Films minces magnétiques sur substrat flexible : Etude des effets magnéto-mécaniques par résonance ferromagnétique

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HAL Id: tel-01730578

https://tel.archives-ouvertes.fr/tel-01730578

Submitted on 13 Mar 2018

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des effets magnéto-mécaniques par résonance ferromagnétique

Mouhamadou Gueye

To cite this version:

Mouhamadou Gueye. Films minces magnétiques sur substrat flexible : Etude des effets magnéto-

mécaniques par résonance ferromagnétique. Mechanics of materials [physics.class-ph]. Université

Sorbonne Paris Cité, 2017. English. �NNT : 2017USPCD007�. �tel-01730578�

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T H E S E Doctorat de physique

TH ` ESE

pour obtenir le grade de docteur d´ elivr´ e par

l’Universit´ e Paris XIII

Sp´ ecialit´ e “Science des Mat´ eriaux”

pr´ esent´ ee par

Mouhamadou Gueye

soutenue le 27 Mars 2017

Magnetic thin films on flexible substrates:

magnetomechanical study by ferromagnetic resonance

Jury

Mme. Alexandra Mougin Rapporteur M. Vincent Repain Rapporteur M. Mohamed Belmeguenai Examinateur M. Manuel Bibes Examinateur M. Damien Faurie Examinateur M. Philippe Goudeau Examinateur M. Michel Viret Examinateur M. Fatih Zighem Examinateur

Universit´ e Paris XIII

Laboratoire des Sciences des Proc´ ed´ es et des Mat´ eriaux (LSPM)

UPR CNRS 3407, 99 avenue J. B. Cl´ ement, 93430 Villetaneuse, France

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T H E S E Doctorat de physique

TH ` ESE

pour obtenir le grade de docteur d´ elivr´ e par

l’Universit´ e Paris XIII

Sp´ ecialit´ e “Science des Mat´ eriaux”

pr´ esent´ ee par

Mouhamadou Gueye

soutenue le 27 Mars 2017

Magnetic thin films on flexible substrates:

magnetomechanical study by ferromagnetic resonance

Jury

Mme. Alexandra Mougin Rapporteur M. Vincent Repain Rapporteur M. Mohamed Belmeguenai Examinateur M. Manuel Bibes Examinateur M. Damien Faurie Examinateur M. Philippe Goudeau Examinateur M. Michel Viret Examinateur M. Fatih Zighem Examinateur

Universit´ e Paris XIII

Laboratoire des Sciences des Proc´ ed´ es et des Mat´ eriaux (LSPM)

UPR CNRS 3407, 99 avenue J. B. Cl´ ement, 93430 Villetaneuse, France

(4)

❆❝❦♥♦✇❧❡❞❣♠❡♥+, ①✐✐✐

■♥+0♦❞✉❝+✐♦♥ ✶

❇✐❜❧✐♦❣0❛♣❤② ✶✶

✶ ❋✉♥❞❛♠❡♥+❛❧ ❝♦♥❝❡♣+, ✐♥ ♠❛❣♥❡+✐,♠ ✶✸

✶✳✶ ▼❛❣♥❡'✐❝ ✐♥'❡*❛❝'✐♦♥, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸

✶✳✶✳✶ ▼❛❣♥❡'✐❝ ❞✐♣♦❧❛* ✐♥'❡*❛❝'✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸

✶✳✶✳✷ ❊①❝❤❛♥❣❡ ✐♥'❡*❛❝'✐♦♥, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹

✶✳✶✳✷✳✶ ❉✐*❡❝' ❡①❝❤❛♥❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹

✶✳✶✳✷✳✷ ■♥❞✐*❡❝' ❡①❝❤❛♥❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✶✳✷ ▼❛❣♥❡'✐❝ ❛♥✐,♦'*♦♣② ❡✛❡❝', ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✶✳✷✳✶ ▼❛❣♥❡'♦❝②,'❛❧❧✐♥❡ ❛♥✐,♦'♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✶✳✷✳✶✳✶ ❯♥✐❛①✐❛❧ ❛♥✐,♦'*♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✶✳✷✳✶✳✷ ❈✉❜✐❝ ❛♥✐,♦'*♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼

✶✳✷✳✷ ❙❤❛♣❡ ❛♥✐,♦'*♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✶✳✷✳✸ ▼❛❣♥❡'♦❡❧❛,'✐❝ ❛♥✐,♦'♦♣② ❛♥❞ ♠❛❣♥❡'♦,'✐❝'✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✶✳✸ ▼❛❣♥❡'✐③❛'✐♦♥ ❉②♥❛♠✐❝, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

✶✳✸✳✶ ▲❛♥❞❛✉ ▲✐❢,❝❤✐'③ ●✐❧❜❡*' ✭▲▲●✮ ❡K✉❛'✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

✶✳✸✳✷ ▼❛❣♥❡'✐❝ ,✉,❝❡♣'✐❜✐❧✐'② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

✶✳✸✳✷✳✶ ▲♦,,❧❡,, ▼❛❣♥❡'✐❝ ❙✉,❝❡♣'✐❜✐❧✐'② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

✶✳✸✳✷✳✷ ▲♦,,② ♠❛❣♥❡'✐❝ ,✉,❝❡♣'✐❜✐❧✐'② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻

✶✳✹ ❙♣✐♥ ✇❛✈❡, ♠♦❞❡, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

✶✳✹✳✶ ❯♥✐❢♦♠ ♣❡❝❡,,✐♦♥ ♠♦❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

✶✳✹✳✷ ▼❛❣♥❡'♦,'❛'✐❝ ,♣✐♥ ✇❛✈❡, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✶✳✹✳✸ ❙'❛♥❞✐♥❣ ,♣✐♥ ✇❛✈❡, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

✶✳✹✳✹ ❘❡❧❛①❛'✐♦♥ ♠❡❝❤❛♥✐,♠, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

✶✳✹✳✹✳✶ ■♥'*✐♥,✐❝ ♠❡❝❤❛♥✐,♠, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

✶✳✹✳✹✳✷ ❊①'*✐♥,✐❝ ♠❡❝❤❛♥✐,♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

❇✐❜❧✐♦❣0❛♣❤② ✸✻

✷ ▼❡❝❤❛♥✐❝❛❧ +❡,+✐♥❣ ✸✽

✷✳✶ ❇❛,✐❝, ✐♥ ❡❧❛,'✐❝✐'② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✷✳✶✳✶ ❙'❡,, ❛♥❞ ❙'❛✐♥, ✐♥ ,♦❧✐❞, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✷✳✶✳✷ ❊❧❛,'✐❝✐'② ✐♥ ,✐♥❣❧❡ ❝*②,'❛❧✿ '❤❡ ❝✉❜✐❝ ❝❛,❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

✷✳✷ ❊❧❛,'✐❝✐'② ✐♥ ♣♦❧②❝*②,'❛❧, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶

✐

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✷✳✸ ❊①♣❡'✐♠❡♥+❛❧ ❞❡/✐❣♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✷✳✸✳✶ ❇❡♥❞✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✷✳✸✳✶✳✶ ❯♥✐❛①✐❛❧ ❇❡♥❞✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✷✳✸✳✶✳✷ ❊5✉✐❜✐❛①✐❛❧ ❜❡♥❞✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✷✳✸✳✷ 9✐❡③♦❡❧❡❝+'✐❝ ❆❝+✉❛+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻

✷✳✸✳✷✳✶ 9✐❡③♦❧❡❝+'✐❝ ❊✛❡❝+ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻

✷✳✸✳✷✳✷ 9❩❚ ♣✐❡③♦❡❧❡❝+'✐❝ ❆❝+✉❛+♦' ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

✷✳✹ ❙+'❛✐♥ ♠❡❛/✉'❡♠❡♥+/ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽

✷✳✹✳✶ ❉✐❣✐+❛❧ ✐♠❛❣❡ ❝♦''❡❧❛+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽

✷✳✹✳✶✳✶ ❇❛/✐❝ ♣'✐♥❝✐♣❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽

✷✳✹✳✶✳✷ ❙♣❡❝✐♠❡♥ ♣'❡♣❛'❛+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

✷✳✹✳✶✳✸ ❊①♣❡'✐♠❡♥+❛❧ /❡+✲✉♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

✷✳✹✳✶✳✹ ❇❛/✐❝ '❡/✉❧+/ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

✷✳✹✳✷ ❆++❛✐♥❛❜❧❡ /+'❛✐♥/ ❛♥❞ /+'❡//❡/ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷

❇✐❜❧✐♦❣&❛♣❤② ✺✹

✸ ❋❡&&♦♠❛❣♥❡2✐❝ &❡4♦♥❛♥❝❡ ✺✻

✸✳✶ ❊①♣❡'✐♠❡♥+❛❧ /❡+✲✉♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✸✳✶✳✶ ▼✐❝'♦/+'✐♣ ❧✐♥❡/ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽

✸✳✶✳✷ ▲♦❝❦✲✐♥ ❞❡+❡❝+✐♦♥ +❡❝❤♥✐5✉❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾

✸✳✶✳✷✳✶ ▲♦❝❦✲✐♥ ✐♥ ♣❤❛/❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾

✸✳✶✳✷✳✷ ❋✐❡❧❞ ♠♦❞✉❧❛+✐♦♥ ❧♦❝❦✲✐♥ +❡❝❤♥✐5✉❡ ❛♥❞ ❞❡'✐✈❛+✐✈❡ /♣❡❝+'✉♠ ✻✵

✸✳✷ ▲♦❝❦✲✐♥ ♣❛'❛♠❡+❡'/ ♦♣+✐♠✐③❛+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

✸✳✷✳✶ ❆♠♣❧✐+✉❞❡ ♦❢ +❤❡ ♠♦❞✉❧❛+✐♦♥ ✜❡❧❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

✸✳✷✳✷ ❚❤❡ ❧♦❝❦✲✐♥ ♣❤❛/❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷

✸✳✷✳✸ ❚❤❡ ❧♦❝❦✲✐♥ ❢'❡5✉❡♥❝② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

✸✳✸ ❋▼❘ /✐❣♥❛❧ ♦♣+✐♠✐③❛+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

✸✳✸✳✶ ❚✐♠❡ ❝♦♥/+❛♥+ ❛♥❞ /✇❡❡♣✐♥❣ +✐♠❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

✸✳✸✳✷ ▼✐❝'♦✇❛✈❡ ♣♦✇❡' ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹

✸✳✸✳✸ ❙❡♥/✐+✐✈✐+② ♦❢ +❤❡ ❋▼❘ /♣❡❝+'❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹

✸✳✹ ■♥✲#✐%✉ ♠❡❝❤❛♥✐❝❛❧ +❡/+✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹

