Dr. Vadym Zayets

Content

all pages of web site of Vadym Zayets

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the most of these Web pages I have made in a clean room waiting for temperature to stabilized or a required vacuum to be reached. Therefore, the Web pages may content some English errors or my thoughts may be not fully explained or some explanation may be missed. I do my best to correct all these errors.

click on image to enlarge it.

Spin Transport

Introduction

Transport Eqs.

Spin Proximity/ Spin Injection

Spin Detection

Boltzmann Eqs.

Band current

Scattering current

Mean-free path

Current near Interface

Ordinary Hall effect

Anomalous Hall effect, AMR effect (New)

Spin-Orbit interaction

Spin Hall effect (New)

Non-local Spin Detection

Landau -Lifshitz equation

Exchange interaction

sp-d exchange interaction

Thermally-activated magnetization switching. Coercive field. Retention time. Δ

Perpendicular magnetic anisotropy (PMA)

Voltage- controlled magnetism (VCMA effect)

Spin vs. Orbital moment in a solid. Quenching of orbital moment

All-metal transistor

Spin-orbit torque (SOT effect)

measurement of Spin Polarization

What is a hole?

e-Drugs (Electronic drugs & Electronic Antibiotics.). PMA sensor.

Charge accumulation

MgO-based MTJ

Magneto-optics

Spin vs Orbital moment

What is the Spin?

model comparison

Questions & Answers

EB nanotechnology

Reticle 11

Measurement of Magnetic and Magneto- transport properties of FeCoB nanomagnets (New)

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Spin and charge Properties

(model based on fact of distribution of conduction electrons into two groups of spin-polarized and spin-unpolarized electrons)

Introduction

Scatterings

Spin-polarized/ unpolarized electrons

Spin statistics

electron gas in Magnetic Field

Pauli paramagnetism. Pauli and Stoner models. Features and limitations.

Spin Torque

Spin-Torque Current

Spin-Transfer Torque

Quantum Nature of Spin

Questions & Answers

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Classical model of spin-up/down bands of the spin transport

(The applications of this model are limited, because this model has some incorrect assumption)

Introduction

Basic Transport equations

Spin and charge currents

Spin drain

Non-magnetic metals

Ferromagnetic metals

Semiconductors (Basic)

Threshold spin current

Spin gain/damping

Spin Relaxation

Spin Hall/ Inverse Spin Hall effects

ee- interaction

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Spin-Photon memory

click on image to enlarge it.

This topic is about my development of high-speed non-volatile optical memory

Introduction

Applications

Operational principal

High-speed demultiplexing experiment

Reading

High-Speed Spin Injection

Spin-photon memory with MTJ

Fabrication Technology

EB nano fabrication

Reticle 10

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Magneto-optical effect

Faraday rotation angle

MCD

Isolation

Kerr rotation

non-linear constants

Origin of Magneto-optics

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Transverse Magneto-Optical effect

Introduction

Experimental observation of transverse MO effect

Properties of transverse MO effect

Origin of transverse MO effect

Transverse Ellipticity

Two contributions to transverse MO effect

Magnetization-dependent optical loss

Calculations of transverse MO effect in the case of multilayer structure

Optical excitation of spin-polarized electrons utilizing transverse MO

Plasmons

Giant Enhancement of Transverse MO effect

History and Future

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Plasmonic. Plasmonic isolator. Si nanowire waveguides

Introduction

Si nanowire fabrication technology

fiber/waveguide coupling setup

devices made of Si-waveguides

directional coupler

integration: plasmonic + Si waveguides

Comparison of two technologies of Integration of Si nanowire waveguide and plasmonic waveguide

Out-plane plasmonic confinement

plasmonic isolator

III-V plasmonic

AlGaAs waveguide (800 nm)

AlGaAs waveguide (1550 nm)

Si wire waveguide (1550 nm)

plasmonic on GaAs (800 nm)

plasmonic on GaAs (1550 nm)

plasmonic on Si (1550 nm)

plasmons in metal strip

in-plane confinement of plasmons

samples very old

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Introduction ot the toy model in the framework of statistical mechanics

Abstract 

This chapter presents a simple “toy model” to illustrate the concepts of energy, entropy, and free energy. In this model, multiple microstates are grouped together into a single macrostate through a process of coarse-graining. The system tends to go into the macrostate that minimizes the free energy. At low temperature, this is the ordered state with the lowest energy. At high temperature, it is the disordered state with the highest entropy or multiplicity.

