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PHYS 575-Special Topics in Physics (Fall 2019) Magnetism, magnetic materials and spintronics
Dipanjan Mazumdar, Department of Physics
Part I - Fundamentals of magnetism
Even though many elements in the periodic table have a magnetic moment in the atomic form, only a few are either paramagnetic or ferromagnetic in the solid-state.
Most elemental solids are diamagnetic. Even rarer is room-temperature ferromagnetism. Only three elements are Ferromagnetic at room temperature, namely Fe, Co, Ni.
In this part of the course, we shall build our understanding of magnetism starting from atoms and end with the Stoner Model of Ferromagnetism. The magnetism of metals will receive particular attention.
Week 1 : Atomic and ionic magnetism
Here we will learn about atomic magnetism and magnetism of ions (ionic solids, which are electrical insulators) starting from a discussion of angular momentum.
Week 2 : Paramagnetism of ionic solids
The various models of paramagnetism for ionic solids are developed as a collection of non-interacting (free) ions.
We begin with the classical theory of paramagnetism (Langevin Paramagnetism). Next, paramagnetism of spin 1/2 particles is discussed and extended to
systems with both spin and orbital angular momentum.
Magnetic susceptibility is shown to have a strong temperature dependence. Ferromagnetism within this model is also discussed.
Week 3 : Diamagnetism of ionic solids
Many metals and semi-metals are diamagnets (e.g., Cu, Bi) even though they have uncompensated atomic moments. Diamagnetism is a change in the orbital moment due to a magnetic field.
Both classical and quantum treatments give identical diamagnetic susceptibility. The treatment described here applies to atoms and ions and metals will be discussed later.
Week 4: Free electron gas theory (Sommerfield model)
Free-electron gas subject to the Pauli exclusion principle ( Fermi-Dirac Distribution) is THE starting point to understand any physical properties related to metals such as magnetism. Important physical quantities such as the Fermi energy, Fermi velocity, and Fermi Temperature enter the language of the free electron gas.
A natural outcome is the concept of density of states, which is very important to understand any solid-state property.
Week 5: Pauli Paramagnetism and Landau Diamagnetism
Unlike ionic solids, the paramagnetic susceptibility of most metals is significantly lower with little temperature dependence. To explain this behavior, Pauli successfully invoked the exclusion principle (Fermi-Dirac statistics) to the free electron gas. Landau also showed that the application of a
magnetic field changes the wavefunction of the electron gas and induces a diamagnetic susceptibility. Further, it can be shown that Landau susceptibility = -1/3 Pauli susceptibility.
Week 6: Stoner Enhancement of paramagnetic susceptibility
There can be a significant enhancement of paramagnetic susceptibility if electrons favor to align themselves. This can happen through an internal magnetic field, as hypothesized by Weiss. It can be shown that under appropriate conditions, called the Stoner criterion, a new ground state spontaneously emerges without
the application of an external field. This new state is the Ferromagnetic state. We rationalize the tendency of electrons to line up through quantum mechanical exchange interactions.
Week 7: Stoner Model of Ferromagnetism for electron gas
The Stoner model is developed in the absence of a magnetic field. The Stoner criterion is derived and shown to be satisfied by the late 3d elements such as Fe, Co, and Ni that have a high density of states close to the Fermi level.
Materials that almost satisfy the Stoner criterion show higher susceptibility than Pauli paramagnets. Pt and Pd fall in this category (incipient Ferromagnets).
Week 8: Exchange interactions
Exchange interactions that lead to ferromagnetism are a consequence of the Pauli exclusion principle and Coulomb repulsion between electrons. Exchange interactions can be demonstrated
quite simply in a two-electron system, such as a Helium atom. The two possible ground state spin configurations are shown to have different energies controlled by exchange interactions.
Week 9: Heisenberg model of magnetism for localized moments
Heisenberg in 1928 proposed his now famous model which is a starting point in treating both Ferromagnetism and anti-ferromagnetism.
Part II- Application of magnetism
The 1980s witnessed the birth of the area of spintronics, primarily through the discovery of the Giant Magnetoresistance effect, which was recognized with a Nobel Prize in 2007.
Since then, remarkable progress in magnetoresistive technologies has led to their commercialization in magnetic hard drives as read-head sensors.
In this part, the physics of different magnetoresistive effects are introduced starting with the Normal (or ordinary) MR, then Anisoptropic MR, and conclude with the Giant MR. Currently,
technologies such as Magnetoresistive Random Access Memmory (MRAM) and antiferromagnetic spintronics are active areas of research. These topics will be covered next semester.
Week 10: The Drude Theory of transport
Drude's model of electrical transport was proposed a few years after the electron was discovered and predates the atomic model and quantum mechanics.
More importantly, the famous Drude's relation relating conductivity to relaxation time has withstood all future scrutiny.
Drude model was later adapted to the free electron gas model by Sommerfield.
Week 11: Success and failure of Drude Model
One of the many successes of Drude's theory is that it gives the right Hall coefficient for electronic systems. But it also predicts zero magnetoresistance,
contrary to experimental observations. Also, Hall effect measurements show behavior consistent with both negative and positive charges that cannot be explained using Drude's Model.
Week 12: Magnetoresitance (MR) in metals and semi-metals
The resistance of most non-magnetic materials increases under a magnetic field with a B^2 dependence at low fields.
This behavior is called the normal magnetoresistance and cannot be explained using Drude-Sommerfield theory of metals.
Week 13: Semi-classical transport and Normal MR
Band theory is necessary to explain the normal magnetoresistance behavior of metals. Such a model of transport that includes the essential features of the band structure
is called the semi-classical theory. Basic principles of semi-classical transport are introduced here that leads us to the concept of hole transport, apart from the electron.
The low-field normal MR behavior (B^2 dependence) can be explained by extending the Drude-Sommerfield model to include two types of carriers.
Week 14: Anistropic Magnetoresistance and Two-current model
Apart from the normal MR effect, magnetic materials display anisotropic magnetoresistance (AMR), where the resistance depends on the magnetization of the magnet.
Discovered by Lord Kelvin in 1857, AMR is a relatively small effect at low fields, but useful for technological purposes. Currently, AMR technology is used for
GPS navigation in smartphones as magnetic field sensors, among other applications.
There is no simple phenomenological model to explain the AMR effect, and requires quantum mechanical perturbation theory applied to Neville Mott's
two-current model for even a qualitative agreement with experimental results. Physically, the AMR effect is induced by spin-orbit coupling.
Week 15 and 16: Giant and Tunnel Magnetoresistance
Magnetic multilayers can produce large magnetoresistance at room temperature, as exemplified by the Giant and Tunnel Magnetoresistance effects.
Giant MR was observed in 1989, and room temperature Tunnel MR was observed in 1993. Both discoveries spurred the rapid commercialization of spintronics technology as read head sensors in magnetic hard drives.
Even though the GMR and TMR effects are similar experimentally, their physical origins are different. GMR depends on a spin-dependent scattering, while TMR is a spin-dependent quantum mechanical tunneling effect.