more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11
more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11
more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11

What is the Spin? Spin & Time Inverse Symmetry. Spin and Charge TransportAbstract:The spin describes the properties related to the breaking of the timeinverse symmetry for an elementary particle. An electron has a magnetic moment and angular moment due to the spin (broken timeinverse symmetry).The time inverse symmetry is broken, when a quantum state is occupied by one electron. Such a state is spin active. The time inverse symmetry is not broken, when a quantum state is occupied by two electrons. Such a state is spin inactive. Contentclick on the chapter for the shortcut(Part 1) Origin of the Spin1.1. Spin & Time Inverse symmetry1.2. Incorrect view of the spin as an internal rotation of an electron1.3.Spin & the timeinverse symmetry1.4. Spin & Magnetic Moment1.5.Spin & Dirac Equations1.6 Quantum Mechanic and Magic in Physics1.7. Magical (Incorrect) explanation of the Spin1.8. Stern–Gerlach experiment. Magic, which lived over a hundred years.1.9. Classical explanation of the Spin by Dr. Matt O`Dowt(Part 2) Mechanical forces & Mechanical torque due to the Spin & Magnetic field(2.1) Difference of mechanical force acting on a single electron and on an assembly of electrons(2.2) Origin of a mechanical force(2.2) Mechanical force 1:Due to a gradient of magnetic field(2.3) Mechanical force 2: Due to an artificial magnetic charge. The torque of compass pointer.(2.4) Mechanical force 3: Due to Einstein–de Haas effect.(Part 3) What is the magnetic field?(3.1) What is the magnetic field? 3 origins of the magnetic field.(3.2) 3 types of the magnetic field: (1) conventional magnetic field; (2) Spinorbit magnetic field; (3) magnetic field of the exchange interaction.(part 5) Inflation, breaking symmetry, origin of an elementary particle & Spin() Why is understanding of the Inflation important for understanding of the spin?() A few facts aboaut the Inflation() How to create a particle from the vacuum() Size of an elementary particle() Standard model and "post Standard model"() Symmetry & Conservation Laws() Transformation of two elementary particles into one particle.() Exchange interaction. Spininactive electrons(). Questions & Answers()about spinmixed state
.........Spin & Time Inverse symmetry(fact) The spin describes the degree of breaking of the time inverse symmetry. The spin is not magnetic moment or angular momentum or anything else. The breaking if the time inverse symmetry is only parameter, which corresponds to the spin and is measured by the spin.
(note) Each conserved property of an elementary particle (like an electron) correspond to some breaking of the spacetime symmetry. For example, the particle energy corresponds to the continuity of the time. The continuity of the time means that the Laws of Physics are the same today and tomorrow. A particle with a nonzero energy, which is always the case, breaks the symmetry of the continuity of the time. Each moment of time is individually different for the particle. For example, when the particle is moving, its spatial position is different at each moment of time and each moment of time is different and not symmetrical for the particle. The particle momentum corresponds to the continuity of the space, which means that the laws of the Physics are the same here and near the Moon. A particle with a nonzero momentum breaks the symmetry of the continuity of the space. The spatial positions, which are one meter away from the center of the particle and, therefore, the symmetry of the continuity of the space is individually broken for the particle. . Each moment of time is individually different for the particle. For example, when the particle is moving, its spatial position is different at each moment of time and each moment of time is different and not symmetrical for the particle. The spin corresponds to the breaking of the time inverse symmetry. It means that some of particle properties changes if the direction of time flow would be reversed..
(note) The spin magnetic moment and the spin angular momentum are the properties, which are consequence of breaking of the time inverse symmetry. E.g. the breaking of the timeinverse symmetry makes the number of Dirac equation twice as many. There are 4 Dirac equations.
Incorrect view of the spin as an internal rotation of an electron
Q. Is it possible that the origin of the electron spin is the rotation of the electron around itself??
A. No. It is not correct assumption. An electron does does not have parts and it does not have a defined shape. Therefore, it can not rotate around its own axis. The electron is an elementary particle and it does have any parts. Therefore, the electron can not be rotated around itself The rotation of an object around itself literally means that the parts of the object rotates relatively each other. In case when the object is monolithic without any parts, it can not be rotated around itself, because there is nothing, which could be rotated. An electron may rotate around another object. For example, in an atom an electron rotates around a nuclear. An electron has length, which equals to the electron meanfree path. The length of conduction electrons in a semiconductor could be as long as micrometers. In a metal, the electron length is about of a few nanometers. A localized electron has a size of atom, which is about ~0.1 nm. An electron has a width as well. It is defined by electron wave vector and the meanfree path. 
Note: The spin and charge are two independent features of the electron. For example, when two electrons of opposite spin occupy one quantum state. The state has the charge of 2e, but no spin. The neutron has no charge, but it has the spin.
Incorrect view: The spin of electron is not due to the movement (the rotation) of charge inside the electron. The spin of electron is not due to the charge of the electron.!!!!! It is due the timeinverse breaking for the electron!!However, the magnetic moment of electron is because the electron is a charged elementary particle.
All particles in Universe are created by breaking of spatial symmetry of vacuum.(See Fig. 10) When additionally the timeinverse symmetry of vacuum is broken, an elementary particle has the Spin.
Spin & the timeinverse symmetryThe timeinverse symmetry breaking is the most common and simple breaking of symmetry of the vacuum. Therefore, nearly all particles have the spin
Since the spin describes the breaking of the timeinverse symmetry, there are only two possible spin eigen values for any elementary particle!! For this reason, the spin of an elementary particle is described maximum by two wave functions. Often it is called states of the leftrotation and the state of the rightrotation. In case of an electron, the states are called the spinup and spindown states. In the case of a photon, the states correspond to left and right circular polarized photon. The timeinverse symmetry symmetry of the vacuum is not broken. Therefore, the spin can interact with the field, which timesymmetry symmetry is broken, and the result of such interaction should be the timeinverse symmetric. The timeinverse symmetry symmetry of the magnetic field is broken. As result, the spin interacts with the magnetic field.