❇✐❜❧✐♦❣&❛♣❤② ✻✼

✹ ▼❛❣♥❡2♦❡❧❛42✐❝ ♣&♦♣❡&2✐❡4 ♦❢ ❤✐❣❤ ♣♦2❡♥2✐❛❧ ❛❧❧♦②4 ❢♦& 4♣✐♥2&♦♥✐❝4 ✻✽

✹✳✶ ❇❡❢♦'❡❤❛♥❞ ❝❤❛'❛❝+❡'✐③❛+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾

✹✳✷ ❉❡+❡'♠✐♥❛+✐♦♥ ♦❢ +❤❡ ♠❛❣♥❡+♦/+'✐❝+✐♦♥ ❝♦❡✣❝✐❡♥+/ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✹✳✷✳✶ 9✐❡③♦❡❧❡❝+'✐❝ ❛❝+✉❛+✐♦♥ ♦❢ +❤❡ ♠❛❣♥❡+✐❝ /♣❡❝✐♠❡♥/ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✹✳✷✳✷ ▼♦❞❡❧✐♥❣ ♦❢ +❤❡ '❡/♦♥❛♥❝❡ ✜❡❧❞ /❤✐❢+ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

✹✳✸ ▼❛❣♥❡+♦❡❧❛/+✐❝ ❡✛❡❝+✿ ❡5✉✐✈❛❧❡♥+ /+'❡//❡/ ❝♦♥❝❡♣+ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹

✹✳✸✳✶ ▼✉❧+✐✲❛①✐❛❧ /+'❡// ❛♥❞ '❡/✉❧+✐♥❣ ❛♥✐/♦+'♦♣② ✜❡❧❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺

✹✳✸✳✷ ❘❡/♦♥❛♥❝❡ ✜❡❧❞ ❛/ ❢✉♥❝+✐♦♥ ♦❢ ❡5✉✐✈❛❧❡♥+ ✉♥✐❛①✐❛❧ /+'❡// ✳ ✳ ✳ ✳ ✳ ✳ ✼✼

✹✳✸✳✸ ❈♦♥❢'♦♥+❛+✐♦♥ ♦❢ ♣✐❡③♦✲❛❝+✉❛+✐♦♥ ❛♥❞ ❜❡♥❞✐♥❣ /+'❛✐♥/ ❡✛❡❝+/ ✳ ✳ ✳ ✳ ✼✾

❇✐❜❧✐♦❣&❛♣❤② ✽✻

✐✐

(6)

✺ ❘❡#✐❞✉❛❧ ❛♥✐#♦+,♦♣② ✐♥ ♠❛❣♥❡+✐❝ ✜❧♠# ❞❡♣♦#✐+❡❞ ♦♥ ♣♦❧②♠❡, #✉❜#+,❛+❡ ✽✽

✺✳✶ #$❡❛♠❜❧❡* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽

✺✳✷ ❘❡✐❞✉❛❧ ♠❛❣♥❡3✐❝ ❛♥✐♦3$♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵

✺✳✸ ❖$✐❣✐♥ ♦❢ 3❤❡ $❡✐❞✉❛❧ ♠❛❣♥❡3✐❝ ❛♥✐♦3$♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷

❇✐❜❧✐♦❣,❛♣❤② ✾✼

✻ ■♥✢✉❡♥❝❡ ♦❢ ❛♥♥❡❛❧✐♥❣ ♦♥ +❤❡ ♠❛❣♥❡+♦❡❧❛#+✐❝ ♣,♦♣❡,+✐❡# ♦❢ ❈♦

20

❋❡

60

❇

20

+❤✐♥

✜❧♠# ✾✾

✻✳✶ ❆* ❞❡♣♦✐3❡❞ ✜❧♠✿ ❡❧❛3✐❝✱ ♠❛❣♥❡3✐❝ ❛♥❞ ♠❛❣♥❡3♦✲❡❧❛3✐❝ ♣$♦♣❡$3✐❡ ✳ ✳ ✳ ✳ ✾✾

✻✳✶✳✶ ❊❧❛3✐❝ ♣$♦♣❡$3✐❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵

✻✳✶✳✷ ▼❛❣♥❡3✐❝ ❛♥❞ ♠❛❣♥❡3♦✲❡❧❛3✐❝ ♣$♦♣❡$3✐❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶

✻✳✷ ❆♥♥❡❛❧✐♥❣ 3❡♠♣❡$❛3✉$❡ ❡✛❡❝3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺

✻✳✷✳✶ ❨♦✉♥❣✬* ♠♦❞✉❧✉* ❛♥❞ #♦✐**♦♥✬* $❛3✐♦ ✈❛$✐❛3✐♦♥* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻

✻✳✷✳✷ ▼❛❣♥❡3✐❝ ❛♥❞ ♠❛❣♥❡3♦✲❡❧❛3✐❝ ♣$♦♣❡$3✐❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽

❇✐❜❧✐♦❣,❛♣❤② ✶✶✶

✼ ❱♦❧+❛❣❡ ❝♦♥+,♦❧ ♦❢ +❤❡ ♠❛❣♥❡+✐③❛+✐♦♥ ♣,♦❜❡❞ ❜② ❢❡,,♦♠❛❣♥❡+✐❝ ,❡#♦♥❛♥❝❡ ✶✶✸

✼✳✶ #$❡❛♠❜❧❡* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸

✼✳✷ ▼❛❣♥❡3✐③❛3✐♦♥ ❞✐$❡❝3✐♦♥ ♣$♦❜❡❞ ❜② ❢❡$$♦♠❛❣♥❡3✐❝ $❡*♦♥❛♥❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹

✼✳✸ ❊①♣❡$✐♠❡♥3❛❧ $❡✉❧3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼

❇✐❜❧✐♦❣,❛♣❤② ✶✷✶

❈♦♥❝❧✉#✐♦♥# ✴ ❖✉+❧✐♥❡# ✶✷✸

▲✐#+ ♦❢ ♣✉❜❧✐❝❛+✐♦♥# ✶✸✵

❆❜#+,❛❝+ ✶✸✶

✐✐✐

(7)

