Top page (correct Bohr model including helium )

Strange "spin" is NOT a real thing

Kondo effects do NOT mean "spin".

BCS theory makes mistakes. (13/12/12)

- Why do top journals and researchers believe "fantasied" spin even now ?
- Reason why "spin" in condensed matter physics is wrong.
- BCS theory and Cooper pair are wrong.
- Spin-orbit coupling ( interaction ) is an illusion !
- True form of "Spin" and "orbital" is de Broglie wave.

*(Fig.1) Spinning speed of an electron is much faster than light !*

According to actual experiments, a single electrons is a very small **point**-like particle.

But quantum mechanics insists this **point**-like electron has **1/2 ħ** angular momentum.

As you know, the angular momentum means mv× r ( m= electron mass, v=rotation speed, r is electron radius ).

Considering electron's very **small** mass and radius, this rotating speed "v" must be **more than 100** times **light speed** to reach 1/2 ħ ! ( See also this page. )

This means quantum mechanical spin is **unrealistic** and just a **fantasy**.

*(Fig.2) Fermions CANNOT return by one 360-degree rotation !*

Strange to say, according to unrealistic quantum mechanics, all fermions such as electron, neutron, and proton **CANNOT** return to their original states by 360-degree rotation !

Because these particles has spin angular momentum 1/2ħ.

Of course, if this acgular momentum is an integer times ħ like Bohr's orbit, it **can** return by 360-degree rotation.

( This is a quite **natural** thing. )

Surprisingly, as shown in this page, this fantasied phenomenon was actually observed in experiments, they insist.

The important point is that these experiments assume that fermions have **1/2 ħ** as **precondition**.

If we change this **one-side** assumption, and suppose they have natural **ħ** angular momentum. these experiments only showed particles return by **360**-degree rotation.

So these experiments clearly showed spin angular momentum 1/2 ħ is **wrong** and **fantasy**.

*(Fig.3) Bohr's orbit (= Bohr magneton ) = electron spin (= Bohr magneton ) ?*

As shown in this page, the magnetic monent of Bohr's ground state orbit is **Bohr magneton**.

Surprinsingly, electron spin magnetic moment is **ALSO** this Bohr magneton !

( Though spin has **NOTHING** to do with Bohr's orbit. )

Because the ground state of quantum mechanical hydrogen has **NO** angular momentum, and instead has this spin.

The **experimental** value of this hydrogen magnetic moment is just **Bohr magneton** gotten from Bohr's orbit.

So they started to insist if electron "spin" also has Bohr magneton, it agrees with experimental results.

That's all.

*(Fig.4) If strange spin is wrong, almost all theories become dead.*

Though strange spin is very **unrealistic** and unreasonable, top journals and researchers **NEVER** give up this "spin", and **NEVER** ask what "spin" really is.

Because if this spin is **wrong**, and changed into usual classical circular orbit, all theories such as entanglement, standard model, superstring, spintronics, and Cooper pair would **collapse**.

So in fact, this methematical "spin" has the **greatest** influence in fictions existing in the present world !

Of course, considering these theories are all **unrealistic** and problematic, we have to **revise** all these concepts, and proceed to develop "**real**" science.

It's very easy. Just **stop** "Shut up and calculate !" about what spin really is.

*(Fig.5) Spin - spin interaction is illusion !*

In the present condensed matter physics, they often use the relation fo Fig.5 to describe ferromagnetism and diamagnetism.

In Fig.5, when the exchange interaction constant J is positive, parallel spins make energy negative and stable (= ferromagnetism ).

So they insist one spin **influences** other spins in ferromagnetism.

But if spin means "magnetic moment" (= Bohr magneton ), this ferromagnetism is **impossible.**

*(Fig.6) Spin - spin interaction is unrealistically weak.*

The lattice constant of iron is 2.84 Å.

In this distance, the energy difference between parallel and antiparallel spin interactions are **too small**, as shown in Fig.6.

Using Boltzmann constant k, this energy difference is equal to only **0.22** kelvin. ( See appendix. )

So if spin-spn interaction is caused by their magnetic moments, a magnet is easily **broken** in room temperature !

According to this book ( Story of Spin by S.tomonaga ), the energy difference between singlet and triplet spectrums **cannot** be explained only by spin-spin interaction.

Because this spin-spin interaction is too weak (= about 0.00005 eV of fine structure level, see also this page. )

So they just **change the name** of some **Coulomb** energy difference into spin-spin interaction !