If an elementary particle with the spin is not charged (like the neutrino), does it interact with magnetic field?The magnetic field represents the timeinversebreaking part of the electromagnetic interaction. The neutrino, which does not interact electromagnetically, should not interact with the magnetic field. However, the common origin of the weak and the electromagnetic interactions, it could be some a very weak interaction of the neutrino with a magnetic field.
In atom an electron is circulating around a proton. Why a reversed atom, where a proton is circulating around an electron, can not be observed? Is that because of the differences of masses (the proton is heavier)?It is because the electron is an elementary particle, but the proton is a composite particle, which consists of three quarks. The electron can not have a fix tiny length (size), but a composite particle is more close to a pointlike particle. Because the proton is a composite particle, its mass is ~2000 times larger than mass of the electron. The difference of masses has some influence, but it is not major influence. For example, the proton has a diameter about 1 femtometer. It is defined by a longest possible length of a gluon. See Wikipedia about pointlike particles (There are many parts, with which I do not agree)
Spin & Magnetic Moment
Origin of the spinrelated magnetic moment: The origin of the electron magnetic moment is nearly the same as the origin of the electron charge. The electron charge is originated from the breaking of the symmetry of the phase of the electron wave function with respect to spatial transformation. Similarly, the electron magnetic moment (spinrelated) is originated from the breaking of the symmetry of the phase of the electron wave function with respect to timereversal.
(gauge symmetry) The electron wave function has both the phase and magnitude. Only magnitude has a physical meaning which the probability of electron to be at certain spacial point at fixed moment of time (See here for more details). The phase has no physical meaning for a single electron in absence of any neighbor particle. In this case, the changing of the phase does not affect any of the physical parameter of the electron. However, in the electromagnetic field, the phase of the electron wavefunction is locally changed by the electromagnetic the electron energy
(origin of charge) The gauge symmetry becomes locally broken for a spacial transition (e.g. transition along the xaxis) (origin of spinrelated magnetic moment) The gauge symmetry becomes locally broken for a time inverse+ rotation
Spin & Dirac Equations
(fact 1) The Dirac equations describes the quantum mechanical properties of an electron. The solution of the Dirac equation is a 4rank spinor. The 4rank spinor is a 4 dimensional vector of 4 wave functions, which transformation properties are following the symmetry of a spinor. (fact 2): The Dirac tensor for electron quantum field describes all states of the electron. A possibility to have either a negative or positive charge and a possibility to have either spinup or spindown spin direction. ( C symmetry): The symmetry of reversal sign of the chargeThe plus and minus charge are fully equivalent. There is nothing, which makes the plus charge better than the minus charge or vice versa. As a result, the spinor of electron quantum field should describe equally the particle of the minus charge (the electron) and the particle of the plus charge (the positron). ( T symmetry): The time inverse symmetry, which is described by the spin.The breaking of the timeinverse symmetry means that for any state (e.g. spinup state), there is a state (the spindown state), which is the time inverse transform from the original state. It means that if the time flow is inverse, the spinup state becomes spindown state and the spindown state becomes the spinup states. Additionally, the breaking the timeinverse symmetry causes some new properties of particle such as the magnetic moment and the angular moment.
The electron can never be transformed to the positron. Why does the Dirac spinor describe both the positron and electron wave functions?A1. (general description of all symmetries of quantum field) An actual particle (e.g. an electron) is described by a scalar wavefunction. In contrast, the Dirac spinor describes all possible states of the electron Quantum A2. (possibility of the annihilation of the electron and positron. Restoring of the Csymmetry) For each the electron and the positron, the C  symmetry is broken. However, the symmetry breaking is opposite. The charge of the electron is negative, but the charge of the positron is positive. When the electron and positron collide to each other, the breaking of the Csymmetry disappears and a result of the colliding is a chargefree photon. A3. (relativistic decrease of the charge, when the particle speed becomes close to the light speed) An In fact, a moving electron has a small component of the positron wave function. The positron component becomes larger and the charge of the electron becomes smaller, when the electron speed becomes close to the light speed. A particle, which moves at the light speed, cannot have a charge, because the charge is originated from breaking the gauge transformation symmetry (See above) and such symmetry breaking is not possible at the light speed. The time flows in one direction from the past to the future. There is no time flow from the future to the past. Since time inverse can never occur, why the time inverse wave function is included into the Dirac spinor?A1. It only means that a specific symmetry for a particle is broken.
Quantum Mechanic and Magic in Physics
Physics has no magic Maybe the desire to create a magic lies deep in the human nature. Anything what humans were not able to explain, is considered to be the magical until a scientist logically explains it and all magic vanishes.
Everything in Quantum Mechanic can be explained with logic and reasons. All magic in Quantum Mechanic is originated from poor knowledge, tricks and lies. There is nothing in Quantum Mechanic which could not be explained logically and based on the Laws of the Symmetries and the Conservation Laws of the Physics.