✵✳✵✳✶ ❛✮ ❙❦❡(❝❤ ♦❢ ❛ ❧❛②♦✉( ♦❢ 0✐❧✐❝♦♥✱ ♠❡(❛❧✱ ❛♥❞ ♣♦❧②♠❡7 ❧❛②❡70 ✐♥ ❛ ✉♥✐( ❝❡❧❧

♦❢ ❛ 0✐❧✐❝♦♥ ❝✐7❝✉✐( ♠❡0❤ (❡0( 0(7✉❝(✉7❡✳ ❜✮ ❈✉77❡♥(✕✈♦❧(❛❣❡ ❝❤❛7❛❝(❡7✐0(✐❝0

♠❡❛0✉7❡❞ ❜② ❝♦♥(❛❝(✐♥❣ (❤❡ ❝♦♥(✐♥✉♦✉0 ♠❡(❛❧ ❧✐♥❡✳ ❝✱❞✮ =❤♦(♦❣7❛♣❤0 ♦❢

(❤❡ ❝✐7❝✉✐( ♠❡0❤ (7❛♥0❢❡77❡❞ ♦♥(♦ (❤❡ (✐♣ ♦❢ ❛ ✜♥❣❡7 ♦♥ ❛ ♣❧❛0(✐❝ 0✉❜0(7❛(❡

✇✐(❤ (❤❡ 0❤❛♣❡ ♦❢ ❛ ❤✉♠❛♥ ❤❛♥❞✳ ❞✮ ▼❛❣♥✐✜❡❞ ✈✐❡✇ ♦❢ (❤❡ 7❡❣✐♦♥ ✐♥❞✐❝❛(❡❞

❜② (❤❡ ❜♦① ✐♥ ✭❝✮✳ ❡✮ ▼❛❣♥✐✜❡❞ ✐♠❛❣❡ ♦❢ (❤❡ 7❡❣✐♦♥ ✐♥❞✐❝❛(❡❞ ❜② (❤❡ ❜❧✉❡

❜♦① ✐♥ ✭❞✮ ❝♦❧❧❡❝(❡❞ ✉0✐♥❣ ❛ 0❝❛♥♥✐♥❣ ❢♦❝❛❧ (❡❝❤♥✐C✉❡✳ ❢✱ ❤✮ ❈♦❧♦7✐③❡❞

❛♥❣❧❡❞✲✈✐❡✇ ❙❊▼ ✐♠❛❣❡0 ♦❢ (❤❡ 0❛♠♣❧❡ 0❤♦✇♥ ✐♥ ❝✮✳ ❣✱❤✮ ▼❛❣♥✐✜❡❞ ✈✐❡✇0

♦❢ ❛7❡❛0 ✐♥❞✐❝❛(❡❞ ❜② (❤❡ ❞❛0❤❡❞ ❜♦①❡0 ✐♥ ❢✮✳ ❚❤❡ ❣7❛②✱ ②❡❧❧♦✇✱ ❛♥❞ ❜❧✉❡

❝♦❧♦70 ❝♦77❡0♣♦♥❞ (♦ 0✐❧✐❝♦♥✱ =♦❧②✐♠✐❞❡ ✭=■✮✱ ❛♥❞ =❉▼❙✱ 7❡0♣❡❝(✐✈❡❧② ❬✺❪✳ ✷

✵✳✵✳✷ ❛✮ ❆77❛② ♦❢ ✢❡①✐❜❧❡ ♠❛❣♥❡(♦0❡♥0♦7② 0②0(❡♠0✳ ❚❤❡0❡ ❛7❡ ♠❛❞❡ ♦❢ ❈♦✴❈✉

♠✉❧(✐❧❛②❡70 ❞❡♣♦0✐(❡❞ ♦♥ ❑❛♣(♦♥ ❢♦✐❧0✳ ❚❤❡0❡ ✢❡①✐❜❧❡ ♠❛❣♥❡(♦0❡♥0✐(✐✈❡

0❡♥0♦70 ❝❛♥ ❜❡ ✉0❡❞ (♦ ♠♦♥✐(♦7 ❞✐0♣❧❛❝❡♠❡♥(0 ♦7 ♠♦(✐♦♥ ❛♥❞ ♣7♦✈✐❞❡ ❢❡❡❞✲

❜❛❝❦ ❛0 ♥❡❡❞❡❞✳ ❜✮ ❘❡0♣♦♥0❡ ♦❢ (❤❡ ♠❛❣♥❡(✐❝ 0❡♥0♦7 ❜7✐❞❣❡ ♠❡❛0✉7❡❞ ❛(

❞✐✛❡7❡♥( ❜❡♥❞✐♥❣ 7❛❞✐✐ ❛♥❞ ♣❧♦((❡❞ ✈❡70✉0 ❛♣♣❧✐❡❞ ♠❛❣♥❡(✐❝ ✜❡❧❞✳ ✳ ✳ ✳ ✳ ✳ ✸

✵✳✵✳✸ ❛✮ =❤♦(♦❣7❛♣❤ ♦❢ (❤❡ ❜❡♥❞✐♥❣ ❛♥❣❧❡ ♠❛❣♥❡(♦(7❛♥0♣♦7( ❡①♣❡7✐♠❡♥(❀ (❤❡

7❛❞✐✉0 ♦❢ (❤❡ ❝✉7✈❡❞ 0✉♣♣♦7( ✐0 ✉0❡❞ ❛0 ❛ ♣❛7❛♠❡(❡7 ✐♥ (❤❡ ❞❡✈✐❝❡ ❝❤❛7❛❝✲

(❡7✐③❛(✐♦♥✳ ❜✮ ▼❘ 7❛(✐♦ ♦❢ ✢❡①✐❜❧❡ ●▼❘ 0②0(❡♠✱ ❛0 ❛ ❢✉♥❝(✐♦♥ ♦❢ ❛♣♣❧✐❡❞

♠❛❣♥❡(✐❝ ✜❡❧❞ ❬✶✷❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸

✵✳✵✳✹ ❛✮ ❚❤❡ ❧❛②❡7 0(❛❝❦ ♦❢ ❛ 0❡♥0♦7 ♦♥ ❛ ❑❛♣(♦♥ 0✉❜0(7❛(❡✳ ❜✶✮ ❆ ❧❛②❡7 0(❛❝❦

❞❡♣♦0✐(❡❞ ♦♥ ❛ ✢❡①✐❜❧❡ ❑❛♣(♦♥ 0✉❜0(7❛(❡✳ ❜✷✮ ▼■ 0❡♥0♦7 0(7✐♣ ♦❢ ✷✷ ♠♠

✶✳✺ ♠♠ ❛❢(❡7 ♣❛((❡7♥✐♥❣✳ ❝✮ =✐❝(✉7❡ ♦❢ (❤❡ ✢❡①✐❜❧❡ ▼■ 0❡♥0♦7 ♠♦✉♥(❡❞ ♦♥

(❤❡ 0❛♠♣❧❡ ❤♦❧❞❡7✳ ❞✮ ❙❝❤❡♠❛(✐❝ ♦❢ (❤❡ ❤✐❣❤✲❢7❡C✉❡♥❝② ♠✐❝7♦0(7✐♣✲❜❛0❡❞

❝✉7✈❛(✉7❡ ♠❡❛0✉7❡♠❡♥( 0❡(✉♣ ❢♦7 (❤❡ ✢❡①✐❜❧❡ ♠❛❣♥❡(✐❝ 0❡♥0♦7 ❬✶✸❪✳ ✳ ✳ ✳ ✳ ✹

✵✳✵✳✺ ▼■ 7❛(✐♦ ♦❢ (❤❡ 0❛♠♣❧❡ ✉♥❞❡7 ❞✐✛❡7❡♥( ❜❡♥❞✐♥❣ ❧❡✈❡❧0 ❛( ✭❛✮ ✵✳✺ ●❍③ ❛♥❞

✭❜✮ ✶✳✶ ●❍③ ❬✶✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✵✳✵✳✻ ❈❤❛♥❣❡ ♦❢ (❤❡ ♣❡7♠❡❛❜✐❧✐(② ❛0 ❛ ❢✉♥❝(✐♦♥ ♦❢ ❛♣♣❧✐❡❞ (❡♥0✐❧❡ 0(7❛✐♥ ❢♦7 ❛ ♣♦0✲

✐(✐✈❡ ♠❛❣♥❡(♦0(7✐❝(✐✈❡ ♠✉❧(✐❧❛②❡7 ✭❋❡❈♦✭✷✳✶ ♥♠✮✴❈♦❇✭✵✳✾♥♠✮✮ (❤✐♥ ✜❧♠ ♦♥

♣♦❧②✐♠✐❞❡ ❬✷✷❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✵✳✵✳✼ ▼✐♥♦7 ❧♦♦♣ ♦❢ (❤❡ ❢7❡❡✲❧❛②❡7 ♠❛❣♥❡(✐③❛(✐♦♥ ✐♥ ✉♥0(7❛✐♥❡❞ 0(❛(❡ ❛♥❞ ✉♥❞❡7

❢♦✉7 ❞✐✛❡7❡♥( 0(7❛✐♥ ❧❡✈❡❧0✿ ✵✪ ✭0♦❧✐❞ ❧✐♥❡✮✱ ✵✳✺✪ ✭❞❛0❤❡❞ ❧✐♥❡✮✱ ✶✪ ✭❞♦((❡❞

❧✐♥❡✮✱ ✶✳✺✪ ✭❞❛0❤ ❞♦((❡❞ ❧✐♥❡✮✱ ✷✪ ✭0❤♦7( ❞❛0❤❡❞ ❧✐♥❡✮ ❬✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

✵✳✵✳✽ ❊①♣❡7✐♠❡♥(❛❧ ❛♥❞ ❝❛❧❝✉❧❛(❡❞ ❝✉7✈❡0 ❢♦7 ❈♦ ✭✽ ♥♠✮✴❈✉ ✭✹✳✷ ♥♠✮✴◆✐ ✭✽ ♥♠✮

●▼❘ 0②0(❡♠0 ❢♦7 ✹ ❞✐✛❡7❡♥( ❛♣♣❧✐❡❞ 0(7❛✐♥0 ✭✵✪✱ ✵✳✷✺✪✱ ✵✳✺✪ ❛♥❞ ✵✳✼✺✪✮

❬✽❪✳ ✭❛✮ ●▼❘ ❝✉7✈❡0 ❛♥❞ ✭❜✮ ▼❖❑❊ ❝✉7✈❡0✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

✐✈

(8)

✵✳✵✳✾ ❍②%&❡(❡%✐% ❧♦♦♣% ❢♦( Fe

₈₁

Ga

₁₉

✴ /❊❚ ♦❜&❛✐♥❡❞ ✉♥❞❡( ✈❛(✐♦✉% ❡①&❡(♥❛❧ %&(❛✐♥%

✉%✐♥❣ ❞✐✛❡(❡♥& ♠❡❛%✉(✐♥❣ ❝♦♥✜❣✉(❛&✐♦♥%✱ ✭❛✮ ▼❛❣♥❡&✐❝ ✜❡❧❞ H ♣❡(♣❡♥❞✐❝✲

✉❧❛( &♦ &❤❡ &❡♥%✐❧❡ %&(❛✐♥ ✭♦✉&✇❛(❞ ❜❡♥❞✐♥❣ ♦❢ /❊❚ %✉❜%&(❛&❡%✮✱ ✭❜✮ H

♣❡(♣❡♥❞✐❝✉❧❛( &♦ &❤❡ ❝♦♠♣(❡%%✐✈❡ %&(❛✐♥ ✭♦✉&✇❛(❞ ❜❡♥❞✐♥❣ ♦❢ /❊❚ %✉❜✲

%&(❛&❡%✮ ❬✶✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼

✵✳✵✳✶✵❛✮ ❙❝❤❡♠❛&✐❝ ✐❧❧✉%&(❛&✐♦♥ ♦❢ &❤❡ ❢❡((♦♠❛❣♥❡&✐❝ &❤✐♥ ✜❧♠✴♣✐❡③♦❡❧❡❝&(✐❝ ❛❝&✉✲

❛&♦( ❤②❜(✐❞✳ ❜✮✱ ❞✮ ❚❤❡ ❛♣♣❧✐❝❛&✐♦♥ ♦❢ ❛ ✈♦❧&❛❣❡ V

_p

6= 0 ❱ &♦ &❤❡ ❛❝&✉❛&♦(

(❡%✉❧&% ✐♥ ❛ ❞❡❢♦(♠❛&✐♦♥ ♦❢ &❤❡ ❛❝&✉❛&♦( ❛♥❞ &❤❡ ❛✣①❡❞ ❢❡((♦♠❛❣♥❡&✐❝

✜❧♠✳ ❚❤❡ (❡❧❛①❡❞ ❛❝&✉❛&♦( ❛& V

p

= 0 ❱ ✐% %❤♦✇♥ ❜② ❞♦&&❡❞ ❝♦♥&♦✉(%✳ ❝✮✱

❡✮ ❙❝❤❡♠❛&✐❝ ❢(❡❡ ❡♥❡(❣② ❝♦♥&♦✉(% ✐♥ &❤❡ ✜❧♠ ♣❧❛♥❡✳ ❚❤❡ ♠❛❣♥❡&✐❝ ❡❛%②

❛①✐% ✭❡✳❛✳✮ %❤♦✇♥ ❜② &❤❡ &❤✐❝❦ ❞❛%❤❡❞ ❧✐♥❡ ✐% ♦(✐❡♥&❡❞ ♣❛(❛❧❧❡❧ &♦ &❤❡ ❝♦♠✲

♣(❡%%✐✈❡ %&(❛✐♥ ❛♥❞ ❝❛♥ &❤✉% ❜❡ (♦&❛&❡❞ ❜② ✾✵➦ ❜② ❝❤❛♥❣✐♥❣ &❤❡ ♣♦❧❛(✐&② ♦❢

V

_p

❬✷✹❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

✵✳✵✳✶✶❛✮ ❋▼❘ %♣❡❝&(❛ (❡❝♦(❞❡❞ ❛& ❞✐✛❡(❡♥& ✈♦❧&❛❣❡% V

_p

. ❜✮ ❚❤❡ ❞❡♣❡♥❞❡♥❝❡ ♦❢

(❡%♦♥❛♥❝❡ ✜❡❧❞ ♦♥ V

p

❢♦( &✇♦ ♣❡(♣❡♥❞✐❝✉❧❛( ❝♦♥✜❣✉(❛&✐♦♥ ✭❧♦♥❣✐&✉❞✐♥❛❧

%&(❛✐♥ ♣❛(❛❧❧❡❧ ♦( ♣❡(♣❡♥❞✐❝✉❧❛( &♦ ❍✮ ❬✷✹❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

✵✳✵✳✶✷❆♥❣✉❧❛( ❞❡♣❡♥❞❛♥❝❡ ♦❢ &❤❡ (❡%♦♥❛♥❝❡ ✜❡❧❞ ❢♦( &✇♦ ❛♣♣❧✐❡❞ ✈♦❧&❛❣❡% ✭ V

_p

=

−30 ❱ ❛♥❞ V

p

= +20 ❱✮ ❬✷✹❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

✶✳✶✳✶ ❇❡&❤❡✕❙❧❛&❡( ❝✉(✈❡✿ ❡❧❡♠❡♥&% ❛❜♦✈❡ &❤❡ ❤♦(✐③♦♥&❛❧ ❛①✐% ❛(❡ ❢❡((♦♠❛❣♥❡&✐❝✱

❜❡❧♦✇ &❤❡ ❛①✐% ❛(❡ ❛♥&✐❢❡((♦♠❛❣♥❡&✐❝✳ a ❝♦((❡%♣♦♥❞% &♦ &❤❡ ✐♥&❡(❛&♦♠✐❝

❞✐%&❛♥❝❡ ❛♥❞ r ✐% &❤❡ (❛❞✐✉% ( ♦❢ &❤❡ 3d ❡❧❡❝&(♦♥ %❤❡❧❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✶✳✶✳✷ ▲❡❢&✿ ■❧❧✉%&(❛&✐♦♥ ♦❢ &❤❡ ✐♥❞✐(❡❝& ♠❛❣♥❡&✐❝ ❡①❝❤❛♥❣❡ ✐♥&❡(❛❝&✐♦♥ ❜❡&✇❡❡♥