                                To see a world in a grain of sand, 
                                      And a heaven in a wild flower, 
                                             Hold infinity in the palm of your hand, 
                                                       And eternity in an hour. 
                                                                           ... 
                                                               William Blake, Auguries of Innocence

Physicists are always looking for the Big Ideas—ideas that are fundamentally simple in concept but can be applied to understand many phenomena throughout nature. In my field of statistical mechanics and phase transitions, the Big Idea is the balance between order and disorder, a balance that is controlled by temperature. In this chapter, I would like to introduce you to this Big Idea through a toy model, i.e., a model which is not a serious theory but is just meant as a simple way to illustrate a basic point. I want to see the world not in a grain of sand, but in a speck of dust.

Let us begin with the situation shown in Fig. 1.1. Here, a speck of dust can have two states: it can be either on the floor or on the table. Each of these states has some energy Efloor or Etable. Based on the  Boltzmann distribution,2 these two states have the probabilities pfloor = (e−Efloor/kB T )/Z and ptable = (e−Etable/kB T )/Z, where kB is Boltzmann’s constant,3 T is the temperature, and Z = e−Efloor/kB T + e−Etable/kB T is the partition function that makes the probabilities add up to 1.

Which state is more likely? Let us compare the two probabilities: The speck of dust is more likely to be on the floor if

Hence, the speck is more likely to be on the floor than the table if the floor energy is lower than the table energy. That is not a big surprise!

Now let us consider a slightly more interesting problem. Suppose there are N tables, where N is some large number, as shown in Fig. 1.2. The probability of being on the floor is (e−Efloor/kB T )/Z. The probability of being on a particular table is (e−Etable/kB T )/Z. The probability of being on any of the N tables is N(e−Etable/kB T )/Z. Here, the partition function that normalizes the probabilities must be Z = e−Efloor/kB T + Ne−Etable/kB T .

In this new problem, let us compare the probabilities again. The speck is more likely to be on the floor than on any of the tables if

This little calculation shows that we should not just compare the energy Efloor and Etable. Instead, we should compare some adjusted energy that takes into account the multiplicity of the states. The adjustment (without the factor of T ) is called the entropy, and the adjusted energy is called the free energy. For the group of all table states, the entropy is

                                                   Stable = kB log N,                                       (1.3)

and the free energy is

                                            Ftable = Etable − T Stable = Etable − kB T log N.            (1.4)

Likewise, because there is only one floor state, the entropy of the floor is

                                               Sfloor = kB log(1) = 0,                                (1.5)

and the free energy of the floor

                                   Ffloor = Efloor − T Sfloor = Efloor − kB T log(1) = Efloor.            (1.6)

Hence, the speck is more likely to be on the floor than on any of the tables if

                                                         Ffloor < Ftable.                                                              (1.7)

From this toy model, I think we learn three general lessons. First, we see the importance of grouping states together. If we care about whether the speck is on any table, and we do not care which table, then it is appropriate to group all of the table states together. In this grouping, we are treating a collection of microstates as a single macrostate. This macrostate has an energy E and a multiplicity N (and hence an entropy S = kB log N). This grouping is our first example of the concept of coarse-graining, which will be fundamental throughout statistical mechanics.

Second, we see the concept of free energy, which combines the energy and entropy of a macrostate into the quantity F = E − T S. This quantity is essential for understanding what macrostate is most likely to occur at a nonzero temperature T .

Third, we see that the relative importance of energy and entropy depends on temperature. At low temperature, energy is the dominant part of the free energy, and the system is most likely to go into whatever macrostate has the lowest energy. That is usually a single, special state, which might be called an ordered state. By contrast, at high temperature, entropy is the dominant part of the free energy, and the system is most likely to go into whatever macrostate has the highest entropy. That is usually a big collection of many microstates. They each have a high energy, so they are individually unlikely, but there are a lot of them! That collection might be called a disordered state.