Magical (Incorrect) explanation of the nature of the SpinFollowing incorrect explanation of the results of the Stern–Gerlach experiment (See below), the magical nature of the Spin was accepted for a long time. Even though the magical nature of the spin contradicts with several Laws of Physics and Quantum Mechanics
(magical nature of the Spin) The direction of the electron spin is not fixed, but depends on the measurement geometry. When the direction is fixed (e.g. the vertical direction), it fixed the possible spin direction and the spin can have either spinup or spindown directions along the fixed measurement direction
Contradictions of the magical nature of the spin with several well known well verified Laws of Physics and Quantum Mechanics(contradiction with spin conservation law): The claim, that the spin direction is not fixed, but determined by the measurement geometry, directly contradicts with the wellverified spin conservation law. Any the conservation law in Physics corresponds to some symmetry of the space time of our Universe (See below). The spin conservation law corresponds to the time inverse symmetry of our Universe. This symmetry is a similar to the symmetry of continuos time flow, which means that all Physics laws will be same tomorrow as they are today. Therefore, the violation of the spinconservation law as incorrect as the violation of the energy conservation law! (contradiction with Dirac equations): The claim, that the spin direction is not fixed, but determined by the measurement geometry, directly contradicts with the Dirac equations, which only have a physical meaning when both the electron charge and the electron spin are fixed. The solution of the 4 Dirac equations is a 4rank spinor. However, a particle (an electron) is described by a scalar wave function. The 2 x functions describe a particle with opposite charge and 2x functions of the opposite spin. In order for spinor to become a scalar wavefunction both the electron charge and the electron spin should be firmly fixed. As a result, any realistic particle (an electron or a positron) has the fixed charge e or +e and the fixed spin (the fixed spin direction) (contradiction with fact of a single direction of the time flow): The time flows in one direction in our Universe from the past to the future. The claim, that the spin direction is not fixed, but determined by the measurement geometry, directly means that the flow of time is not fixed. The spin describes the breaking of time inverse symmetry. The breaking of timeinverse symmetry is described by a 2rank spinor, which contains two wavefunction. The first wavefunction describes the actual wavefunction of the electron. The second function describes the wave function of electron, which would be if the direction of the time flow were reversed. The claim, that the spin direction is not fixed, but determined by the measurement geometry, directly means that the direction of the time flow is not fixed, but is determined by the measurement geometry. It is clear that it is a nonsense. (contradiction with experimentally observed spinrelated effects): The
Why so many people, including some science, does not accept the fundamental conservation Laws like the energy conservation law and the spin conservation law? The people need a magic. The straightforward facts and laws of Physics are bored. For the magic people are willing to pay. Stern–Gerlach experiment. Magic, which lived over a hundred years.wiki page about Stern–Gerlach experiment is hereSee classical explanation below in Dr. Matt O`Dowt video time: 5:10(idea of experiment): Electrons of different spin polarization, which are emit by an electron gun, pass through a spatially varying magnetic field and are at a detection screen. In a spatial gradient of a magnetic field, an electron experience a mechanical force (See above), which pushes the electron to move along the gradient in order to minimize its magnetic energy. (result of experiment): The electrons are detected at two spots (the left and the right spot). When the gradient of the magnetic field is rotated 90 deg, the two spots are also rotated 90 deg.
(why the measured result is a problem? Why the magic needs to be introduced?): At the muzzle of the electron gun, the electron are not spin polarized and may have any spin direction. The mechanical force, which an electron experience, is proportional to the spin direction with respect to the gradient. Since spin direction of each electron is different, each electron should experience a different force and therefore be detected and different spots of screen. The suggested problem is that the electrons are detected at two spots instead of a continuous distribution (Magical explanation of Stern–Gerlach experiment): As a quantum mechanical parameter, the direction of the electron spin cannot be defined exactly, but defined by a measurement. When measurement is from the right to the left ( the magnetic field increases from the right side to the left side ), the direction of electron spin can be only to the left or to the right. There are no up or forward or up/left directions. When the measurement direction is changed, the spin directions at the gun muzzle are magically change. For example, when measurement is from the down to the up ( the magnetic field increases from the bottom side to the top side), the direction of electron spin can be only to the up or to the down. There are no left or right or forward or up/left directions. (NonMagical explanation of Stern–Gerlach experiment ): There is an additional effect, which the electron spin is experiences and which is ignored in the magical explanation. (additional ignored effect): The electron spin is aligned along the magnetic field.
(problems of magical explanation) The magical explanation severely violates several very fundamental and wellverified laws of the Physics: (problem 1) Spin conservation law The conservation of the spin, which corresponds to the conservation of the time inverse symmetry. The spin conservation law is similar and as strong as the energy conservation law. (note): Each conservation law (e.g. the energy conservation law, the momentum conservation law) is originated from a specific symmetry of our Universe (See below). The energy conservation law is originated from the symmetry of continuos time flow. It means that all Physics laws will be same tomorrow as they are today. The spin conservation law is originated from the time inverse symmetry. It means that all Physics laws will be same if the flow direction of the time is reversed. Therefore, the Energy and Spin conservation Laws are very similar and have very similar origins.(incorrect claim of Stern–Gerlach experiment): The direction of the electron spins is determined by a measuring device. It means that the electron spin is not conserved and can change the direction influenced by a different measurement device. It is a fully incorrect claim, which severely violate the fundamental spin conservation law. (problem 2) Dirac equations The solution of the Dirac equations is a 4rank spinor. However, a particle (an electron) is described by a scalar wave function. The 2 x functions describe a particle with opposite charge and 2x functions of the opposite spin. In order for spinor to become a wavefunction both the electron charge and the electron spin should be firmly fixed. As a result, any realistic particle (an electron or a positron) has the fixed charge e or +e and the fixed spin (the fixed spin direction) The statement, that the electron spin is not fixed, but defined by a measurement, is fully equivalent to the statement, that the charge of the electron is not fixed, but defined by a measurement.
(problem 3) Precise definition of the direction of the time flow in our Universe. The requirement that the spin direction is precisely fixed also means that the direction of the time flow in our Universe is fixed. At any moment of time, the electron has a possibility to have one two wave functions. The first wavefunction corresponds to the forward time flow. The second wavefunction corresponds to the reversed time flow. From these two possible wave functions, the electron always has the first one, because the direction of the time flow is firmly fixed. The direction of the time flow is only in the forward direction. Assumption, that the spin direction is undefined, directly means the direction of the time flow is not defined.