❛♥✐♦♥✲♠❡❞✐❛&❡❞ ♠❛❣♥❡&✐❝ ❝❛&✐♦♥%✳ ❘✐❣❤&✿ ❱❛(✐❛&✐♦♥ ♦❢ &❤❡ ✐♥❞✐(❡❝& ❡①✲

❝❤❛♥❣❡ ❝♦✉♣❧✐♥❣ ❝♦♥%&❛♥&✱ J

_RKKY

✱ ♦❢ ❛ ❢(❡❡ ❡❧❡❝&(♦♥ ❣❛% ✐♥ &❤❡ ♥❡✐❣❤❜♦(✲

❤♦♦❞ ♦❢ ❛ ♣♦✐♥& ♠❛❣♥❡&✐❝ ♠♦♠❡♥& ❛& &❤❡ ♦(✐❣✐♥ r = 0 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✶✳✷✳✶ ❋✐(%& ♦(❞❡( ❛♥✐%♦&(♦♣② ❡♥❡(❣② %✉(❢❛❝❡ ❢♦( ✐(♦♥ ❝✉❜✐❝ ❝(②%&❛❧ ❢♦( ❛ ♣♦%✐&✐✈❡

K

_u1

✭❧❡❢&✮ ❛♥❞ ♥❡❣❛&✐✈❡ K

_u1

✭(✐❣❤& ✮ ❛♥✐%♦&(♦♣② ❝♦❡✣❝✐❡♥&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✶✳✸✳✶ ❲❤❡♥ ❞✐%&✉(❜✐♥❣ &❤❡ ❡]✉✐❧✐❜(✐✉♠ ❝♦♥✜❣✉(❛&✐♦♥✱ &❤❡ ♠❛❣♥❡&✐③❛&✐♦♥ M ~ ♣(❡✲

❝❡%%❡% ❛(♦✉♥❞ &❤❡ ❡✛❡❝&✐✈❡ ♠❛❣♥❡&✐❝ ✜❡❧❞ H ~

_{ef f}

✭❧❡❢&✮✳ ❚❤❡ &♦(]✉❡ ❛❝&✐♥❣

♦♥ &❤❡ ♠♦♠❡♥& ✐% ❣✐✈❡♥ ❜② ❡]✉❛&✐♦♥ ✶✳✸✳✸✳ ❲❤❡♥ ✐♥&(♦❞✉❝✐♥❣ ❞❛♠♣✐♥❣✱

&❤❡ ♠❛❣♥❡&✐③❛&✐♦♥ ❢♦❧❧♦✇% ❛ ❤❡❧✐❝♦✐❞❛❧ &(❛❥❡❝&♦(② ❜❛❝❦ &♦ ✐&% ❡]✉✐❧✐❜(✐✉♠

♣♦%✐&✐♦♥ ✭(✐❣❤&✮✱ ❞❡%❝(✐❜❡❞ ❜② ❡]✉❛&✐♦♥ ✶✳✸✳✹✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹

✶✳✸✳✷ ❚❤❡ (❡❛❧ ✭%♦❧✐❞ ❧✐♥❡✮ ❛♥❞ &❤❡ ✐♠❛❣✐♥❛(② ✭❞❛%❤❡❞ ❧✐♥❡✮ ♣❛(& ♦❢ &❤❡ ❝♦♠♣❧❡①

❤❢ %✉%❝❡♣&✐❜✐❧✐&②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

✶✳✹✳✶ ❘❡♣(❡%❡♥&❛&✐♦♥ ♦❢ &❤❡ ♠❛❣♥❡&✐③❛&✐♦♥ M ~ ❛♥❞ &❤❡ ♠❛❣♥❡&✐❝ ✜❡❧❞ H ~ ✐♥ &❤❡

%♣❛❝❡ ♦❢ %♣❤❡(✐❝❛❧ ❝♦♦(❞✐♥❛&❡ %②%&❡♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾

✶✳✹✳✷ ❉❡♣✐❝&✐♦♥ ♦❢ &❤❡ ♣♦%%✐❜❧❡ ♣❛&❤% ♦❢ &❤❡ (❡❧❛①❛&✐♦♥ ♦❢ &❤❡ ♠❛❣♥❡&✐③❛&✐♦♥

♣(❡❝❡%%✐♦♥✳ ❆❞❛♣&❡❞ ❢(♦♠ ❬✷✷❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

✷✳✶✳✶ ❚❤❡ ❢♦(❝❡% ♦♥ &❤❡ ❢❛❝❡% ♦❢ ❛✳ ✉♥✐& ❝✉❜❡ ✐♥ ❛ ❤♦♠♦❣❡♥❡♦✉%❧② %&(❡%%❡❞ ❜♦❞②✳ ✸✾

✷✳✸✳✶ ❆♥ ✐❧❧✉%&(❛&✐♦♥ ♦❢ %&(❡%% ❞✐%&(✐❜✉&✐♦♥ ✐♥ ❛ ❜❡♥& %♣❡❝✐♠❡♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹

✈

(9)

✷✳✸✳✷ ❛✮ ❱❛&✐❛(✐♦♥ ♦❢ Γ ❛, ❢✉♥❝(✐♦♥ ♦❢ (❤❡ ✜❧♠ (❤✐❝❦♥❡,, ❢♦& ❞✐✛❡&❡♥( ✈❛❧✉❡, ♦❢ (❤❡

,✉❜,(&❛(❡ ❨♦✉♥❣✬, ♠♦❞✉❧✉, ✭ Y

_s

= ✹✱ ✶✵✱ ✷✵✱ ✺✵ ❛♥❞ ✷✵✵ ●C❛✮✳ ❜✮ ❱❛&✐❛(✐♦♥

♦❢ ε

xx

❛, ❢✉♥❝(✐♦♥ ♦❢ t

_f

❢♦& ❞✐✛❡&❡♥( ❜❡♥❞✐♥❣ ✈❛❧✉❡, ✭ρ =✶✵✱ ✷✵✱ ✺✵✱ ✶✵✵

❛♥❞ ✐♥✜♥✐(❡ ✭✢❛( ,✉❜,(&❛(❡✮✮✳ ■♥ ❛✮ ❛♥❞ ❜✮ (❤❡ ,✉❜,(&❛(❡ (❤✐❝❦♥❡,, ❛♥❞ (❤❡

✜❧♠ ❨♦✉♥❣✬, ♠♦❞✉❧✉, ❤❛✈❡ ❜❡❡♥ &❡,♣❡❝(✐✈❡❧② ✜①❡❞ (♦ t

_s

= 125 ➭♠ ❛♥❞

Y

_f

= 200 ●C❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻

✷✳✹✳✶ C✐❝(✉&❡ ,❤♦✇✐♥❣ (❤❡ ❢❡&&♦♠❛❣♥❡(✐❝ (❤✐♥ ✜❧♠ ❝❡♠❡♥(❡❞ ♦♥ (❤❡ C❩❚✲❛❝(✉❛(♦&

✇✐(❤ ❛ &❛♥❞♦♠❧② ,♣❡❝❦❧❡ ♣❛((❡&♥ ♦❢ (❤❡ ,②,(❡♠ ❢❡&&♦♠❛❣♥❡(✐❝ (❤✐♥ ✜❧♠ ❛♥❞

C❩❚ ❛❝(✉❛(♦&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

✷✳✹✳✷ ❙❝❤❡♠❛(✐❝ ✐❧❧✉,(&❛(✐♦♥ ♦❢ &❡❢❡&❡♥❝❡ ,P✉❛&❡ ,✉❜,❡( ❜❡❢♦&❡ ❞❡❢♦&♠❛(✐♦♥ ❛♥❞

❛ (❛&❣❡( ,✉❜,❡( ❛❢(❡& ❞❡❢♦&♠❛(✐♦♥✳ ❆❞❛♣(❡❞ ❢&♦♠ ❬✸✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

✷✳✹✳✸ ❙(❡&❡♦ ❝❛♠❡&❛ ❡①♣❡&✐♠❡♥(❛❧ ,❡( ✉♣ ✉,❡❞ ❞✉&✐♥❣ (❤✐, (❤❡,✐,✳ ❚❤❡ ❡❧❡❝(&✐❝

✜❡❧❞ ✐♥,✐❞❡ (❤❡ ❛❝(✉❛(♦& ✐, ❣❡♥❡&❛(❡❞ (❤❛♥❦, (♦ ❛ ✈♦❧(❛❣❡ ❛♣♣❧✐❡❞ ❜② ✉,✐♥❣

❛ ❑❡♣❝♦ ❇✐♣♦❧❛& ♣♦✇❡& ,✉♣♣❧②✳ ❚❤❡ ❆&❛♠✐* ,♦❢(✇❛&❡ ✐, ✉,❡❞ (♦ ❛♥❛❧②③❡

(❤❡ ✐♠❛❣❡,✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

✷✳✹✳✹ ▲❡❢(✿ ♠❡❛♥ ✐♥✲♣❧❛♥❡ ,(&❛✐♥, ✭ ε

_xx

❛♥❞ ε

_yy

✮ ✐♥ (❤❡ ✜❧♠ ❛♥❞ ❛❝(✉❛(♦& &❡❣✐♦♥,

❛, ❢✉♥❝(✐♦♥ ♦❢ (❤❡ ❛♣♣❧✐❡❞ ✈♦❧(❛❣❡✳ ❘✐❣❤(✿ ❛ ,❦❡(❝❤ ,❤♦✇✐♥❣ (❤❡ ,❡❧❡❝(❡❞

&❡❣✐♦♥ ♦❢ ✐♥(❡&❡,( ✭❘❖■✮ ♦♥ (❤❡ ,✉&❢❛❝❡ ♦❢ (❤❡ ✜❧♠ ❛♥❞ ❛❝(✉❛(♦& ❢♦& (❤❡

❛♥❛❧②,✐, ♦❢ (❤❡ ,(&❛✐♥ (&❛♥,♠✐,,✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