( Officially, these energy differences are caused by "antisymmetry" or "symmetry" of wavefunctions. )

*(Fig.7) Real spin state ? Point particle ?*

In spintronics and condensed matter physics, they often use the relation of Fig.7.

So according to quantum mechanics, "real" spin angular momentum is **NOT** 1/2 ħ !

Strange to say, they insist **point**-like spin is **precessing**, and almost **leans** toward the direction **different** from magnetic field B.

This spin relation of Fig.7 is NOT gotten from Schrodinger's hydrogen, different from usual anglar momentum L.

And they **cannot** explain why this **angle of inclination** is always constant even in different magnetic fields.

The **origin** of this mysterious **inclination** remains a **riddle** even in 21th century now.

This is strange.

*(Fig.8) Proof of spin ?*

As shown in this page, complicated Lande g-factor is gotten mainly from anomalous Zeeman effect of **sodium**.

First, this Lande g-factor does **NOT** apply to simple hydrogen atom, because when Lande introduced this relation, they believe S means total magnetic moment of inner **core** electrons ( NOT spin ! ).

Furthermore, this Lande g-factor **doesn't** agree with experimental results
in important metals and ions such as Fe, Co, Ni, Fe2+, Co2+, Ni2+, Sm...

*(Fig.9) Angular momentum is zero ?*

To **fit** Lande g-factor to experimental results, they **artificially erase** angular momentum ( L=0 ) in **3d** electrons in Fe2+, Co2+, Ni2+.

They insist 3d electrons of these ions are freely flying around, NOT bound to nuclei, so their angular momentum become zero.

But this interpretation is strange, because 3d orbitals have **large** angular momentum, and they are **attracted** towards **2+** positive ions ( If we remove 3d electrons, Fe2+ becomes **Fe4+, Fe5+** .. Impossible ! )

These manipulations are clearly only to make the calculation results close to experimental results.

Furthermore, atoms such as Fe, Co, Ni, Pm, Sm .. are completely **inconsistent** with this Lande g-factor **even after** these manipulations.

So they started to introduce various **other** effects caused by other atoms. ( ex. **other** "artifical" spin-orbit interactions. )

The present spintronics is completely **dependent** on these various **artificial** manipulations.

*(Fig.10) We CANNOT directly see these orbitals !*

As shown in Fig.8 this Lande g-factor is completely **dependent** on combinations of various orbitals ( s, p, d, s ... )

The problem is whether these orbitals and electron's arrangements are **really** correct or not.

For example, in K and Ca atoms, electrons first enter **4s** orbitals.

And in other atoms after that, electrons can enter **3d** orbitals. **True** mechanism remains a riddle.

In Lanthanoids, orbitals are **5d-6s2** in La, **4f-5d-6s2** in Ce, **4f3-6s2** in Pr ..... ??

These orders are very **complicated** !

The important point is that we **cannot** see these orbitals in actual experiments.

Because, in coordinate bonds, these fictional orbitals become **mixed** into **other** things like sp2, sp3..

They can **artificially** define these orbitals to agree with various spectrum results.

*(Fig.11) Angular momentum zero (= s state ) → outer electron penetrates ??*

As I said many times, the "**s**" state with **zero** angular momentum ( L=0 ) is **impossible** in **real** atomic structures.

Because outer electron **cannot penetrate** inner electrons due to the strong **repulsive** Coulomb forces.

Instead of admitting this strange **zero** angular momentum, it is more natural that we think the outer electron is orbitting around the inner electrons. ( **NOT** penetrating them ! )

If we consider elliptic and circular orbits, we can explain the energy difference between 2s and 2p states, and on the other hand, Dirac's hydrogen includes **wrong** orbitals, as shown in this page.

*(Fig.12) 3d orbitals are very doubtful.*

As shown in Fig.12, the first ionization energies become slightly bigger as P → S → Cl → Ar.

And in Potassium (K), this ionization energy becomes **suddenly smaller** (= 4.3 eV ), which means different orbital starts from K.

Ionization energies are **smoothly** increased in 4s and 3d mixed orbitals. ( 4.3 → 6.1 → 6.5 → 6.8 .. )

Considering these ionization energies, it is natural that we think 4s and 3d are in the **same** "n" energy number.

So this definition of "3d" is very **unnatural**.