Classical explanation of the Spin by Dr. Matt O`Dowt Video
Mechanical forces & Mechanical torque due to the Spin & Magnetic field(fact) There are more magnetic field induced mechanical forces acting on assembly of electrons with a non zero spin spins than on a single electron
Mechanical force, act on a single electron,(only force) gradient of magnetic field
Mechanical force/torque, act on an assembly of electrons,(force 1, strongest) gradient of magnetic field (force 2, moderate) artificial magnetic charge. Compass torque. (force 3) Einstein–de Haas torque
vs Q. Why mechanical force & torque are acting differently on a single electron and on an assembly of electrons?As an elementary particle, the electron does not have parts. For this reason, it cannot have the north part , for example, at the left part and the south part at the right side. Both the south and north are distributed homogeneously and equally all over whole volume of the electron. Additionally, a single electron cannot experience different forces at its different parts. The electron experience the same mechanical force for its all parts. For example, the left part of electron cannot experience a different mechanical force than its left part. Since the electron does not have the parts, the left and right parts always experiences the same force. In contrast, an assemble of electrons can experience different forces at different parts. For example, the electrons at the left part may experience the larger mechanical force than the electron at the right part. Origin of the mechanical forceAn object is forced to accelerate in space when object energy is dependent on its spacial position. For example, the object is forced to accelerated towards the left or, similarly, experiences a mechanical force towards the left, when the object energy is smaller when it is shifted to the left.
(Mechanical force 1 (strongest)):Due to a gradient of magnetic field
According to the Laws of Mechanics, a force acts on an object in the direction, in which the total energy of the is minimized. The electron energy in a magnetic field is S*H/2. In a gradient of magnetic field, a force acts on an electron. The direction of this force depends on the electron spin. When spin is parallel to the magnetic field, the force acts so that electron moves in the direction from a smaller to a larger magnetic field. When spin is antiparallel to the magnetic field, the force acts so that electron moves in the direction from a larger to smaller magnetic field.
(note) This force causes the repelling or attraction between two permanent magnets, which we may experience in everyday life.
Why and at which condition does a particle experience a mechanical force?A particle experiences a mechanical force, when the particle energy depends on the particle special position. The particle is mechanically forced into the position where its total energy is smaller. Why particle is forced to the position of a lower energy?interpretation of the mechanical force: (interpretation 1): classic quantum electrodynamics. Gaining a momentum In a gradient of electrical field (e.g. from the left to right) , the number of virtual photons, which are absorbed from the left and from the right side, are different. Since each photon transforms a mechanical moment to the particle, the mechanical moment of the particle is changes and the particle is forced to accelerate. (interpretation 2): quantum vibrations. Gaining energy. Due to interaction with virtual particles, the elementary particle position is randomly changed in time. The change is extremely tiny and it is called the quantum oscillations. In the absence of the gradient of the field, the distribution of the virtual particle and, therefore, the quantum vibrations are fully symmetrical. as a result, the particle average position remains a constant. However, in the case when at one spacial point the particle energy is smaller and at another special point the energy is larger, the quantum vibrations became asymmetrical and the particle is forced to accelerate towards the larger quantum vibration. A virtual particle of a fixed energy makes a quantum oscillation larger into region of a lower energy and a shorter in region of a higher energy. It is because the movement into the the region of the higher energy requires a virtual particle of a higher energy, which live time of the virtual particle is shorter and, therefore, the movement distance of the elementary particle shorter. This is the reason why the particle is forced to accelerate towards the region of the lower energy.
(Levitation):When an object with a magnetic moment is placed in a local maximum of magnetic field, the object is forced to stay there. In the case when the object moves out of the levitation point towards a region of a smaller magnetic field, its magnetic energy decrease. As a result, there is a mechanical force which moves the object back to the levitation point.
(Mechanical force 2 (moderate) ): Due to an artificial magnetic charge. The mechanical force of compass pointer.(fact) An elementary particle cannot have a magnetic charge. An elementary particle only can have an electrical charge and/or a magnetic moment.
(reason) why an elementary particle cannot have a magnetic charge Any property of an elementary particle corresponds to a breaking of a very specific symmetry of the timespace of our universe. The electrical charge corresponds to the breaking of the gauge symmetry, the spin corresponds to the breaking of the timeinverse symmetry and the magnetic moment corresponds to the breaking of the breaking of both the timeinverse symmetry and the gauge symmetry (See here) There is no symmetry, the breaking of which, could create the magnetic charge.
(fact) A single elementary particle cannot create an artificial magnetic charge. (fact) An assembly of elementary particles with spin can create an artificial magnetic charge at a boundary of the assembly.
How to distinguish an existence of a magnetic charge?If an assembly of particle has a magnetic charge inside, it will experience a mechanical force in a homogeneous magnetic field (a constant magnetic field). If an assembly of particle does not have a magnetic charge inside, there is any mechanical force on the assembly when it is in a homogeneous magnetic field .
Magnetic charge is also called a pole. The two opposite magnetic charges are called the "North pole" and "South pole". rges. (fact) (rotation torque vs. linear force) Conventional understanding is that the compass arrow experiences a mechanical torque in a magnetic field. However, the compass arrow can experience a linear force in one direction. For example, if the external magnetic field chance its direction at positions of "N" and "S" magnetic charges.
Artificial magnetic charge: (origin)The artificial magnetic charge or the magnetic pole is originated in an assemble of electrons with aligned spins, when the electron magnetic moment is only partiality compensated by magnetic moments of its neighbor electrons. The magnetic moment is not fully compensated at edge of the sample along direction of aligned magnetic moments. Each localized electron has a magnetic moment, but it does not have a magnetic charge. Each "S" pole is in contact with "N" pole of a neighbor electron and, therefore, the "S" pole is compensated, the "N" pole is not compensated by this electron. Similarity, if there is an electron at other side, each "N" pole is compensated by "S" pole of the neighbor electron at other side. At the edges of the bulk nanomagnet, there is no compensation. As a result, the artificial magnetic charge (a magnetic pole) is formed at the edges.
How large the artificial magnetic charge?
Does artificial magnetic charge exists in an antiferromagnetic material?