✷✳✹✳✺ ▼❡❛♥ ✐♥✲♣❧❛♥❡ ,(&❛✐♥, ✭ ε

_xx

❛♥❞ ε

_yy

✮ ❛, ❢✉♥❝(✐♦♥ ♦❢ (❤❡ ❛♣♣❧✐❡❞ ✈♦❧(❛❣❡

❢♦& ❛ ,②♠♠❡(&✐❝❛❧ ❝②❝❧❡ ❛♥ ✉♥❧♦❛❞✐♥❣ ❢&♦♠ ✷✵✵ (♦ ❂✷✵✵ ❱ ❢♦❧❧♦✇❡❞ ❜②

❛ ❧♦❛❞✐♥❣ ❢&♦♠ ❂✷✵✵ (♦ ✷✵✵ ❱✳ ❆ ❇✉((❡&✢②✲❧✐❦❡ ❜❡❤❛✈✐♦& ♦❢ (❤❡ ❝✉&✈❡

✐, ♦❜,❡&✈❡❞✳ ❚❤✐, ❜❡❤❛✈✐♦& ✐, ❞✉❡ (♦ (❤❡ ♣♦❧❛&✐③❛(✐♦♥ ,✇✐(❝❤✐♥❣ ♦❢ (❤❡

♣✐❡③♦❡❧❡❝(&✐❝ ❛❝(✉❛(♦&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷

✷✳✹✳✻ ❛✮ ε

_yy

❛, ❛ ❢✉♥❝(✐♦♥ ♦❢ ε

_xx

❢♦& ♣✐❡③♦❡❧❡❝(&✐❝ ❛❝(✉❛(✐♦♥ ✭❵❧♦♦♣✬ ❛♥❞ ❵❜✉((❡&✢②✬

❜❡❤❛✈✐♦&✮ ❛♥❞ ✉♥❛①✐❛❧ ❜❡♥❞✐♥❣✳ ❜✮ σ

_yy

❛, ❛ ❢✉♥❝(✐♦♥ ♦❢ σ

_xx

❢♦& ♣✐❡③♦❡❧❡❝(&✐❝

❛❝(✉❛(✐♦♥ ✭❵❧♦♦♣✬ ❛♥❞ ❵❜✉((❡&✢②✬ ❜❡❤❛✈✐♦&✮ ❛♥❞ ✉♥❛①✐❛❧ ❜❡♥❞✐♥❣✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✸✳✵✳✶ ❩❡❡♠❛♥♥ ,✉❜✲❧❡✈❡❧, ✐♥ ❢❡&&♦♠❛❣♥❡(✐❝ &❡,♦♥❛♥❝❡ ,♣❡❝(&♦,❝♦♣②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✸✳✶✳✶ ❘❡♣&❡,❡♥(❛(✐♦♥ ♦❢ (❤❡ ❋▼❘ ❛❜,♦&♣(✐♦♥ ,♣❡❝(&✉♠ ✇❤✐❝❤ ✐, ❛ ▲♦&❡♥(③✐❛♥

❛♥❞ ✐(, ❞❡&✐✈❛(✐✈❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽

✸✳✶✳✷ ❆ ,❦❡(❝❤ ♦❢ ❛ ♠✐❝&♦,(&✐♣ (&❛♥,♠✐,,✐♦♥ ❧✐♥❡ ✇✐(❤ ✭❛✮(❤❡ ❣❡♦♠❡(&② ❛♥❞ ✭❜✮

(❤❡ ❡❧❡❝(&✐❝ ❛♥❞ ♠❛❣♥❡(✐❝ ✜❡❧❞, ❧✐♥❡,✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾

✸✳✶✳✸ ❆♥ ✐❧❧✉,(&❛(✐♦♥ ♦❢ ❛ (②♣✐❝❛❧ ❋▼❘ ,♣❡❝(&❛✿ ❛ ▲♦&❡♥(③✐❛♥ ♣&♦✜❧❡ ♦❢ (❤❡ ❛❜✲

,♦&♣(✐♦♥ ♣♦✇❡& ❛♥❞ ❛ ❞❡&✐✈❛(✐✈❡ ♦❢ ❛ ▲♦&❡♥(③✐❛♥ ♣&♦✜❧❡ ✇❤❡♥ ❛ ♠♦❞✉❧❛(✐♦♥

✜❡❧❞ ✐, ✉,❡❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

✸✳✷✳✶ ❚❤❡ ✈❛&✐❛(✐♦♥ ♦❢ (❤❡ ❛♠♣❧✐(✉❞❡ ♦❢ (❤❡ ❋▼❘ ,✐❣♥❛❧ ✇✐(❤ (❤❡ ♠♦❞✉❧❛(✐♦♥

✈♦❧(❛❣❡ ✇✐(❤ ✭❛✮✿ ❚❤❡ ,✐❣♥❛❧ ,❤❛♣❡ ♦❢ (❤❡ ❋▼❘ ,✐❣♥❛❧ ❛, ❛ ❢✉♥❝(✐♦♥ ♦❢

✐♥❝&❡❛,✐♥❣ ♠♦❞✉❧❛(✐♦♥ ❛♠♣❧✐(✉❞❡❀✭❜✮✿ (❤❡ ❛♠♣❧✐(✉❞❡ ✭✷❆✮ ♦❢ (❤❡ ❋▼❘

,♣❡❝(&❛ ✇✐(❤ (❤❡ ♠♦❞✉❧❛(✐♦♥ ✈♦❧(❛❣❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷

✸✳✷✳✷ ❚❤❡ ✈❛&✐❛(✐♦♥ ♦❢ (❤❡ ❋▼❘ ,✐❣♥❛❧ ❛♠♣❧✐(✉❞❡ ✇✐(❤ (❤❡ ♣❤❛,❡ ♦❢ (❤❡ ❧♦❝❦✲✐♥

❛♠♣❧✐✜❡&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

✸✳✷✳✸ ❛✮ ■♥✢✉❡♥❝❡ ♦❢ (❤❡ ♠♦❞✉❧❛(✐♦♥ ❢&❡P✉❡♥❝② ❜✮ (❤❡ &❢ ♣♦✇❡& ♦♥ (❤❡ ❋▼❘

,♣❡❝(&❛ ❛♥❞ (❤❡ ,❡♥,✐(✐✈✐(② ♦❢ (❤❡ ❧♦❝❦✲✐♥ ❞❡(❡❝(✐♦♥ ❛♠♣❧✐✜❡&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

✈✐

(10)