Actually, to get magnetic moments of V4+, V3+, V2+, Cr3+ ..., they **artificially** make angular momentum **zero** (= **ignoring** Lange g-factor ), though they **include** 3d orbitals.

These magnetic moments are about 2 (= V4+), 3 (= V3+ ), 4 (= Cr3+ ), 5 (= Cr2+ ) times **Bohr magneton**.

*(Fig.13) What causes ferromagnetism ?*

Even in unrealistic quantum mechanics, classical **Lorentz force** is very important.

As shown in Fig.13 left, when outer electrons are loosely bound to nuclei, their magnetic moments turn in the **same** direction as the external magnetic field (= B ).

The important point is that these materials showing ferromagnetism need to be **regularly arranged** crystals.

In most materials and molecules, magnetic moment of each electron ( orbit ) turns in **various** direction, which **cancels** eath other and causes diamagnetism.

Of course, due to crystals, de Broglie waves are thought to synchronize with each other, too.

Because, as shown in helium in top page, it is natural to think that **magnetic field** is caused by **de Broglie waves** (= electron's motion ).

In **superconductivities**, due to completely free electrons and Lorentz force, they show strong diamagnetism, as shown in Fig.13 right.

*(Eq.1) What are "Phonons" ? → Shut up and calculate !*

In condensed matter physics, they often use very vague concepts of **phonons**.

Consider a cube of side L, and wavelength satisfying **boundary** condition, they suppose the relation of Eq.1.

*(Eq.2) Phonons mean de Broglie waves !*

Here λ is wavelength of phonon, and k means wave number.

These relations indicate these vague phonons are equal to some real **de Broglie waves**.

So in condensed matter physics, they tacitly **depend** on some de Broglie waves.

*(Eq.3) Number of resonating modes*

Here we get the total number of oscillating modes included in spherical shell of wave number k, as shown in Eq.3.

This relation is often used in lattice models of condensed matter physics.

According to Meissner effect, the magnetic field inside superconductivity becomes zero.

These effects could be explained by usual **classical** Maxwell equations by London.

*(Eq.4)*

In Eq.4, electron density is "n", and electron's velocity is "v".

In the electric field E, moving electrons (= current density "j" ) are accelerated.

*(Eq.5) London equation = diamagnetism.*

Using Eq.4 and Eq.5 (= Faraday's law ), we get London equation of Eq.5, which shows (perfect) **diamagnetism** of superconductivity.

Because according to Faraday's law, moving charge tries to **cancel** external magnetic field obeying **classical** Lorentz force.

*(Eq.6) Other Maxwell equations *

Here we use other Maxwell equations of Eq.6.

Combining all equations above, we get

*(Eq.7) *

where

*(Eq.8) *

Λ_{L} is **London penetration depth**, which means how **deeply** external magnetic field can enter superconductivity.

So external magnetic fields are more **decreased** inside the superconductivity.

As shown in Faraday's law and Maxwell equaions, this Meissner effect is completely caused by **classical** electromagnetism

*(Fig.14) "Cooper pair" really exists ??*

According to the present condensed matter physics, it is said that a Cooper pair is two electrons **attracting** each other at low temperature through very **vague** existence of "**phonons**".

Surprisingly, the distance between the two electrons in the Cooper pairs is about **100- 1000 nanometer** (nm) !

For example, in the hydrogen molecule (H2), the distance between two nuclei is about **0.073 nm**.

How can these two electrons bind stably to each other in the superconductor, overcoming **repulsive** Coulomb force ? This is strange.

The important point is that phonons they introduced are very **artificial** concepts.

And these phonons are only "mathematical" products ( Not real onject ), so the present BCS theory **cannot** be more developed escaping from this **mathematical** restrictions. ( See also this page. )

*(Eq.9) *

Here we simply explain why these **phonons** are very **artificial** and only **mathematical** ( NOT physical ) concepts.

Eq.9 is Fourier components of **replusive** Coulomb force between two electrons.

They **intentionally** change **permittivity** (= ε ) to add **attractions** by phonons, as follows,

*(Eq.10) *

where they defined the following relations by force,

*(Eq.11) *

In Eq.11, the **negative** sign is the point of this attraction by phonons.

Strange to say, in Eq.11, Ω_{p} means **phonon**'s angular frequency, they insist.

But is it **allowable** that they **suddenly** introduced this **vague** concept to explain attractive force ?

There are **NO** reasonable explanations about this manipulations at all.