Compass arrow and artificial magnetic charge:A bar of ferromagnetic material, which is fixed on a rotation axis and can be rotated around this axis under an external force, aligned itself along an external magnetic filed (e.g. Earth magnetic field). The ferromagnetic bar experiences the mechanical torque due to the magnetic charges (magnetic poles) on sides of the bar. The mechanical force acts on the magnetic charges from the external magnetic field causing the mechanical torque. In contrast to a single electron, the compass arrow experience a magnetic force in a homogenous (constant) magnetic field. (fact ) (difference between magnetic moments of an electron and compass error) The electron does not have any magnetic charge or magnetic poles. The electron only has a magnetic moment. In contrast, the compass arrow has two opposite magnetic charges (poles) on its sides, which are separated by a substantial distance. Such configuration of opposite magnetic charges makes a magnetic moment. Therefore, the primary property of the compass arrow is the magnetic charge. The magnetic moment is the result of specific configuration of the magnetic cha
(Mechanical force 3 (weakest) ): Due to Einstein–de Haas effect.wiki page is hereSee classical explanation below in Dr. Matt O`Dowt video time: 0:24This torque occurs due to a change of the rotational moment of an object, when the total spin of the object is change. (case 1) changing of domain structure A relatively large ferromagnetic object (sizes > domain size) has a multi domain structure and its total spin is close to zero. In an external magnetic field, the magnetic domains are realign in one direction and the total spin of the object becomes a substantial. The rotation moment related to the spin become larger,, but the total orbital momentum of the object should not change due to the domain rearrangement. As a result, the whole bulk object gains
What is the magnetic field?3 origins of the magnetic field.
(Origin 1 of magnetic field ) Relativistic component of the electromagnetic field(source of magnetic field): electrical charge
Electromagnetic field has two components; electrical field and magnetic field, which relativistically transformed to each other. The magnitudes of the observed components of the electric and magnetic fields dependent on the speed of an observer. E.g. if in the first coordinate system an observer experiences only an electrical field, but no magnetic field, in coordinate system, which is moving with respect to the first coordinate system, the observer experiences both the electrical and magnetic fields. The transformations between field are described by the the Lorentz transformation rules as where E_{static}, H_{static}_{} are the electric and magnetic field in the static coordinate system (reference frame) and E_{move}, H_{move}_{} are the electric and magnetic field in the coordinate system, which moves with a constant speed v. This magnetic field is originated from the nature of the electromagnetic field itself. There are two effects due to this source of the magnetic field (effect 1): Ampère's law The Ampère's law describes the fact that an electron current creates a magnetic field.
The charge of the electron creates an electrical field. There is no magnetic field component of this field only coordinate system, which the electron does not move. When the electron move, the electrical field, which has only the electricalfield component in the coordinate system moving together with the electron, has both the electricalfield and magneticfield components in a static coordinate system. (effect 2): Spinorbit interaction The spinorbit interaction describes the fact that an electron, which moves perpendicularly to an electrical field, experience a magnetic field and the electron spin is aligned along that magnetic field. See here more details about the spinorbit interaction.Even though there is only an electrical field there is no a magnetic field in a static coordinate system, there is a magnetic field in a coordinate system moving together with the electron and this magnetic field interacts with the electron spin. Dependence on electron movement speedMagnetic field of source 1 increases, when the electron moves faster
(Origin 2 of magnetic field ) magnetic moment due to the spin of electron(source of magnetic field ): electrical charge+ broken timeinverse symmetry +
Due to its spin and its charge, the electron has a magnetic moment, which generates a magnetic field An elementary particle, which has a nonzero spin and nonzero charge, has a nonzero magnetic moment, which induces a magnetic field around the electron. (note) The electron has a spin, because its timeinverse symmetry is broken. The electron has a charge, because its gauge symmetry is broken. Simultaneous breaking the timeinverse symmetry and the gauge symmetry creates a magnetic moment for an elementary particle (See here for more details)
(Zero spin + nonzero charge) spininactive electron no magnetic moment For example, the electron of filled orbitals are charged, but their spin is compensated, has no magnetic moment. Formally the timeinverse symmetry is not broken for these electrons and therefore they have no spin. (Nonzero spin + zero charge) circular polarized photon no magnetic moment For example, the spin of a circular polarized photon is 1, but the the photon has no charge. As a result, the photon has no magnetic moment and does not produce any permanent magnetic field. Of course, the electromagnetic field of a photon has a magnetic component. Dependence on electron movement speedMagnetic field of source 2 decreases, when the electron moves faster It is because the electron electron charge decreases with a faster speed. Since the magnetic moment is proportional to the electron charge, the magnetic moment decreases as well. A particle, which moves at speed of light, can not be charged and therefore cannot have a magnetic moment. It is a feature of the gauge symmetry.
(Origin 3 of magnetic field ): spin dependent Coulomb interaction (exchange interaction)(source of magnetic field ): broken timeinverse symmetry
The Coulomb interaction between electrons depends on their mutual direction of their spins. It makes the electron energy dependent on its spin direction. There is a spin direction, at which the electron energy is smallest and which is the equilibrium spin direction. There is a spin precession for any any different spin direction and spin damping align the electron spin along its equilibrium direction. All these features are exactly the same of the case of the magnetic field of origins 1 and 2. Therefore, the exchange field can be assigned as a magnetic field of origin 3. (note) Even though the exchange field is completely different from the relativistic magnetic component of the electromagnetic field, which is usually associated with a magnetic field, in a solid its feature are nearly indistinguishable from features of the conventional magnetic field. It is convenient to handle the exchange field in a solid as a magnetic field. For example, the features and properties of antiferromagnetic resonance, which is created by the exchange field, are very similar to that of the ferromagnetic resonance (FMR), which is created by the conventional magnetic field.
