*(Fig.1) But electron "spinning" speed is much faster than light, so unreal ! *

It is known that certatin materials such as iron form permanent **magnets**, or are attracted to magnets, which is called ferromagnetism.

The present quantum mechanics claims when electron spins are aligned parallel, it causes ferromagnetism in iron.

But an electron is so tiny and **point**-like that its spinning speed must be much faster than light ( > c ) to cause its *magnetic* field.
So this "spin" model is **unrealistic**.

*(Fig.2) ↓ Spin model is broken at room temperature !*

Quantum mechanics claims that (anti)ferromagnetism is caused by electron spin. But this is a big **lie**.

The **magnetic** energy by electron spin is too **weak** to cause ferromagnet.

Spin-spin interaction is easily broken at low temperature ( ~ 0.3 K ).

But actual iron can keep ferromagnetic at 1043 K ( this p.7 ).

In fact, electron's spin **disagrees** with many experimental results !

"Spin" is used only as a "mark" with **No** physical meaning.

So we must give up contradictory spin model to investigate further mechanism !

It's natural to think that ferromagnet is maintained stably by Coulomb interaction among electrons' **orbits** ( not spin ! )

*(Fig.3) Spin magnet is too weak to explain ferromagnet.*

You may think Spintronics and excitonics are **useful** (← ? ) for your career.

But almost **nobody** knows electron spin **lacks** reality !

Its spinning far **exceeds**
light speed.

You may hear spin is tiny magnet with the magnitude of Bohr magneton.

This spin magnet can explain stable ferromagnetism ? Unfortunately **NOT**.

Spin-spin *magnetic* interaction is too weak to explain actual ferromagnet.

See this p.6 this p.7. So spin model **failed** from the beginning.

Then, what the heck does this spin model mean ?

It uses "Heisenberg" spin model ( this p.3 ).

But this *Heisenberg* spin model is too **old**, which was introduced in **1920s**, and it's too **abstract** to describe actual phenomena ( this p.2 ).

This spin model just puts nonphysical symbols side by side. So **useless**.

Parameter J is **arbitrarily** chosen. J > 0 = antiferromagnet, J < 0 = ferromagnet.

*(Fig.4) Orbital motion is stable due to Coulomb interaction between atoms.*

As I said, electron spin magnetism ( measured by Stern-Gerach ) is **too weak** to cause actual stable ferromagnetism.

This is the reason physicsits invented **artifcial** concpet (= "exchange force" ) in ferromagnet and Pauli exclusion principle, and parameter J is freely **chosen**, so useless.

Instead of relying on artificial "exchange force", we can naturally explain this stable ferromagnetism using *realistic* electron's **orbital** motion.

Each electron orbital motion **synchronizes** with neighboring ones to generate macroscopic magnet due to **Coulomb** attraction between electron and nucleus.

Coulomb force is far stronger and more stable than "spin *magnetic*" interaction, and this **orbital** motion can explain why iron ferromagnet is stable even at high temperature

*(Fig.5) Quantum orbit satisfies an integer times de Broglie wavelength.*

Only Coulomb force is insufficient to explain why atomic energy levels are quantized, and why an electron doesn't fall into nucleus.

Bohr model succeeded in getting actual atomic energies, proposing each orbit is an integer times de Broglie wavelength, as well as Schrodinger's hydrogen .

An **integer** multiple of *de Broglie* wavelength means an electron can **avoid** destructive interference and be stable.

Without this de Broglie wave, each electron can be attracted to positive nuclei, until they **stick** to each other and its energy is **unlimitedly** lower !

So the repulsive force by electron's de Broglie wave is **strong** enough to keep the electron away from the nucleus and cause Pauli exclusion force.

*(Fig.6) Opposite phases of two de Broglie waves cancel each other*

In old Bohr's helium, **two** electrons are moving on the **opposite** sides of the nucleus in the *same* circular orbit (= **one** de Broglie wavelength ).

Considering Davisson-Germer interference experiment, *two* electrons of old Bohr's helium are clearly **unstable**.

**1**-de Broglie wavelength orbit consists of a pair of the opposite wave phases (= ±ψ ), which **cancel** each other by *destructive* interference.

Due to Coulomb repulsion between two electrons, one is always on the opposite side of another where the opposite de Broglie wave phases cancel each other.

Actually, old Bohr's helium of Fig.6 gives wrong ground state energy of helium, when you calculate it.

Old helium gives the total energy of **-83.33** eV, which is a little lower than the actual value of **-79.005** eV (= 1st + 2nd ionization energy of this ).

*(Fig.7) Actual Helium must avoid "destructive interference".*

If two 1 × de Broglie wavelength orbits are in the same plane in old Bohr's helium model, their **opposite** wave phases cause **destructive** interference and vanish.

To **avoid** *vanishing* de Broglie's wave, two electron orbits in actual helium must be perpendicular to each other. Each orbit is **one**-de Broglie wavelength.

If the two orbits are **perpendicular** to each other, their wave phases are **independent** from each other and can be **stable**, not canceling each other.

This helium model considering actual de Broglie wave interference just agrees with experimental results of all atoms !