*(Eq.12) *

Substituting Eq.10 and Eq.11 into Eq.9, we obtain Eq.12.

In Eq.12, when electron's energy ( ħω ) is **less** than **fictional** phonon's energy (= ħΩ ), this repulsive Coulomb force is **changed** into attraction !

But as you feel, this attraction between two electrons (= Cooper pair ) was **suddenly** introduced **without** offering reasons.

So these Cooper pair and phonons are only **speculation**, and does **NOT** prove the existence of strange "spin" at all.

Here we show quantized magnetic flux is caused by **real** de Broglie waves, and it **doesn't** mean Cooper pair.

Because phonons themselves are **unreal** quasiparticles, and the **attractions** between two electrons are very **unnatural**.

*(Fig.15)*

The magnetic flux quantum (Φ_{0}) is the quantized magnetic flux passing through the hole of a superconductor in Fig.15.

This maxgatic flux is known to become an integer times the follwoing quantized value.

( So, Φ = Φ_{0} × an integer. )

*(Eq.13) *

First we try to get Eq.13 using *Schrodinger equation*.

To get Eq.13 in Schrodinger equation, we must hypothesize the "**Cooper pair**", which consists of two electrons.

In the superconductor at very low temperature, **phases** of the all electrons become almost same, as shown in Eq.14.

Unfortunatelly, they try **NOT** to clarify **what** this phase of electron really is.

(= Again, Shut up and calculate ! )

*(Eq.14) *

where the phase (Θ) consists of momentum (p) and energy (E), as follows,

*(Eq.15)*

If we forget the *repulsive force* between two electrons, and suppose the "Cooper pair (= -2e )", the momentum (p) and the energy (E) become

*(Eq.16)*

where considering the **Lorentz force**, we use magnetic potential (= A ), and electric potential (= φ ).

This replacement is based on classical Lorentz force. see also this page.

When we pay attention to only the space part, Eq.15 is

*(Eq.17)*

If we consider the *phase of the wavefunction returns to its original*, by rotating it around the hole of Fig.15,

*(Eq.18)*

wehre K is an integer.

According to the Meissner effect, the magnetic field and electron's current in an superconductor can be ignored.

So we can suppose the electron's velocity (= v ) of Eq.18 is zero, as follows,

*(Eq.19)*

where Φ means the total magnetic flux surrounded by the vector potential (= A ) according to Maxwell's law.

( B = ∇ × A. Φ = BS. )

From Eq.19, the magnetic flux (Φ) in the hole becomes *quantized*, as follows,

*(Eq.20)*

"K" is an integer.

Here we can define quantized magnetic flux unit, as follows,

*(Eq.21)*

Eq.21 is called "magnetic flux quantum (Wb)".

So they insist Cooper pair can explain quantized magnetic flux.

But they **don't** explain what the wave phases of Eq.14 really is.

( Of course, as you notice, these phases are related to **real** de Broglie waves. )

*(Fig.16) An integer times de Broglie wavelength.*

Here we suppose the electron is rotating around near the hole of Fig.16 to cancel the magnetic field.

When the *centrifugal force* is equal to the **Lorentz force**,

*(Eq.22)*

When one round of the orbit is equal to an **integer (= K ) times de Broglie's wavelength**,

*(Eq.23)*

where λ = h/mv.

From Eq.22 and Eq.23, we have

*(Eq.24)*

So,

*(Eq.25)*

Eq.25 means the magnetic flux (Φ) passing through the hole of Fig.16

( πr^{2} is the area of the hole. )

As a result, we can get the magnetic flux quantum of superconductor using "**real**" de Broglie waves.

*(Eq.26) = Eq.21.*

And Cooper pair is **not** needed here.

Of course, if Cooper pair does not exist, the problem of **high-temperature** superconductivity **never** happen from the beginning.

( They try to solve this problem using conformal field theory of the string. But these methods have **NO reality**. )

This de Broglie wave's **phase** is related to quantum **tunnel** and **Josephson** effect.

So quantum tunnel is caused just by **real** de Broglie waves ( NOT **fantasied** quantum mechanics ).

See also this page.

*(Fig.17)*

In quantum hall effects, electrons are moving in the dirrection perpendicular to external electric and magnetic fields.

As shown in this page, we can explain these phenomena including fractional quantum hall effects by **real** de Broglie wave's quantization.

*(Fig.18) Conductivity ( currents ) are quantized.*

In quantum hall effect, conductivity ( and current ) is quantized.