✸✳✸✳✶ ■❧❧✉&'(❛'✐♦♥ ♦❢ '❤❡ ❋▼❘ &♣❡❝'(❛ &❡♥&✐'✐✈✐'② ❛❝❝♦(❞✐♥❣ '♦ '❤❡ ❛♥❣❧❡ ❜❡'✇❡❡♥

'❤❡ ♠❛❣♥❡'✐③❛'✐♦♥ ❛♥❞ '❤❡ (❢ ✜❡❧❞✳ ❛✮ ❆ ❧♦✇ &❡♥&✐'✐✈✐'② ✇✐'❤ ♠✐♥✐♠❛❧ ❋▼❘

&✐❣♥❛❧ ✐♥ ✇❤✐❝❤ '❤❡ ❛♥❣❧❡ ❜❡'✇❡❡♥ '❤❡ ♣✉♠♣✐♥❣ ✜❡❧❞ ❛♥❞ '❤❡ &'❛'✐❝ ♦♥❡ ✐&

❡@✉❛❧ '♦ ③❡(♦ ❧❡❛❞✐♥❣ '♦ ❛ ✇❡❛❦ '♦(@✉❡ ❡①❡('❡❞ ❜② '❤❡ ♠✐❝(♦✇❛✈❡ ❞(✐✈❡♥

♦♥ '❤❡ ♠❛❣♥❡'✐③❛'✐♦♥✳ ❜✮ ❍✐❣❤ &❡♥&✐'✐✈✐'② ✇✐'❤ ❛ ♠❛①✐♠❛❧ ❋▼❘ &✐❣♥❛❧ ✐♥

✇❤✐❝❤ '❤❡ ♣✉♠♣✐♥❣ ✜❡❧❞ ✐& ❞✐(❡❝'❡❞ ♣❡(♣❡♥❞✐❝✉❧❛( '♦ '❤❡ ♠❛❣♥❡'✐③❛'✐♦♥

❧❡❛❞✐♥❣ '♦ ❛ &'(♦♥❣ '♦(@✉❡ ❡①❡('❡❞ ❜② '❤❡ ♠✐❝(♦✇❛✈❡ ❞(✐✈❡♥ ✜❡❧❞ ♦♥ '❤❡

♠❛❣♥❡'✐③❛'✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺

✸✳✹✳✶ ❚♦♣ ✜❣✉(❡✿ &❦❡'❝❤ ♦❢ '❤❡ ♠✐❝(♦&'(✐♣❧✐♥❡ (❡&♦♥❛'♦( ❛❧❧♦✇✐♥❣ ❢♦( '❤❡ (❡&♦✲

♥❛♥❝❡ ✜❡❧❞ ❞❡'❡❝'✐♦♥ ♦❢ '❤❡ ❜❡♥❞❡❞ ❈❋❆ ✜❧♠ ❞❡♣♦&✐'❡❞ ♦♥'♦ ✢❡①✐❜❧❡ &✉❜✲

&'(❛'❡✳ I

_rfⁱⁿ

❛♥❞ I

_rf^out

❝♦((❡&♣♦♥❞ '♦ '❤❡ ✐♥❥❡❝'❡❞ ❛♥❞ '(❛♥&♠✐''❡❞ (❛❞✐♦

❢(❡@✉❡♥❝② ❝✉((❡♥' ✭✜①❡❞ ❛' ✶✵ ●❍③ '❤❡(❡❛❢'❡(✮✳ ❚❤❡ &'❛'✐❝ ♠❛❣♥❡'✐❝ ✜❡❧❞

H ~ ✐& ❛♣♣❧✐❡❞ ❛❧♦♥❣ '❤❡ ♠✐❝(♦&'(✐♣❧✐♥❡✳ ❇♦''♦♠ ✜❣✉(❡✿ ✭❛✮ &❡'✉♣ ✐♠❛❣❡ ♦❢

'❤❡ ❝♦♠❜✐♥❡❞ ❋▼❘✴❉■❈ ❡①♣❡(✐♠❡♥'✳ ❚❤❡ ❝✐(❝❧❡❞ ♥✉♠❜❡(& ❝♦((❡&♣♦♥❞ '♦✿

✭✶✮✿ ❑❡✐'❤❧❡② ▼♦❞❡❧ ✷✹✵✵❀ ✭✷✮✿ ❈❈❉ ❝❛♠❡(❛ ✭❆❱❚W✐❦❡✲ ❢✹✷✶❜✮❀ ✭✸✮✿ ♦❜❥❡❝✲

'✐✈❡ ❧❡♥& ❢♦( '❤❡ ❈❈❉ ❝❛♠❡(❛❀ ✭✹✮✿ ✇❤✐'❡ ❧✐❣❤' &♦✉(❝❡❀ ✭✺✮✿ ❡❧❡❝'(♦♠❛❣♥❡'❀

✭✻✮✿ ❙❝❤♦''❦② ❞❡'❡❝'♦(❀ ❛♥❞ ✭✼✮✿ ♠♦❞✉❧❛'✐♦♥ ❝♦✐❧&✳ P

_in

❛♥❞ P

_out

❛(❡ '❤❡

✐♥❥❡❝'❡❞ ❛♥❞ '(❛♥&♠✐''❡❞ (❛❞✐♦ ❢(❡@✉❡♥❝② ❝✉((❡♥'✳ ✭❜✮ ❩♦♦♠ ✐♥ &❤♦✇✐♥❣

'❤❡ &❛♠♣❧❡ ♠♦✉♥'❡❞ ♦♥'♦ '❤❡ ♠✐❝(♦&'(✐♣❧✐♥❡✳ ❆ '②♣✐❝❛❧ ❝❛❧❝✉❧❛'❡❞ &'(❛✐♥

✜❡❧❞ ♠❛♣ ✐& ♣(❡&❡♥' ❛' '❤❡ '♦♣ ♦❢ '❤❡ &❛♠♣❧❡✳ ✭❝✮ ❩♦♦♠ ✐♥ ♦❢ '❤❡ &♣❡❝❦❧❡❞

♣❛''❡(♥ ✭&♣(❛②✲♣❛✐♥'❡❞✮ ❛' '❤❡ '♦♣ ♦❢ '❤❡ &❛♠♣❧❡ ♥❡❝❡&&❛(② ❢♦( '❤❡ &'(❛✐♥

✜❡❧❞& ❝❛❧❝✉❧❛'✐♦♥&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻

✹✳✶✳✶ ❛✮ ❆♥❣✉❧❛( ❞❡♣❡♥❞❡♥❝❡ ♦❢ '❤❡ (❡&♦♥❛♥❝❡ ✜❡❧❞ ❛& ❛ ❢✉♥❝'✐♦♥ ♦❢ ✐♥✲♣❧❛♥❡ ❛♥❣❧❡

❢♦( '❤❡ ❞✐✛❡(❡♥' ✜❧♠&✳ ❜✮ ❋(❡@✉❡♥❝② ❞❡♣❡♥❞❡♥❝❡ ❛& ❢✉♥❝'✐♦♥ ♦❢ '❤❡ ❛♣♣❧✐❡❞

♠❛❣♥❡'✐❝ ✜❡❧❞ ❢♦( '❤❡ ❞✐✛❡(❡♥' ✜❧♠&✳ ■♥ ❛✮ ❛♥❞ ❜✮✿ Co

₄₀

Fe

₄₀

B

₂₀

✭❜❧✉❡✮ ❛♥❞

Co

₂

FeAl ✭(❡❞✮ ❛♥❞ ◆✐ ✭❜❧❛❝❦✮✳ ❚❤❡ &♦❧✐❞ ❧✐♥❡& ❝♦((❡&♣♦♥❞ '♦ ✜'& ♦❢ '❤❡

❡①♣❡(✐♠❡♥'❛❧ ❞❛'❛ ✉&✐♥❣ ❡@✉❛'✐♦♥& ✹✳✷✳✸ ❛♥❞ ✹✳✶✳✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾

✹✳✶✳✷ ❙❦❡'❝❤ ♦❢ '❤❡ ❝♦♦(❞✐♥❛'❡ &②&'❡♠ ✉&❡❞ ✐♥ '❤✐& &❡❝'✐♦♥✳ ■♥ '❤❡ ❡①♣❡(✐♠❡♥'&

♣(❡&❡♥'❡❞ ❤❡(❡✱ '❤❡ ♠❛❣♥❡'✐❝ ✜❡❧❞ ✐& ❛♣♣❧✐❡❞ ✐♥ '❤❡ ✭ xy ✮ ♣❧❛♥❡✳ ◆♦'❡ '❤❛' H

_u

✐& ❛❧✐❣♥❡❞ ❛❧♦♥❣ ~e

_x

❢♦( &✐♠♣❧✐❝✐'②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✹✳✷✳✶ ❙❦❡'❝❤ &❤♦✇✐♥❣ '❤❡ ✜❧♠✴&✉❜&'(❛'❡ ❣❧✉❡❞ ♦♥'♦ '❤❡ ♣✐❡③♦❡❧❡❝'(✐❝ ❛❝'✉❛'♦(✳ ✳ ✼✷

✹✳✷✳✷ ❊①♣❡(✐♠❡♥'❛❧ &♣❡❝'(❛ (❡❝♦(❞❡❞ ❛' ✽ ●❍③ ❢♦( ❛♥ ✐♥✲♣❧❛♥❡ ♠❛❣♥❡'✐❝ ✜❡❧❞

❛' ✾✵ ❞❡❣(❡❡ ✇✐'❤ (❡&♣❡❝' '♦ '❤❡ ♠❛✐♥ ♣♦&✐'✐✈❡ &'(❛✐♥ ❛①✐& ♦❢ '❤❡ ❛❝'✉❛'♦(

✭❛❧♦♥❣ y✲❛①✐&✮ ❛♥❞ ❛❧♦♥❣ '❤❡ ❡❛&② ❛①✐& ♦❢ '❤❡ ♠❛❣♥❡'✐③❛'✐♦♥✳ ❆ ♥❡❣❛'✐✈❡

&❤✐❢' ♦❢ '❤❡ ❋▼❘ &♣❡❝'(❛ ✐& ♦❜&❡(✈❡❞ ✐♥ ◆✐ ✜❧♠ ✇❤✐❧❡ ♣♦&✐'✐✈❡ &❤✐❢'& ❛(❡

♥♦'✐❝❡❞ ❢♦( ❈❋❆ ❛♥❞ ❈❋❇ ✜❧♠&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

✹✳✷✳✸ ❛✱ ❜✮ ❘❡&♦♥❛♥❝❡ ✜❡❧❞ &❤✐❢' δH

_res

❛& ❢✉♥❝'✐♦♥ ♦❢ '❤❡ ❛♣♣❧✐❡❞ ✈♦❧'❛❣❡ ✭❜❡✲

'✇❡❡♥ ✵ ❛♥❞ ✷✵✵ ❱ ❢♦( '❤❡ ❈❋❆ ✜❧♠✮✳ ❙②♠❜♦❧& (❡♣(❡&❡♥' ❡①♣❡(✐♠❡♥'❛❧

❞❛'❛ ✇❤✐❧❡ &♦❧✐❞ ❧✐♥❡& (❡❢❡( '♦ ✜' ♦❜'❛✐♥❡❞ ❢(♦♠ '❤❡ ♠♦❞❡❧ ❞❡&❝(✐❜❡❞ ✐♥ '❤❡

'❡①'✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

✹✳✸✳✶ ❙❝❤❡♠❛'✐❝ ✐❧❧✉&'(❛'✐♦♥ &❤♦✇✐♥❣ '❤❡ ❛♥❣❧❡& ❛♥❞ '❤❡ ❝♦♦(❞✐♥❛'❡ &②&'❡♠ ✉&❡❞

✐♥ '❤❡ '❡①'✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻

✹✳✸✳✷ ❋(❡@✉❡♥❝② ❞❡♣❡♥❞❡♥❝❡ ♦❢ H

_me^{F M R}

❢♦( ❛ ❧❛(❣❡ ❢(❡@✉❡♥❝② (❛♥❣❡✳ ❚❤❡ ✐♥&❡'

&❤♦✇& '❤✐& ❢(❡@✉❡♥❝② ❞❡♣❡♥❞❡♥❝❡ ❢♦( ✉&✉❛❧ ❋▼❘ ❢(❡@✉❡♥❝② (❛♥❣❡ ✭✵✲✸✵

●❍③✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾

✈✐✐

(11)

✹✳✸✳✸ ❛✮ ε

_xx

❛♥❞ ε

_yy

❛' ❢✉♥❝+✐♦♥ ♦❢ ✈♦❧+❛❣❡ ❛♣♣❧✐❡❞ +♦ ♣✐❡③♦❡❧❡❝+4✐❝ ❛❝+✉❛+♦4✱

♠❡❛'✉4❡❞ ❜② ❉■❈✱ ❢♦4 ❛ '✐♠♣❧❡ ❡❧❡❝+4✐❝ ❧♦❛❞✐♥❣✲✉♥❧♦❛❞✐♥❣✳ ❜✮ ε

_xx

❛♥❞

ε

yy

❛' ❢✉♥❝+✐♦♥ ♦❢ ✈♦❧+❛❣❡ ❛♣♣❧✐❡❞ +♦ ♣✐❡③♦❡❧❡❝+4✐❝ ❛❝+✉❛+♦4✱ ♠❡❛'✉4❡❞ ❜②

❉■❈✱ ❢♦4 ❛ '②♠♠❡+4✐❝ ❡❧❡❝+4✐❝ ❧♦❛❞✐♥❣ ♣❛+❤✳ ❝✮ ε

_yy

❛' ❛ ❢✉♥❝+✐♦♥ ♦❢ ε

_xx

❢♦4 ♣✐❡③♦❡❧❡❝+4✐❝ ❛❝+✉❛+✐♦♥ ✭✏❧♦♦♣✑ ❛♥❞ ✏❜✉++❡4✢②✑ ❜❡❤❛✈✐♦4✮ ❛♥❞ ✉♥❛①✐❛❧

❜❡♥❞✐♥❣✳ ❞✮ σ

yy

❛' ❛ ❢✉♥❝+✐♦♥ ♦❢ σ

xx

❢♦4 ♣✐❡③♦❡❧❡❝+4✐❝ ❛❝+✉❛+✐♦♥ ✭✏❧♦♦♣✑

❛♥❞ ✏❜✉++❡4✢②✑ ❜❡❤❛✈✐♦4✮ ❛♥❞ ✉♥❛①✐❛❧ ❜❡♥❞✐♥❣✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵

✹✳✸✳✹ ❛✮ ✳ ❘❡'♦♥❛♥❝❡ ✜❡❧❞ '❤✐❢+✱ ❞❡✜♥❡❞ ❛' δH

_R

= H

_R

(V ) − H

_R

(V = 0) ✱ ❛'

