Dr. Vadym Zayets

Abstract:

The heat affects both localized d-electrons and conduction electrons. The localized electrons starts to vibrate or swing with respect to each other. At room temperature, the average swing angle with respect to magnetic easy axis is about 15 degrees. The heat affects the conduction electrons very differently. All spins of the spin- polarized conduction electrons remains perfectly aligned along the easy axis under the heating. Due to the heating the number of spin- polarized conduction electrons decreases and the number of spin- unpolarized conduction electrons increases.

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Content

 

1.Heating of localized d- electrons

2. Heating of conduction electrons

3. Why the effect of heating is so different for conduction and localized d- electrons???

4. Thermal properties of localized d- electrons. Curie–Weiss law. Curie temperature. Langevin's and Brillouin's Formulae.

5. Why localized d- electrons support a spin wave, but conduction electrons do not ????

6. Magnetostatic energy. Domain vibration

7. Increase of Curie temperature under external magnetic field

Questions & Answers

 

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(fact 1) Both localized d- electrons and conduction electrons are greatly affected by the heated. The degree of their alignment along one direction is reduced when temperature increases.

(fact 2) The spins of neighbor localized d- electrons are aligned in one direction by the ferromagnetic exchange interaction. Due thermal fluctuation, the spins of neighbor d- electrons are vibrating and swinging with respect to each other. At a temperature higher than the Curie temperature the neighbor alignment of the spins is fully broken by the thermal fluctuations.

(fact 3) All conduction electrons are divided into groups of spin- polarized and spin- unpolarized electrons. The spins of all spin- polarized electrons are aligned precisely along one direction independently of the temperature. The spins of spin- unpolarized electrons are distributed equally in all directions. The numbers of spin- polarized and spin- unpolarized electrons are determined by a balanced by spin relaxation and spin- pumping mechanisms. When the temperature increases the spin pumping rate decreases and the spin relaxation rate increases. It leads to a decrease of the number spin- polarized electrons and an increase of the number spin- unpolarized electrons

(fact 4) Additionally to the neighbor- to- neighbor vibration of the localized d- electrons, the d-electrons are vibrating in groups of aligned spins. Often the vibration (swinging) angle for the vibrations in groups is substantially larger than the neighbor to- neighbor vibrations. The vibrations in groups causes a creation of the magnetic domains. When the alignment between magnetic domains is fully broken, but still there is an neighbor-to- neighbor alignment, a ferromagnetic material is changed into the super paramagnetic phase.

 

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Heating of localized d- electrons

The localized d- electrons are swinging substantially around its easy axis due to thermal fluctuations and interactions with spin waves.

 

(exchange interaction) It forces spins of neighbor orbital to be parallel each other

(thermal fluctuation interaction) It forces spins to be randomly distributed in all directions

 

Heating of localized d-electrons
thermal swinging of spin of localized d-electrons at room temperature swinging angle at room temperature localized electron at absolute zero temperature T=0K Neighbor- to- neighbor swinging of spin of localized d-electrons around its easy axis. Blue arrows show spin direction of localized d- electrons. Average swinging angle at room temperature as a function of material Curie temperature. At absolute zero temperature, all spins of the localized d- electrons aligned perfectly in one direction. The case of the swinging at 15 degree angle with respect to perpendicularly- to-plane axis is shown. It is a common swing angle for spin of a d- electron in a ferromagnetic metal at room temperature. At the room temperature the average swinging angle of d-electrons is 10 deg. for Fe, 13 deg. for Fe, 20 deg. for Ni
click on image to enlarge it

 

 

 

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Quantum vs. classical mechanisms of magnetization reversal

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Heating of conduction electrons

All conduction electrons can be divided into two groups: (1) group of spin- polarized electrons and (2) group of spin- unpolarized electrons. In the group of spin-polarized electrons, all spin are directed precisely in one direction. In the group of the spin- unpolarized electrons, the spins are equally distributed in all directions.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Why the effect of heating is so different for conduction and localized d- electrons

 

 

(reason 1. Why) Frequency of scatterings

conduction electrons: scatterings are very frequent. About each 100 fs (10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Thermal properties of localized d- electrons.

Curie–Weiss law. Curie temperature. Langevin's and Brillouin's Formulae.

 

Langevin's Formulae.

See detailed Calculations in Langevin.pdf

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Curie–Weiss law

 

Curie–Weiss law wiki page is here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Curie-Weiss law
Effective magnetization M vs. temperature. Fit of experimental data. Experiment vs. theory. Low T/Tc. Experiment vs. theory. All range.         N. Gusack "The Electrical and Magnetic Properties of Solids" pp.322 (1958) N. Gusack "The Electrical and Magnetic Properties of Solids" pp.317 (1958)
click on image to enlarge it

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Comparison of magnetic and thermal energies

 

(thermal energy)

Increase of temperature per 1 degree increases the thermal energy per a particle on k ·1K= 1.38×10^-23 J

k is the Boltzmann constant equals to 1.38×10^-23 J/K.

(magnetic energy)

Applying magnetic field H of 1T (=10⁴ Gauss) to an electron with spin increase its magnetic energy on H·μ_B=0.93 ×10^-23 J

μ_B is Bohr magneton equals to 9.27 ×10^-24 J/T

 

(comparison)

Applying 1 T of magnetic field increases the electron magnetic energy on the same increase amount of the electron thermal energy when temperature increases on 0.67 degrees

 

 

The exchange interaction aligns spins of neighbor atoms in a ferromagnetic material. In contrast, thermal fluctuations disaligns the spins. The Curie temperature T_c is the temperature until which there is neighbor - neighbor alignment in ferromagnetic material. At there is a balance between the energy of the exchange interaction and the thermal energy. From this balance condition the exchange energy and the effective magnetic field H_exchange of the exchange interaction are calculated.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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(Spin waves)Why localized d- electrons support a spin wave, but conduction electrons do not????

 

 

Reasons why conduction electrons cannot support a spin wave

(reason 1): frequent scatterings of conduction electrons

The spin wave

(reason 2): large size of a conduction electron

The spin wave

(reason 3): fast movement of a conduction electrons

The spin wave

(reason 4): weak exchange interaction between conduction electrons

The spin wave

 

 

 

 

 

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Increase of Curie temperature under external magnetic field

 

(note) Applying an external magnetic field of 1 Tesla (10 kGauss) increases the energy of a localized d- electron similarly as the increase of temperature of 0.5 K.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Magnetostatic energy. Domain vibration.

 

 

 

 

 

 

 

 

 

 

 

 

 

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Questions & Answers

 

 

 

 

 

 

 

 

 

 

 

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I am strongly against a fake and "highlight" research