Considering electron's de Broglie waves, it is obvious that their wave **phases** are related to these effects.

*(Fig.19) Why strange fractional charges appear ONLY in 2D system ??*

The true mechanism of fractional quantum hall effect remains unknown.

In some theories, they introduced very strange particles called "**anyon**".

Anyons are **neither** bosons nor fermions !

Furthermore, these anyons have **fractional charge** ! Impossible.

As you notice, the present quantum mechanics tends to be just a **fantasy** ( from the beginning ).

*(Fig.20) Spin hall effect ? Really "spin" ?*

Spin hall effect is completely different from usual hall effect.

Moving electrons turn in the direction perpendicular to electric field ( **no** magnetic firld ), dependeng on their magnetic moment's direction ( up or down ).

Some "**scattering**" between particles are thought to be related to this effect.

This effects is much weaker than usual hall effect, so very difficult to detect.

They insist these magnetic momemts are caused by "spin".

But how they distinguish directions of them, though electrons are **point**-like particles ? **Impossible**.

First, very tiny point-like particles **cannot** collide with each other.

It is natural that we think the difference of directions in **orbital** motions (= de Broglie waves ) causes this effect.

*(Fig.21) Spin magnetic interaction is an illusion !*

In quantum mechanics, spin orbit interaction ( coupling ) is derived from Dirac equation and electromagnetic interaction.

In fact, in the process of this calculation, they use a kind of "mathematical" **trick**.

In this calculation, they artificially **change** de Broglie wavelength of an electron into external magnetic field !

As you feel, **de Broglie** wavelength of an electron has **NOTHING** to do with **external** ( not internal ) magnetic field B.

Here we explain about this trick simply.

*(Fig.22) Lorentz force → replacements.*

The electromagnetic interactions in quantum mechanics and electrodynamics (QED) completely depend on **classical** Lorentz force.

As shown in this page, first they get Lagrangian which gives Lorentz force.

Second, they derive **Hamiltonian** (= H ) based on this Lagrangian.

In this final Hamiltonian, magnetic (= A ) and electric (= φ ) **potentials** are **added** to the original equations of motion.

*(Fig.23) Free-particle equation → A, φ potentials are added → spin-magnetic interaction ??*

The first equation of Fig.23 is Hamiltonian of free particle.

σ is Pauli matrices (= spin ), which is hidden in the first equaion.

The second equation is gotten using replacements of Fig.22 last line (= **external** electromagnetic fields ).

They insist **spin magnetic** interaction term can be obtained in this calculation.
But is it really so ??

( Here, μ_{B} is "Bohr magneton". )

*(Fig.24) de Broglie wave of an electron is changed into "external" magnetic field ??*

In Fig.23, they use the **differential** operator (= de Broglie wavelength ) of an electron as a **part** of **external** magnetic field !

Magnetic field B is equal to ∇ × A (= magnetic potential ).

( This ∇ is originally "de Broglie wave" of an electron. )

Of course, external magnetic field B is completely **independent** value from this electron.

So this spin-magnetic interaction in quantum mechanics is completely a "mathematical" trick and **wrong**.

*(Fig.25) Spin - orbit interaction is an illusion !*

Spin-orbit inteaction is also gotten from Dirac equation approximately (= Pauli approximation ).

In fact, the strength of this spin-orbit interaction of Dirac equation is **too weak** in comparison with **experimental** values.

( This means spin-orbit interaction is **NOT** a true thing. )

So they insist some **other** strong electric potential may be generated by some **band structure** of metals.

The present condensed matter physics tends to **escape** out of "real" mechanism into very **vague** concepts and explanations.

They **NEVER** try to seek clearer mechanism about these phenomena at all.

*(Fig.26) Spin - orbit interaction is an illusion !*

As shown in this page, Dirac spinors (= fermions ) are 4 × 1 matrices.

And the upper and lower spinors are **mixed**, which is completely differenct from usual non relativistic quantum field theory.

So they need to get **even matrices** from Dirac matrices using diagonal matrix U, as shown in Fig.26 upper.

But when Hamiltonian H includes external magnetic field (= A, φ ), they **cannot** get even matrices.

So they need to rely on some **approximation**.

*(Fig.27) Approximation → spin - orbit interaction term really appears ?*

Relying on some approximation (= Pauli approximation ), spin-orbit interaction term can be gotten, they insist.