*(Fig.8) Hydrogen, Helium with 1 × de Broglie wavelength.*

These orbits are all just *one de Broglie's wavelength*.

In this new helium, the two symmetrical orbits crossing perpendicularly are *wrapping the whole helium atom* completely.

The Bohr model hydrogen which has only one orbit, *can not* wrap the direction of the magnetic moment completely.

It is just **consistent** with the fact of the strong **stability** and the **closed** shell property of helium.

*(Fig.9) Two "opposite" wave phases cancel each magnetic field*

One-electron Hydrogen generates **magnetic** field, while two-electron Helium doesn't. Why ? We can explain it using **de Broglie** waves.

In "actual" Helium model, the *opposite* phases of two electron's de Broglie waves cross each other perpendicularly.

Because two electrons **repel** each other by Coulomb repulsion, an electron tends to approch the opposite phase ( where electron doesn't exist ) of another electron.

From a **distance** (= a third person ), the total magnetic field caused by electron's movement (= de Broglie wave ) is **cancelled** out to be zero by destructive interference.

So crossing between the *opposite* de Broglie wave phases is the reason why Helium has NO magnetic field.

*(Fig.10) ↓ Helium -- two "opposite" wave phases always cross *

When electron's **opposite** de Broglie wave phases cross each other in Helium two orbits, it can get experimental energy.

Opposite wave phases **always** *cross*, so its total magnetic field caused by electron's motion (= de Broglie wave ) is **cancel**led out to be zero, from a third observer,

*(Fig.11) 2 × de Broglie wavelength orbits. Each is a pair of opposite phases.*

One wavelength consists of a pair of "crest" (= + ) and "trough" (= - ) irrespective of transverse and longitudinal waves.

Here we suppose "**+**" phase contains an **electron** itself, and "**-**" phase is **compressed** by the electron's *movement*, --- which is " de Broglie wave ".

**2** × ( *1* × ) de Broglie wavelength orbit contains **two** ( *one* ) pairs of **±opposite** phases and **two** ( *one* ) midpoint lines.

These "**opposite**" wave phases **cancel** each other by *destructive* interference.

To avoid it, two orbits must cross **perpendicularly** in all atoms.

*(Fig.12) 2 × de Broglie wavelenght orbits contain "free" electrons*

Helium two 1 × de Broglie wavelength orbits **always** cross their opposite (anti) wave phases at right angle.

On the other hand, when two 2 × de Broglie wavelength orbits cross each other, they contain "**free** electrons" and "free opposite phases" which are**n't** crossing.

So there is still a *room* for more orbits in 2 × de Broglie wavelength.

*(Fig.13) Two 2 × de Broglie wavelength orbits include "free" electrons*

Compared to 1 × de Broglie wavelength orbits in Helium, a 2 × de Broglie wavelength orbit includes **more** different phases.

As one electron moves **away** from another orbit, its de Broglie wave phase gets **free**, not cancelled out by its opposite phase.

Magnetic field is caused by electron's motion (= de Broglie wave ), so these "free" electron wave phases can be used as a source of magnetic ferromagnetism.

*(Fig.14) All opposite wave phases just cross each other in Neon*

Neon contains **eight** valence electrons. Neon belongs to the 2nd line in periodic table, meaning its orbit is *2 × de Broglie* wavelength.

When just two 2 × de Broglie wavelenght orbits cross each other (= Fig.14 upper ), some electrons are **free** from their opposite wave phases.

With **four** orbits, **all** electrons and their opposite wave phases cross each other, forming stable noble gas Neon with *No* more room.

The fact that all opposite wave phases always cross means this Neon causes **NO** magnetic property.

*(Fig.15) Orbits of Neon cross each other "perpendicularly".*

As shown on this page, we can show the appropriate new **Neon** model, in which orbits can cross each other "**perpendicularly**".

"Perpendicular" crossing means they can **avoid** "*destructive*" interference. Neon consists of four 2 × de Broglie wavelength orbits ( total 4 × 2 = **8** electrons )

*(Fig.16) Maximum orbits = midpoint lines + 2 (= two perpendicular orbits )*

As shown on this page, the number of *midpoint* lines ( related to **de Broglie** wavelength ) influences the number of **maximum** orbital number in the periodic table.

The **maxium** number of orbits in Ne becomes "**4**" (= 2 × *perpendicular* + 2 × **midlines** ).

4 × de Broglie wavelength contains **4** midlines, so the total orbital number of Kr becomes "**6**".

The **odd** numbers of "3", "5", "7" orbits are asymmetrical and **unstable**.

So the orbital numbers of "**Ar**" (= 3 × waveslength ), "*Xe*" (= 5 × waveslength ) remain the **same** as "**Ne**" and "*Kr*".

*(Fig.17) 6 orbits of Kr outer electrons.*

Like Neon (= 4 orbits ), Krypton **six** orbits generate **three** pairs, each contains **two** *perpendicular* orbits with **opposite** phases and opposite *directions* ( e1-e1', e2-e2', e3-e3' ).

Fig.17 is **Krypton** orbits seen from the **upper** side.

