-resistive reading heads Inductive reading heads