(effect ): Exchange interaction The exchange interaction describes the spindependent Coulomb interaction between electrons. The Coulomb repulsion between two electrons is smaller, when their spins are opposite, and is larger, when their spins are parallel. When two electrons of opposite spins approach each other, the breaking of time inverse symmetry slowly disappears and system of two elementary particles transforms into a system of one particle. As a result, their mutual repulsion decreases and their interaction with surrounding electrons and nuclears is changed
The timeinverse symmetry is not broken for an electron state, which occupied by two electrons of opposite spins. It literally means that such state does not have any spin at all. It also means that the state should be considered as one particle without spin with charge 2e instead of two electrons with opposite spins and charge e and e. When two electrons of opposite spins approach each other, they are monotonically transformed from the system of elementary particles into a system of only one elementary particle. As a result, the Coulomb repulsion between these two electrons monotonically decreases and the Coulomb interaction between each and surrounding electrons and nuclears is changed.
Dependence on electron movement speedMagnetic field of source 3 is independent of the electron movement speed. The exchange interaction only depends on the distance between electrons and their spin direction.
3 types of the magnetic field: (1) conventional magnetic field; (2) Spinorbit magnetic field; (3) magnetic field of the exchange interaction.
(part 5) Inflation, breaking symmetry, origin of an elementary particle & SpinContentclick on the chapter for the shortcut() Why is understanding of the Inflation important for understanding of the spin?() A few facts aboaut the Inflation() How to create a particle from the vacuum() Size of an elementary particle() Standard model and "post Standard model"() Symmetry & Conservation Laws() Transformation of two elementary particles into one particle. Exchange interaction.
The The Inflation is an event, which occurred just before the Big Bang and during which there was a selfsustained breaking of the symmetry of the Universe. As a result, all matter of the Universe was created during the Inflation event. Before the Inflation the Universe was fully symmetrical and contained no matter at all. After the Inflation created all matter and diversity (broken symmetries) in our Universe. The Big Bang event shaped the Universe into the present form.
Why should one care about a cosmic event like the Inflation in order to understand the spin? Why is understanding of the Inflation important for understanding of the spin?The spin describes the brokentime inverse symmetry. The Inflation is a big event of the breaking of all possible symmetries of the Universe. Some properties of the spin can be evaluated from general properties of the broken symmetry, which are magnified during the Inflation and, therefore, can be easily understood.
There are several such examples: (example 1: Spin conservation law) In the case when the symmetry of the vacuum (the Emptiness) is broken (something is created from nothing), the total sum of the created quantities should be zero: particle + antiparticle =0; negative charge (e electron) + positive charge (+e positron) = 0; negative energy (gravitational energy) + negative energy (kinetic energy) =0; spinup + spindown =0;
(example 2: spinactive and spininactive states) If a symmetry can be broken, it can be unbroken. (broken/unbroken symmetry of the charge:) Annihilation of a negativelycharged electron and a positivelycharged positron results in particles without any electrical charge. Therefore, two opposite charges (two opposite breaking of a symmetry), when interact, fully disappears
(broken/unbroken symmetry of spin:) Each quantum electron state can be occupied either by none or one or two electrons of opposite spin. The time inverse symmetry is broken, when a quantum state is occupied by one electron. Such a state is spin active. The time inverse symmetry is not broken, when a quantum state is occupied by two electrons. Such a state is spin inactive.
As a symmetry can be broken and next unbroken. The spin and the spin properties can appear and disappear for an electron. For example, deepenergy electrons in an atom do not have any spin properties.The spininactive states are important for the "hole" transport (See here), important for the spin distribution (See here) and important for a spin transport (e.g. the Hall transport).
The inflation  the mechanism of the creation of all matter in the Universe.The inflation explains how all matter was created in our Universe.
The model of the inflation was introduced in70th80th as the model of the launching mechanism of the Big Bang. At beginning, the accelerating expansion of the Universe at earliest time of our Universe was called the inflation. Now there are several proofs that the sum of all energies of the Universe (the positive energy of all matter and the negative energy of gravitational attractions between all matter) equals to exact zero. It proves that all matter in Universe was created from vacuum (from nothing) during inflation time.
How the fact of inflation influences the Law of Physics?1. It explains many facts, which were experimentally found before and which postulated the Quantum Mechanics and the Standard Model.2. It slightly modifies all laws of Physics to comply to the important fact that all particles should be generated from vacuum and they be able to annihilate into vacuum.
The Facts of Physics, which are consequence of the Inflation origin of our Universe:(1) All elementary particles in the Universe are waves. There are no pointlike particlesproof: Any existed particle should be created from vacuum. The mechanism how to create a wavelike particle is clear (See Fig.10). There is no any known mechanism, which could create a pointlike particle from vacuum. (2) An elementary particle does not have a fixed size. The size of the elementary particle is determined by its environmentproof:Since any elementary particle is a wave, the size of the wave is the size of the wave package. The size of the elementary particle is determined by the process how the elementary particle is created from vacuum (See Fig. 4). It is the basic principle, which is postulated by the Quantum Mechanics.(3) All forces of the nature (except the gravitation force) are originated from the processes of creation of particles from the vacuum and processes of annihilation of particles into vacuumproof:When two particles are relatively far from each other and their wave functions are not overcrossed, only possible way of their interaction is by generating and annihilating of other particles. For example, the electrical interaction between two electrons is mediated by a photon. (4) An elementary particle does not have parts. An elementary particle does not interact with itself.proof: (5) Elementary particles do not transform into each other abruptly. The process of transforming from particle to particle is continuous.proof:Since any (6) Any interaction between particles (except gravitational interaction) significantly changes when the distance between particles becomes smaller than their size. Any interaction between two particles are finite, even if distance between two particles approaches to zero.proof:The classical physics states that any interaction between particles (gravitational or electromagnetic interaction) is infinite, when distance between two particles is zero. Since all particles are cracked from vacuum, initially before cracking two particles of opposite phase should be at exactly the same location (therefore, they form the vacuum). However, in the case if the interaction between these two particles (including gravitational interaction and the electromagnetic interaction) is infinite, the particle cold not ever be moved away from each other and any particle could not be created.