**0.5** × de Broglie wavelength orbit is included between two closest **intersections**, like Neon and Argon.

*(Fig.18) All opposite wave phases just cross each other → No magnetic*

Krypton is in the fourth row of periodic table, which means it has **4** × de Broglie wavelength orbit.

If there are **6 orbits** with 4 × de Broglie wavelength, **all** their electron's opposite wave phases always cross
each other, and **cancel** their magnetic property

*(Fig.19) When Krypton contains 24 electrons, their repulsion is too strong*

Seeing the fourth row in periodic table including 18 elements, we can think noble gas Krypton has the maximum **18** valence electrons.

When Krypton with **4** × de Broglie wavelength orbits has **6** orbits, it can have the maximum **24** electrons (= 4 × 6 ) ? Unfortunately **not**.

Kryton orbitals consists of **four** *layers* in vertical direction, with each having six electrons, as seen in Fig.19 upper.

But in this case, each six electrons included in the **top** and **bottom** layers show **stronger** Coulomb repulsion than other two middle layers.

So to be *symmetric* in Coulomb repulsion, the top and bottom orbital layers must decrease electrons in their most stable state ( Fig.19 below ).

Like swing of a pendulum, electrons moving back and forth between unstable and **stable** states with maximum **18** electrons.

*(Fig.20) Why only Fe, Co, Ni, Gd-Tm are ferromagnet ? *

There are only a **limited** number of metals showing ferromagnetism. Most stable ferromagnetic metals are *Fe*, *Co*, *Ni* in the fourth row of periodic table ( this p.2 )

Besides them, some 4f-rare earths such as Gd, Tb, Dy, Ho, Er, Tm show weak ferromagnetism.

**What** on earth determines whether each metal is ferromagnet or not ?

*(Fig.21) Metals with few valence electrons cannot fix magnetic direction*

In the fourth row of periodic table, Potassium (= K ) has only **one** valence electron, and its crystal structure is body-centered cubic.

If this potassium has only one orbit, it means there are free electron's de Broglie wave phases which can be used to generate ferromagnetism ?

But metals with a **small** number of valence electrons **cannot** be ferromagnet causing stable magnetic field.

Because the electron's orbit of potassium has to **move** around to keep links to **all** surrounding electrons, which **cannot** fix its stable magnetic *direction*.

To cause stable ferromagnetism, metals must contain electrons' orbits "**enough**" to **fix** their magnetic direction.

*(Fig.22) Krypton (= Kr ) has 6 orbits with 4 × de Broglie wavelength → NO magnetic*

If Krypton (= Kr ) has 4 × de Broglie wavelength orbit, it can contain the **maximum** **6** orbits.

In this state, **all** electron's "opposite" wave phases just cross each other and **cancel** their total magnetic field from a distance.

It means if Krypton *decreases* its orbits (= electrons ), some electrons can be **free** from other opposite phases, and cause ferromagnetism.

*(Fig.23) Fe has 8 valence electrons (= 2 × 4 orbits ) → magnetic*

Iron (= Fe ) belongs to the *4th* row in periodic table, like Kr and K. It means each orbit of Fe with **8** valence electrons is also 4 × de Broglie wavelength.

We can think Fe has 4 orbits and each orbit include 2 electrons ( 8 = 2 × 4 orbits )

Iron "hexahedral" structure ( with 8 electrons ) can **keep** its stable links to surrounding electrons and its magnetic direction unlike Potassium.

The fact that Fe contains only **4** orbits ( in 4 × de Broglie wavelength ) means some electrons are free from thier opposite phase, and can cause magnetic field.

*(Fig.24) Why only three Fe, Co, Ni show ferromagnetism ?*

To show stable ferromagnetism, metals have to satisfy **two** important conditions. One is electron's orbit needs to be "**fixed**" to cause stable magnetic field.

So matals with a too **small** number of valence electrons ( like K ) **cannot** keep its stable *magnetic direction*, and cannot be ferromagnet.

Second, there must be **free** electrons left to cause magnetic field. When orbital number is maximum like Kr, all electrons's de Broglie waves are **cancel**led by thier opposite phases.

We can think Fe, Co, Ni has **4 ~ 5** orbits in 4 × de Broglie wavelength, which can satisfy these two conditions for ferromagnet.

*(Fig.25) 4f-elements has 5 ~ 7 orbits with "free" electrons.*

4f rare earth metals belong to *6th* row of periodic table which means they have **6** × de Broglie wavelength orbits.

Elements with 6 × de Broglie wavelength can have the maximum **8** orbits. We can estimate Yb has **16** valence electrons (= 2 × **8** orbits ).

So Gd-Tm rare earths have **5 ~ 7** orbits with "*free*" electrons causing ferromagnet.

6 × de Broglie wavelength orbits have more *room* than 4 × de Broglie wavelength, so to **fix** their magnetic direction, more electrons are needed.

So the reason why Gd, Tb, Dy .. Tm are weak ferromagnets is that they also satisfy two important conditions.

**Odd** de Broglie wavelength orbits (= 5th row in periodic table ) are **asymmetric** in electrons' positions, so orbital motions are **unstable** and cancel magnetic property.

2016/9/16 updated. Feel free to link to this site.