The important point is that this spin-orbit interaction based on relativistic quantum field theory is **much weaker** than actual experimental values.

*(Fig.28) Comparison of spin-orbit interactions.*

In Fig.28, k_{F} is approximate wave number, electric potential (= eφ ) is supposed to be about 10 eV (= outer electron ).

Using these values, spin-orbit interaction by Dirac equation becomes about **10 ^{-4} eV**, very weak.

This value is **much weaker** than experimental values in the surface of Au or Ag+Bi ( **0.3 eV** and **3 eV**, respectively ).

So they **artificially** change spin-orbit interaction **coefficient** into much bigger one in various metals.

( It means these are "**free**" parameters. )

In conclusion, spin-orbit interaction is a "theoretically" and "experimentally" **ungrounded** concept.

*(Fig.29) Pauli exclusion principle is a force ? → "Shut up and calculate !"*

If you see some condensed matter physics textbooks, you would find those books are **filled** with unrealistic "spins".

Main reason is "Pauli **exclusion** principle", in which two identical fermions **cannot** enter in the **same** place (= state ).

( But I think, this definition of the "same" place is very **vague**. How can we define these **boundary** lines ?? )

For example, in 1s energy state, only spin "up" and "down" electrons can exist.

They introduced very artificial "colors" (= red, blue, green ) in quarks to satisfy Pauli exclusion principle by force.

So, the force involved in this **mysterious** Pauli exclusion principle is **much stronger** than all other fundamental forces !

The problem is physicists **NEVER** try to ask what this Pauli exclusion principle **really** is, even in 21th century now.

Instead of **wasting** a great deal of money in useless accelerator, they should investigate the **true** form of this Pauli exclusion, first, I think.

*(Fig.30) Spin - spin interaction is illusion !*

As shown in Fig.5 and Fig.6, we explain spin-spin interaction is **too weak** to cause ferromagnetism.

So they inisist strong exchange interaction constant J is the result of some **vague** "quantum" mechanical effects.

So the word of "quantum mechanical" effects is very **convenient** to express unkown phenomena !

They must **clarify** these vague concepts including unrealistic "quasiparticle" as soon as possible.

*(Fig.31) "Synchronizing" de Broglie wave is true nature of ferromagnetism.*

If strange "spin" magnetic moment is **too weak** to cause strong ferromagnetism, there is **ONLY one** thing left to explain this phenomenon.

As you notice, when **de Broglie wave** caused by each electron's motion is **synchronizing** with each other, the **stability** of ferromagnetism can be naturally explained.

As I said above, the present condensed matter physics **tacitly** depends on this de Broglie waves as "**phases**" or **wave number** k.

( But they **NEVER** admit this realistic wave. Instead they just do "Shut up and calculate !" ).

*(Fig.32) Electron spin is an illusion.*

Because as shown in this page, the instant they start to ask what this spin **really** is, they would **notice** this unrealistic spin is just a classical orbital motion.

And it's **too late** for physicists to correct this spin, because denying "spin" means rejecting **all** quantum mechanics and quantum field theory.

As a result, they are wandering around **imaginary** extradimensions and another worlds "**forever**" to explain "quantum" world.

*(Fig.33) s-d interaction is too weak.*

It is said that "spins" of 3d and 4s electrons are interacting with each other and cause various macro effects in materials.

But like Fig.30, this s-d spin interaction is **too weak**, when we think spin magnetic moment is involved in this effect.

*(Fig.34) s-d interaction is too weak.*

Lattice interval is supposed to be 2.5 Å.

In this interval, when they try to get some energy value using "spin" magnetic moment, this energy becomes **too weak** in comparison with actual interaction (= 1 eV ).

So again they insist this is due to some **other** "quantum mechanical" phenomena.

But as you feel, strange "spin" itself is just an **imaginary** concept from the beginning.

This fact clearly shows that these strong s-d interaction are **NOT** by "spin", but by some **other** things such as **de Broglie waves**.

*(Fig.35) AMR is relatied to different de Broglie wave's directions.*

In ferromagnetic materials, it is known that electrical resistance **changes** depending on the relation between magnetic and current's **directions**.

This phenomenon is called "anisotropic magnetoresistance" (= **AMR** ).

They insist the ferromagnetism is caused by spin of "**3d**" electrons of metals such as Fe.

So they insist this AMR is the result of spin and orbit (= current ) interactions

But as shown in Fig.6 and Fig.28, it is **obvious** that some **other** things **different** from "spin" is playing a **main** role in these ferromagnetism and spin-orbit interactions.