❢✉♥❝+✐♦♥ ♦❢ ❛♣♣❧✐❡❞ ✈♦❧+❛❣❡ +♦ +❤❡ ♣✐❡③♦❡❧❡❝+4✐❝ ❛❝+✉❛+♦4 ✐♥ +❤❡ ❝❛'❡ ♦❢

❜❛❝❦✇❛4❞ ❛♥❞ ❢♦4✇❛4❞ ✈♦❧+❛❣❡ ❧♦♦♣' ✭✵ ❀ ✷✵✵ ❱✮✳ ❈✐4❝❧❡❞ ♣♦✐♥+' 4❡❢❡4 +♦

❡①♣❡4✐♠❡♥+❛❧ ❞❛+❛ ✇❤✐❧❡ '♦❧✐❞ ❧✐♥❡ ✐' +❤❡ ✜+ ✉'✐♥❣ +❤❡ ♠♦❞❡❧ ❞❡'❝4✐❜❡❞ ✐♥

+❤❡ +❡①+✳ ❜✮ ❚②♣✐❝❛❧ ❋▼❘ '♣❡❝+4❛ ❢♦4 ❞✐✛❡4❡♥+ ❛♣♣❧✐❡❞ ✈♦❧+❛❣❡' ✭✵ ❱✱ ✶✵✵ ❱

❛♥❞ ✷✵✵ ❱✮✳ ❚❤❡ ♣♦'✐+✐✈❡ '❤✐❢+ ✐' ❝♦❤❡4❡♥+ ✇✐+❤ ❛ ♣♦'✐+✐✈❡ ♠❛❣♥❡+♦'+4✐❝+✐♦♥

❝♦❡✣❝✐❡♥+ ♦❢ ❈❋❆✳ ❝✮ ❘❡'♦♥❛♥❝❡ ✜❡❧❞ '❤✐❢+ ❛' ❢✉♥❝+✐♦♥ ♦❢ ❛♣♣❧✐❡❞ ✈♦❧+❛❣❡

+♦ +❤❡ ♣✐❡③♦❡❧❡❝+4✐❝ ❛❝+✉❛+♦4 ✐♥ +❤❡ ❝❛'❡ ♦❢ ❝②❝❧✐❝ ❡❧❡❝+4✐❝ ❧♦❛❞✐♥❣ ✭✲✷✵✵ ❱

❀ ✷✵✵ ❱✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶

✹✳✸✳✺ ❋▼❘ '♣❡❝+4❛ ❢♦4 ❜❡♥❞❡❞ '❛♠♣❧❡' ✇✐+❤ ❞✐✛❡4❡♥+ ❝✉4✈❛+✉4❡' κ = ±1/R

✭❤❡4❡ ❛❧♦♥❣ ① ❛①✐'✮✳ ❈✐4❝❧❡ '②♠❜♦❧' '❤♦✇ +❤❡ ❝✉4✈❛+✉4❡ κ ❛' ❢✉♥❝+✐♦♥ ♦❢

δH

_R

= H

_R

(κ) − H

_R

(κ = 0) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷

✹✳✸✳✻ ❆③✐♠✉+❤❛❧ ❛♥❣❧❡ ❞❡♣❡♥❞❛♥❝❡ ♦❢ +❤❡ 4❡'♦♥❛♥❝❡ ✜❡❧❞ ✐♥ ♣♦❧❛4 4❡♣4❡'❡♥+❛+✐♦♥

✇✐+❤ +❤❡ ❝♦44❡'♣♦♥❞✐♥❣ ❜❡♥❞✐♥❣ ❡✛❡❝+ ♦♥ +❤❡ '+4❡'' '+❛+❡ ✭❡✐+❤❡4 ♥❡❣❛+✐✈❡

❛✮ ♦4 ♣♦'✐+✐✈❡ ❜✮✮ ❢♦4 ❈❋❆ ✜❧♠ ♣❧❛❝❡❞ ♦♥ ❛❧✉♠✐♥✉♠ ❜❧♦❝❦ ✇✐+❤ ✸✷✳✷ ♠♠

4❛❞✐✉'✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷

✹✳✸✳✼ ❆♥❣✉❧❛4 ❞❡♣❡♥❞❛♥❝❡ ♦❢ +❤❡ 4❡'♦♥❛♥❝❡ ✜❡❧❞ ✭❛+ ✶✵ ●❍③✮ ❢♦4 R = ∞ ✭❛✮✱

R = 59.2 ♠♠ ✭❜✮✱ R = 32.2 ♠♠ ✭❝✮✱ R = 13.2 ♠♠ ✭❞✮✳ ■♥ ✜❣✉4❡' ✭❜✮✱ ✭❝✮

❛♥❞ ✭❞✮ ❛4❡ '❤♦✇♥ +❤❡ ♦♣♣♦'✐+❡ '+4❡'' '+❛+❡'✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸

✹✳✸✳✽ ❚❤❡♦4❡+✐❝❛❧ ✭✐'♦✲❛♥✐'♦+4♦♣② ✜❡❧❞ ❧✐♥❡'✮ ❛♥❞ ❡①♣❡4✐♠❡♥+❛❧ ✭'X✉❛4❡ '②♠❜♦❧'

❢♦4 ♣✐❡③♦❛❝+✉❛+✐♦♥ ❡①♣❡4✐♠❡♥+'✱ ❝✐4❝❧❡ '②♠❜♦❧' ❢♦4 ❜❡♥❞✐♥❣ ❡①♣❡4✐♠❡♥+'✮

❛♥✐'♦+4♦♣② ✜❡❧❞ H

_me

♠❛♣ ✐♥ +❤❡ ♣4✐♥❝✐♣❛❧ '+4❡'' '♣❛❝❡ ✭ σ

_xx

, σ

_yy

✮✳ ✳ ✳ ✳ ✳ ✳ ✽✹

✹✳✸✳✾ ✭❛✮ ❆♥✐'♦+4♦♣② ✜❡❧❞ H

u

❛♥❞ ✭❜✮ ❆♥✐'♦+4♦♣② ❝♦♥'+❛♥+ K

u

✱ ❛' ❢✉♥❝+✐♦♥ ♦❢

3

2

(σ

_xx

− σ

_yy

) ✳ ❑♥♦✇✐♥❣ +❤❡ ♠❛❣♥❡+✐③❛+✐♦♥ ❛+ '❛+✉4❛+✐♦♥✱ +❤❡ '❧♦♣❡ ♦❢ +❤❡

❧✐♥❡❛4 4❡❣4❡''✐♦♥ ❣✐✈❡' ❞✐4❡❝+❧② +❤❡ ♠❛❣♥❡+♦'+4✐❝+✐♦♥ ❝♦❡✣❝✐❡♥+ λ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺

✺✳✶✳✶ ❛✮ ▼♦❤4✬' ❝✐4❝❧❡ 4❡♣4❡'❡♥+❛+✐♦♥ ♦❢ +❤❡ '❤❛♣❡' ♦❢ ❝✉4✈❡❞ '✉4❢❛❝❡' ❞❡'❝4✐❜✐♥❣

❛❧❧ +❤❡ ♣♦''✐❜❧❡ ❝♦♥✜❣✉4❛+✐♦♥' ❢♦4 ✢❡①✐❜❧❡ '②'+❡♠✳ κ

_x

✱ κ

_y

❛4❡ +❤❡ ♣4✐♥❝✐✲

♣❛❧ ❝✉4✈❛+✉4❡' ✇❤✐❧❡ κ

_xy

✐' +❤❡ +✇✐'+ ♦♥❡ ✭♥❡❣❧✐❣✐❜❧❡ ❢♦4 ❛ +❤✐♥ ✜❧♠ ♦♥ ❛ '✉❜'+4❛+❡✮✳ ❜✮ ◆✉♠❡4✐❝❛❧ ♣4❡❞✐❝+✐♦♥' ♦❢ ♣4✐♥❝✐♣❛❧ ❝✉4✈❛+✉4❡' ❛+ ✇❛❢❡4 ❝❡♥✲

+❡4 ♥♦4♠❛❧✐③❡❞ ❜② +❤❡ '♠❛❧❧ ❞❡❢♦4♠❛+✐♦♥ '♣❤❡4✐❝❛❧ ❝✉4✈❛+✉4❡ ✭κ

Stoney

✮ ❛'

❛ ❢✉♥❝+✐♦♥ ♦❢ +❤❡ 4❛+✐♦ A/A

_c

✳ ❚❤❡ ♣❛4❛♠❡+❡4 A ❞❡♣❡♥❞' ♦♥ +❤❡ ✜❧♠ ❛♥❞

'✉❜'+4❛+❡ +❤✐❝❦♥❡'' ❛♥❞ ❡❧❛'+✐❝ ❝♦❡✣❝✐❡♥+'❀ ❇❡❤✐♥❞ +❤❡ ❝4✐+✐❝❛❧ ♣❛4❛♠❡+❡4 A

c

✱ κ

x

6= κ

y

❛♥❞ +❤✉' ❝②❧✐♥❞4✐❝❛❧ '❤❛♣❡ ♦❝❝✉4' ✭❜✐❢✉4❝❛+✐♦♥ ♣❤❡♥♦♠❡♥♦♥✮✳ ✽✾

✈✐✐✐

(12)

✺✳✶✳✷ ❛✮ ❋❛❝✐❧❡ ❢❛❜-✐❝❛.✐♦♥ 1❝❤❡♠❡ ♦❢ 4❉▼❙ ❜✐❧❛②❡-1 ✇✐.❤ ❛ 1♣♦♥.❛♥❡♦✉1 ❝✉-✈❛✲

.✉-❡ ❛♥❞ .❤❡ ✜❧♠1 ❛❝@✉✐-✐♥❣ 1♣❤❡-✐❝❛❧ ❛♥❞ ❝②❧✐♥❞-✐❝❛❧ ❞❡❢♦-♠❛.✐♦♥✱ ❞❡✲

♣❡♥❞✐♥❣ ♦♥ .❤❡ ✜❧♠ 1❛♠♣❧❡ 1✐③❡✳ ❚❤❡ 1♣❤❡-✐❝❛❧❧② ❞❡❢♦-♠❡❞ 1❛♠♣❧❡ ✐1

♣❤♦.♦❣-❛♣❤❡❞ ♦♥ ❛ -❡✢❡❝.✐♥❣ 1✉❜1.-❛.❡✳ ❜✮ 4❊❈❱❉ 1✐❧✐❝♦♥ ♥✐.-✐❞❡ ✜❧♠

❞❡♣♦1✐.❡❞ ♦♥ .✇♦ ❞✐✛❡-❡♥. ♣❧❛1.✐❝ 1✉❜1.-❛.❡1✳ ❚❤❡ 1✉❜1.-❛.❡ .❤✐❝❦♥❡11 ❛♥❞

.❤❡ ❝♦❡✣❝✐❡♥. ♦❢ .❤❡ .❤❡-♠❛❧ ❡①♣❛♥1✐♦♥ ❛-❡ 1❤♦✇♥ ❢♦- ❡❛❝❤ 1✉❜1.-❛.❡✳ ❚❤❡

✜❧♠ ✐1 ❞❡♣♦1✐.❡❞ ♦♥ .❤❡ .♦♣ ❛♥❞ .❤❡ 1.-✉❝.✉-❡1 -♦❧❧ ✐♥.♦ ❝②❧✐♥❞❡-✳ ✳ ✳ ✳ ✳ ✳ ✽✾

✺✳✷✳✶ ❆♥❣✉❧❛- ❞❡♣❡♥❞❛♥❝❡ ♦❢ .❤❡ -❡1♦♥❛♥❝❡ ✜❡❧❞ ❛1 ❛ ❢✉♥❝.✐♦♥ ♦❢ ✐♥✲♣❧❛♥❡ ❛♥❣❧❡

❢♦- .❤❡ ❞✐✛❡-❡♥. ✜❧♠1✿ Co

40

Fe

40

B

20

✭❣-❡❡♥✮✱ Ni

80

Fe

20

✭❜❧✉❡✮✱ ❋✐♥❡♠❡. ➤

✭♠❛❣❡♥.❛✮✱ Co

₂

FeAl ✭-❡❞✮ ❛♥❞ ◆✐ ✭❜❧❛❝❦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶

✺✳✷✳✷ ❆♥❣✉❧❛- ❞❡♣❡♥❞❛♥❝❡ ♦❢ .❤❡ -❡1♦♥❛♥❝❡ ✜❡❧❞ ❛1 ❛ ❢✉♥❝.✐♦♥ ♦❢ ✐♥✲♣❧❛♥❡ ❛♥❣❧❡

❢♦-✿ ✭❛✮ ✷✵✵ ♥♠ ◆✐ .❤✐♥ ✜❧♠ ♦♥ ❑❛♣.♦♥➤ ❛♥❞ ❙✐❀ ✭❜✮ ❋✐♥❡♠❡.➤ ♦♥

❑❛♣.♦♥➤ ❛♥❞ ❙✐✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷

✺✳✸✳✶ ❘❡1♦♥❛♥❝❡ ✜❡❧❞ 1❤✐❢. ✈❛-✐❛.✐♦♥1 ❛1 ❛ ❢✉♥❝.✐♦♥ ♦❢ .❤❡ ❛♣♣❧✐❡❞ ✈♦❧.❛❣❡ ✭❛✮ ❛♥❞