fact 1: All elementary particles in the Universe are waves. There are no pointlike particlesproof: Any existed particle should be created from vacuum. The mechanism how to create a wavelike particle is clear (See Fig.10). There is no any known mechanism, which could create a pointlike particle from vacuum. How to create a particle from vacuum?The sum of two waves, which are exactly the same but have phase difference of 180 degrees, is the zero or nothing or vacuum (See Fig.10 left). When the waves stay at an exactly the same point, they form the vacuum or nothing. In this case two waves are not yet particle, but they are a "virtual possibility for creation of particles". If there is a force, which interacts differently with the wave of opposite phase, two waves move in different locations and from virtual they become real particles . Two waves of opposite phase are very similar. How it is possible that they interact differently with the field?For example, two particles of opposite phase may have different charge. Than, in an electrical field they move in opposite directions. if in a electrical field, the particle are so easily created, why do not we observe the creation of a huge number of particles in an electrical field?From a view of a classic physics, the attraction between two particles of opposite charge are infinite, when the particles are located at the same point. It requires an infinite electrical field in order to move the particles away from each other. The case of real quantum world is different. Still the process of the creation of a particle from a vacuum is very subtle process, which requires existence of additional one, two or more particles at the same location.
Cases of creation of particles from vacuum: case 1. The electromagnetic interactionin this case a charged particle breaks a photon from vacuum. The photon reaches the second charge particle and annihilate itself (it is converted back into vacuum) at the location of the second charged particle. As result, two charged particles repel or attract each other. case 2. The strong interactionin this case a quark breaks a gluon from vacuum. The gluon reaches the second quark and annihilate itself (it is converted back into vacuum) at its location. As result, two quarks attract each other. case 3. The weak interactionin this case three quarks (u,d,d) breaks a W boson from vacuum. Next, the W boson breaks an electron, a neutrino and a quark from the vacuum. As result, a neutron (u,d,d) beta decays into a proton (u,u,d), an electron and a neutrino. case 4. The dark energyIt is the energy of the vacuum, which fills up all Universe. The dark energy is only a substance in the Universe, which was not created during the inflation. The origin of the dark energy is the shortleave particles, which are broken from the vacuum. There is a very small, but a finite probability that particles are broken from the vacuum. However, if there is no other particle in their proximity, these two particles quickly annihilate back into vacuum. The gravitation of these shortlive particles has a substantial influence on our Universe. Even though the probability of such particles from is very small and life time of these particles is very short, in cosmological scale their gravitation is strong and it causes the accelerating expansion of our Universe. It is because these shortlived particles are created at all points of space. case 5. The inflationIt is a selfsustained process of constant breaking of particles from vacuum. During the inflation, the particles, which are just created, make the conditions for the breaking additional particles from vacuum. These particles make another particles and so on. During inflation the number of particles increases exponentially. All substance of our Universe, except the dark energy, were created during the Inflation. The conditions to keep selfsustained breaking of vacuum is extremely subtle. The accelerating expansion of the Universe and an extremely high density of particles are the key conditions to keep selfsustained breaking of vacuum. Only about 100200 consequence breaking of particles by new created particles occurred during the Inflation. It was sufficient to create all matter in our Universe.
The conditions, at which particles can broken from vacuum, are very subtle. First of all, all Conservation Laws should be satisfied!!!Q. The vacuum energy is zero. When two particles are broken from vacuum, each particle has the energy mc² . How the energy is conserved during this process?A. The particles have a positive energy, which the sum of the kinetic energy and mc². The attraction energy between particles is negative energy. The energy of the gravitational attraction is always negative. If charge of particles is opposite, the energy of the Coulomb attraction is also negative. It is very important that during breaking the particles from vacuum the total energy is always zero. As it has been proved already the sum of all energies in our Universe exactly equals to zero. That means that during all existence of our Universe and after unimaginable number of breaking of particles from vacuum the Conservation of the energy has never been compromised. Of course, in the case when another particle participating in breaking of particles from vacuum, its energy can be transferred into the energy of new particles.
fact An elementary particle does not have a fixed size. The size of the elementary particle is determined by its environmentproof:Since any elementary particle is a wave, the size of the wave is the size of the wave package. proof: An elementary particle is a wave package, which length is the distance between two consequence scatterings of the particle or the distance between two events of the interaction of the particle with other particles. For example, the electrons is (1) 110 μm in a highcrystal quality semiconductor. (2) 10100 nm in a metal (3) 0.1 nm in an atom Length of a photon It is called the photon coherence length. It is important characteristic of any light source. Simply it could be understood as an average length of wave packages in an optical beam. In my optical experiments I use light sources of different coherence length. I use Santec tunable laser at lambda=1550 nm. Its light has the coherence length longer than 1 meter. I have a tunable Ti:sapphire laser. When I bought it it has a very short coherence length less than one millimeter. I have installed additional option in order to increase the coherence length. Now the the coherence length of light from this laser is a few centimeters. The coherence length of light from a light bulb is about 0.1 millimeter.
Length of an electron The electron is a wave. Its length is not fixed, but it is determined by the electron environment. In a conductor, the the effective length of a conduction electron equals to its meanfree path λ_{mean} or a distance between two subsequent electron scatterings. It is between 10 nm and 1000 nm in a semiconductor and between 1 nm and 10 nm in a metal.
The size of a localized electron equals to the size of atom (~0.1 nm).
The size of elementary particle and forces of the nature
Important point: The forces between particles depend on the size of particlesThe classical physics and the standard model postulate that all forces between particles (the gravitational force, the electromagnetic force, the strong force and the weak force) depends on the distance between particles and some parameter of the particle (the mass, the electrical and color charge). An elementary particle does not have parts, it attracts or repel other particle as a whole. There are no parts of the particle, which could interact with other particle individually. The interaction between particles (except gravitational interaction) is always mediated by a creation and annihilation of another particle from the vacuum. (1) electromagnetic interaction is mediated by
Standard model and "post Standard model"The Standard Model of particle physicsThe Standard Model assumes that our Universe consists of a finite set of a particles. All possible processes and events in our Universe are only interactions between those particles. Each particle has very fixed number of properties like the energy, spin, charge, rest mass, color charge etc.. These properties of an elementary particle are firmly fixed and are the internal features of each particle. The interactions between these particles describes all processes in our Universe. The elementary particle may be transformed between each other when they crash into each other at a high energy. In this case one elementary particle disappears into nowhere and another particle appears from nowhere. There is only one limitation for this process: The Conservation Laws. As soon as all required conservation Laws are hold, the transformation between elementary particles occurs.