Now, dear students, I imagine that some of you might have an objection. You might say “What do you mean by defining the free energy of a state? I have already learned the definition of free energy in a class on thermal physics or statistical thermodynamics, and it was different! In that class, we did not talk about the free energy of a state; we just talked about THE free energy. It was defined in terms of the partition function Z as”

                                                                F = −kB T log Z.                                                (1.8)

“So what’s going on here?!?”
I am glad you asked that question. Let us look at Eq. (1.8) for THE free energy, and rewrite it as

             e−F/kB T = Z = e−Efloor/kB T + e−Etable 1/kB T +···+ e−Etable N /kB T .            (1.9)

Now we group the N table microstates together into a single macrostate, and rewrite the equation as

                                          e−F/kB T = Z = e−Efloor/kB T + Ne−Etable/kB T                      (1.10)
                                                                 = e−Ffloor/kB T + e−Ftable/kB T .                        (1.11)

Look at this: When we combine many microstates together in the partition function, we get the free energy of the combined macrostate. We can keep combining macrostates together to make super-macrostates, and combining super-macrostates to make super-duper-macrostates, and each of them has a free energy. When we eventually finish combining all possible states together, we reach THE free energy of the system. That is coarse-graining!

At this point, I think we have learned everything we can from this toy model, and we need to move on to something more physical. Onward!


Reference: https://b-ok.cc/book/2617724/522dcf

Introduction to the Theory of Soft Matter: From Ideal Gases to Liquid Crystals

Jonathan V. Selinger (auth.)

SOLID STATE PHYSICS

Fall 2001

Lectures: MWF 9-10 ; Room 13-4101

Recitation: F 11-12 ; Room 38-136

Texts | Assignments | Examinations | Syllabus [HTML] [PDF] | Handouts

INSTRUCTOR: M. S. Dresselhaus

STAFF:

• Oded Rabin -- Head TA; Room 13-3025 oded@mgm.mit.edu
• Marcie Black -- TA assistant; Room 13-3041 mrb@mgm.mit.edu
• Yu-Ming Lin -- TA assistant; Room 13-3037 yming@mgm.mit.edu
• Laura Doughty -- Support; Room 13-3005 laura@mgm.mit.edu

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COURSE OUTLINE

• Part I: Transport Properties

  • Review of Energy Dispersion Relations in Solids
  • Examples of Energy Bands in Solids
  • Time--Independent Perturbation Theory
  • Effective Mass Theory
  • Transport Phenomena
  • Thermal Transport
  • Electron and Phonon Scattering
  • Harmonic Oscillators, Phonons, and Electron-Phonon Interaction
  • Two Dimensional Electron Gas, Quantum Wells \& Semiconductor Superlattices
  • Transport in Low Dimensional Systems
  • Ion Implantation and RBS

• Part II: Optical Properties

  • Review of Fundamental Relations
  • Drude Theory--Free Carrier Contribution to the Optical Properties
  • Interband Transitions
  • Time Dependent Perturbation Theory
  • The Joint Density of States and Critical Points
  • Absorption of Light in Solids
  • Optical Properties of Solids Over a Wide Frequency Range
  • Impurities and Excitons
  • Luminescence and Photoconductivity
  • Harmonic Oscillators, Phonons, and the Electron-Phonon Interaction
  • Optical Study of Lattice Vibrations
  • Non-Linear Optics
  • Electron Spectroscopy and Surface Science
  • Amorphous Semiconductors

• Part III: Magnetic Properties

  • Review of Topics in Angular Momentum
  • Magnetic Effects in Free Atoms
  • Diamagnetism and Paramagnetism of Bound Electrons
  • Magnetism in Solids
  • Paramagnetism of Nearly Free Electrons
  • Landau Diamagnetism
  • The Quantum Hall Effect
  • Magnetic Ordering
  • Magnetic Devices

• Part IV: Superconducting Properties of Solids

  • Review of Superconducting Properties of Solids
  • Macroscopic Quantum Description of the Supercurrent
  • Microscopic Quantum Description of the Supercurrent
  • Superconductivity in High Transition Temperature Cuprate Materials

Back to Course Home Page

http://web.mit.edu/course/6/6.732/www/syllabus.html