So it is quite natural that we think AMR is caused by **de Broglie wave**'s direction, NOT by **point** particle's spin.

*(Fig.36) GMR is spin-orbit interaction or scattering ?*

In Fig.36, very thin (= 10 Å) nonmagnetic layer (= Cu ) is sandwiched by some magnetic material (= Co, Fe ).

In this case, when magnetic directions in upper and lower Co layers are **different** from each other (= Fig.36 left ), the electric resistance in Cu layer becomes too **strong**.

This phenomenon is called "giant magnetoresistance (= **GMR** )".

It is said this GMR is caused by some electron's **scattering** or spin-orbit interactions.

But this mechanism remains **unknown**.

Considering the fact that ferromagnetism happens by some **other** things different from "spin", it is natural that we think GMR is also caused by **de Broglie wave**'s directions.

*(Fig.37) Hall effect.*

In hall effect, charged particle moves in the direction, which is **perpendicular** both to magnetic (= B ) and electric (= E ) fields.

This phenomenon is explained by usual **classical** Lorentz force ( see some hall effect textbooks ).

In Fig.37, electric force ( eE ) is just equal to magnetic Lorentz force (= evB ).

This current (= "v" ) is called "hall current".

*(Fig.38) Anomalous hall effect.*

In anomalous hall effect, magnetic fields of internal **ferromagnetism** play the **same** role as external magnetic field B in hall effect.

So they insist this effect is generated by **spin-orbit** interaction.

( Because they insist ferromagnetism is due to unrealistic "spin". )

In nonmagnetic materials, this current is separeted into **two** opposite directions depending on their magnetic moment's directions ( = **spin hall** effect ).

As shown in Fig.37 an Eq.38, these effects are the result of the interactions between **orbital** magnetic moment ( **NOT** spin ) and currents.

As you see in this page, these experiments did **NOT** prove the existence of unrealistic "spin" at all.

So "spin" is just an "**imaginary**" concept.

*(Ap.1) *

According to **Biot-Savart** law, magnetic field (= B ) is as shown in Ap.1.

"I" is electric current, "ds" is electric current **fragment**, and "r" is the distance between this fragment and some point.

*(Ap.2) *

We think about **circular** current of Ap.2.

The magnetic field B at the point "p" becomes the sum of the current fragments "Ids".

As shown in Ap.2, only cosine component of B is left after summing circular current.

*(Ap.3) *

where

*(Ap.4) *

Considering a single electron is very small, the radius "a" is much smaller than "z" in Ap.2.

So approximately, Ap.3 becomes,

*(Ap.5) *

Of course, even if you leave "a" in the denominator of Ap.3, this magnetic field is much smaller.

As shown in this page, **Bohr magneton** (= μ_{B} ) can be gotten by IS (= current × area ).

*(Ap.6) *

As shown in Ap.6, magnetic moment is equal to magnetic charge (= q ) × distance (= d ).

This "d" is the short distance between "imaginary" ± magnetic charges "q" **inside** one magnetic moment.

( Of course, this is only an assumption. ± magnetic charges don't really exist. )

*(Ap.7) *

The relation between force (N) and magnetic field is Ap.7.

In Ap.7, "B" is magnetic flux density ( Wb/m2 ), and μ_{0} is magnetic permeability.

*(Ap.8) *

When the distance between two spin magnetic moments is "z", the magnetic **energy ** becomes as shown in Ap.8.

Because the energy is equal to magnetic force × distance "d" inside one spin .

(= Energy required to separate two ± magnetic charges q by "d" in magnetic field B. )

This magnetic force is given by Ap.7, and "B" is given by Ap.5.

( Of course, spin magnetic moment is **Bohr magneton** of Ap.6. )

*(Ap.9) *

SI units of permeability and magnetic flux density are as shown in Ap.9.

*(Ap.10) *

Using Ap.9 and Ap.10, we compute Ap.8.

The result is

*(Ap.11) *

Dividing the energy by Boltzmann constant k_{B}, we find that this spin-spin interaction is **extremely weak** ( 0.0539 kelvin ).

If ferromagnetism is caused by spin-spin interaction, this magnet is easily **broken** in room temperature.

So this result shows "ferromagnetism" is caused by completely **other** things different from "spin".

2013/9/10 updated. Feel free to link to this site.