The "post Standard" ModelThe "postStandard" Model assumes that our University has a set of different symmetries. One of symmetries or several symmetries can broken locally. The breaking of symmetry is hard and the symmetry is trying to return to its unbroken state. However, some rare cases exists when several symmetries can be broken simultaneously and this set of the broken symmetries is locally stable. This standalone set of broken symmetries is called an elementary particle. The conditions, at which a set of broken symmetries are locally stable, is subtle and can be possible at very specific parameters or at very specific degree (amount) of breaking of a specific symmetry. This is why each elementary particle has specific parameter (rest mass, spin etc.)
Symmetry & Conservation Laws
Each Conservation Law of Physics always corresponds to one of the continues symmetry of our UniverseThis rule was discovered by Emma Noether. This discovery is one of greatest discoveries in Physics. Along the Quantum Mechanics and the Theory of relativity, it made a largest impact on our modern understanding of our Universe.See Noether's Theorem hereExamples: The time transfer symmetry The energy conservation law The time transfer symmetry The momentum conservation law The timeinverse symmetry The spin conservation law The phase symmetry of electron wavefunctionThe electricalcharge conservation law
How two elemental particles (two electrons) are transformed into one elementary particle?Origin of exchange interaction. Spininactive electrons.
(about spininactive electrons) Two electrons of an opposite spin, which occupy one quantum state, are one particle or two particles?A. It is one particle. At least, its properties are closer to that of one elementary particle than to that of two elementary particles. Two electrons do not repel each other, do not interact with each other and cannot be distinguished as two separated subjects (wave function symmetry, orbital moment etc.) . Such a state fully loses all single electron property. For example, Two electrons of opposite spin, which occupy one quantum state, do not have any exchange interaction with any other electrons. (virtual electrons) Such a state can be considered as a sum of two separate subjects only virtually. When such a state interacts with a photon or other external particle only one of two electrons is transformed to another energy level or to another quantum state. The spin direction of the transformed electrons is either random or is defined by the external particle. The spin of the remaining electron is opposite to the spin of the transformed electron. Only from this virtual point of view, this state can be considered as two electrons. (fact) Two electrons of an opposite spin, which occupy one quantum state, should be considered as one elemental particle. These electrons lose their spin properties and are called the spininactive electrons.  How is it possible that two elementary particles are transformed into one elementary particle and vice versa?A.Since all known elementary particles are waves, it is very common that during an interaction between them, the number of particles changes. For example, the result of interaction of an electron and a positron is only a photon. All matter in the universe was created literally from nothing 13.8 billion years ago during the inflation period. Creation or annihilation of particles waves is very common process. How two particles (waves) can be created from nothing could be understood as follows: When there are two absolutely identical waves, but phase shifted 180 degrees relatively each other, their sum gives zero or nothing. Therefore, two particles (for example, an electron and a positron) can combine that result will be nothing. Similarly, if some force changes the phase shift between particles from 180 degrees to any other, from nothing two particles can be created.
Mathematically the process when two electrons of opposite spins combine and create one elementary particle without spin ("full" state) can be understood as follows. Two electrons with opposite spins, which occupy different states, are described by two spinors They are described by different sets of coordinates (x1,y1,z1) and (x2,y2,z2). It means they are two elementary particles, which interact with other. When these two electrons of opposite spins occupy one state, they are described by a scalar wave function, which is product of spinors (1.1) and (1.2) It is important that the scalar wave function (1.3) is described by one set of coordinate. It means (1.3) describes one elementary particle. More about spin basic properties see here  (about exchange interaction) How is it possible that two elementary particles are transformed into one elementary particle and vice versa?A. Continuous. When the distance between two electrons of an opposite spin decreases, the Coulomb repelling force between them decreases and becomes zero when they occupy exactly one spot. It looks like two electrons continuously transformed into one particle as the distance between electrons decreases. In Quantum Mechanics, this process is described by using a symmetrical and asymmetrical wavefunction (See here for details). Such a reduction of the Coulomb repulsion only occurs only when the spins of two electrons are opposite. Otherwise, the Coulomb repulsion regains its full strength. As a result, the Coulomb repulsion between two electrons is spin dependent. The spin dependency of the Coulomb interaction is called the exchange interaction. It is a very interesting and complex effect. (For details see here)
Questions & AnswersDoes a spinmixed state exist? Is the spinmixed state just a simple sum of spinup and spindown electrons? Can you comment on properties of a spinmixed state?No. The spinmixed state can not exist in reality. The spinmixed state is a trick used sometimes in some theoretical approximations. The spin describes a breaking of the time inverse symmetry. The time inverse symmetry cannot be broken partly. The time inverse symmetry is either broken or not. The time inverse symmetry is broken, when a quantum state is occupied by one electron. Such a state is spin active. The time inverse symmetry is not broken, when a quantum state is occupied by two electrons. Such a state is spin inactive. The spin can be either along (spinup) or opposite (spindown) to the direction of the broken time inverse symmetry. Only another possible and allowed state for the spin (or any subject of the broken timeinverse symmetry) is the spin precession state. The spin precession is a superposition of the spinup and spindown state, but it is not a spinmixed state. Besides, the spinprecession state is not a static state. During the spin precession a photon or a magnon is unavoidably emitted and the spin is aligned along the up direction. Also, either spinup or spindown can be decomposed into components ( e.g. into a sum of spinleft and spinright components). Such a sum of spinleft and spinright components is not a spinmixed state as well.
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