.❤❡ ❛♣♣❧✐❡❞ 1.-❡11 ✭❜✮ ❢♦- Co

40

Fe

40

B

20

✭-❡❞ 1②♠❜♦❧1✮ ❛♥❞ Ni

80

Fe

20

✭❜❧✉❡

1②♠❜♦❧1✮✳ ❙♦❧✐❞ ❧✐♥❡1 -❡❢❡- .♦ .❤❡ ❛❞❥✉1.✐♥❣ ♠♦❞❡❧1 ❢♦- .❤❡ .✇♦ 1❛♠♣❧❡1✳

❚❤❡ ✐♥1❡-. ✐♥ ✭❛✮ ✐1 ❛ ③♦♦♠ ♦❢ .❤❡ Ni

₈₀

Fe

₂₀

❝✉-✈❡✱ ✇❤✐❧❡ .❤❡ ♦♥❡ ✐♥ ✭❜✮

✐1 .❤❡ ♠❡❛1✉-❡❞ ✈❛-✐❛.✐♦♥ ♦❢ .❤❡ ✐♥✲♣❧❛♥❡ 1.-❛✐♥1 ✭ε

xx

❛♥❞ ε

yy

❛. .❤❡ .♦♣

1✉-❢❛❝❡ ♦❢ .❤❡ ✜❧♠1✮ ❛1 ❛ ❢✉♥❝.✐♦♥ ♦❢ .❤❡ ❛♣♣❧✐❡❞ ✈♦❧.❛❣❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸

✺✳✸✳✷ 4❤♦.♦❣-❛♣❤② ♦❢ ✜✈❡ Ni

₈₀

Fe

₂₀

1❛♠♣❧❡1 ✇✐.❤ 1❡✈❡-❛❧ .❤✐❝❦♥❡11❡1 ✭✷✵♥♠✱

✶✵✵♥♠✱ ✷✵✵♥♠✱ ✸✵✵♥♠ ❛♥❞ ✹✵✵♥♠✮ 1❤♦✇✐♥❣ ✐♥❝-❡❛1✐♥❣ ❝②❧✐♥❞-✐❝❛❧ ❜❡♥❞✐♥❣

✇✐.❤ .❤✐❝❦♥❡11✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹

✺✳✸✳✸ ❆♥❣✉❧❛- ❛♥❞ ✈♦❧.❛❣❡ ❞❡♣❡♥❞❡♥❝❡1 ♦❢ .❤❡ -❡1♦♥❛♥❝❡ ✜❡❧❞ ✭❛. f = 10 ●❍③✮

❢♦- .❤❡ Ni

80

Fe

20

✭♦♣❡♥ ❝✐-❝❧❡1✮ ❛♥❞ Co

40

Fe

40

B

20

✭1♣❤❡-❡1✮ .❤✐♥ ✜❧♠1✳ ❚❤❡

1♦❧✐❞ ❧✐♥❡1 ❛-❡ ✜. .♦ .❤❡ ❡①♣❡-✐♠❡♥.❛❧ ❞❛.❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺

✻✳✶✳✶ ❊①♣❡-✐♠❡♥.❛❧ ❛♥❞ .❤❡♦-❡.✐❝❛❧ ❇-✐❧❧♦✉✐♥ 1♣❡❝.-❛ ♦❢ ❛ ✷✺✵ ♥♠ .❤✐❝❦ ❛♠♦-✲

♣❤♦✉1 ❈❋❇ .❤✐♥ ❧❛②❡- ❞❡♣♦1✐.❡❞ ♦♥.♦ ❑❛♣.♦♥➤✳ ❚❤❡ ❜❧✉❡ ✭-❡1♣✳ -❡❞✮

❧✐♥❡ ❝♦--❡1♣♦♥❞1 .♦ .❤❡ ❡①♣❡-✐♠❡♥.❛❧ ✭-❡1♣✳ .❤❡♦-❡.✐❝❛❧✮ 1♣❡❝.-✉♠✳ ❇♦.❤

❘❛②❧❡✐❣❤ ✭ R ✮ ❛♥❞ ❙❡③❛✇❛ ♣❡❛❦1 ✭ S

₁

❛♥❞ S

₂

✮ ❝❛♥ ❜❡ ♦❜1❡-✈❡❞✳ ❚❤❡ 1❦❡.❝❤

✐❧❧✉1.-❛.❡1 .❤❡ ❜❛❝❦✲1❝❛..❡-✐♥❣ ❣❡♦♠❡.-② ✉1❡❞ ✐♥ .❤❡ ♣-❡1❡♥. ❡①♣❡-✐♠❡♥.✳

❚❤❡ .-❛♥1❢❡--❡❞ ✇❛✈❡✲✈❡❝.♦- ✐1 ✜①❡❞ .♦ k

_k

= 2.14 × 10

⁵

❝♠

⁻¹

✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶

✻✳✶✳✷ ❋▼❘ 1♣❡❝.-❛ ♠❡❛1✉-❡❞ ❛. ❞✐✛❡-❡♥. 1.-❡11❡1 1.❛.❡1 ✇✐.❤ ❛♥ ❛♣♣❧✐❡❞ ♠❛❣✲

♥❡.✐❝ ✜❡❧❞ ❛❧♦♥❣ .❤❡ ❛♣♣❧✐❡❞ 1.-❡11✳ ❚❤❡ .❡♥1✐❧❡ 1.-❡11 ✭ +0.75 ●4❛✮ ❧❡❛❞1 .♦ ❛ ♣♦1✐.✐✈❡ 1❤✐❢. ✇❤✐❧❡ .❤❡ ❝♦♠♣-❡11✐✈❡ 1.-❡11 ✭−0.75 ●4❛✮ ❧❡❛❞1 .♦ ❛

♥❡❣❛.✐✈❡ ♦♥❡✳ ❚❤❡ 1♣❡❝.-❛ ❤❛✈❡ ❜❡❡♥ ✈❡-.✐❝❛❧❧② 1❤✐❢.❡❞ ❢♦- ❛ ❜❡..❡- ❝♦♠✲

♣-❡❤❡♥1✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷

✻✳✶✳✸ ❆♥❣✉❧❛- ❞❡♣❡♥❞❡♥❝✐❡1 ♦❢ .❤❡ ✉♥✐❢♦-♠ ♠♦❞❡ -❡1♦♥❛♥❝❡ ✜❡❧❞ ❢♦- .❤❡ ✭❛✮ ✷✵

♥♠ ✭✇✐.❤ f = 9.5 ●❍③✮✱ ✭❜✮ ✷✺✵ ♥♠ ✭✇✐.❤ f = 8 ●❍③✮ ❛♥❞ ✭❝✮ ✶✵ ♥♠

✭✇✐.❤ f = 8 ●❍③✮ ✜❧♠1✳ ❚❤❡ ❢-❡@✉❡♥❝② ❞❡♣❡♥❞❡♥❝❡ ♦❢ .❤❡ ✉♥✐❢♦-♠ ♠♦❞❡ ✐1

♣-❡1❡♥.❡❞ ✐♥ ✭❞✮ ❢♦- .❤❡ ✷✵ ♥♠✲.❤✐❝❦ ✜❧♠ ❛❧♦♥❣ .❤❡ ❡❛1② ❛♥❞ ❤❛-❞ ❛①✐1 ✭✾✵

❞❡❣✳ ❛♥❞ ✵ ❞❡❣✳✮ ✇❤❡♥ ❛♣♣❧②✐♥❣ ❛ .❡♥1✐❧❡ 1.-❡11 ✭❜❧✉❡ ❛♥❞ -❡❞ 1②♠❜♦❧1✮✳

■♥ ❛❧❧ ❣-❛♣❤1✱ .❤❡ ❢✉❧❧ ❧✐♥❡1 ❛-❡ ❜❡1. ✜.1 .♦ .❤❡ ❡①♣❡-✐♠❡♥.❛❧ ❞❛.❛ ❜② ✉1✐♥❣

❡@✉❛.✐♦♥1 ♣-❡1❡♥.❡❞ ✐♥ ❝❤❛♣.❡- ✹✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸

✐①

(13)

✻✳✶✳✹ ❛✮ ❊✛❡❝✐✈❡ ❛♥✐.♦0♦♣② ✜❡❧❞ H

_u

✈❛0✐❛✐♦♥ ❛. ❢✉♥❝✐♦♥ ♦❢ ❤❡ ❛♣♣❧✐❡❞ .0❡..✳

❜✮ ❱❛0✐❛✐♦♥ ♦❢ ❤❡ ❡✛❡❝✐✈❡ ❛♥✐.♦0♦♣② ❝♦♥.❛♥ ✭ K

_u

✮ ❛. ❛ ❢✉♥❝*✐♦♥ ♦❢

*❤❡

³₂

σ❀ ❤❡ ❧✐♥❡❛0 ✜ .❧♦♣❡ ❞✐0❡❝❧② ❣✐✈❡. ❤❡ ♠❛❣♥❡♦.0✐❝✐♦♥ ❝♦❡✣❝✐❡♥

λ = 22.5 × 10

⁻⁶

✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹

✻✳✶✳✺ ❆♥❣✉❧❛0 ❞❡♣❡♥❞❡♥❝❡ ♦❢ ❤❡ 0❡.♦♥❛♥❝❡ ✜❡❧❞ ❢♦0 ❤❡ ✷✵ ♥♠ *❤✐❝❦ ✜❧♠✳ ❙②♠✲

❜♦❧. ❛0❡ ❡①♣❡0✐♠❡♥❛❧ ❞❛❛ ✇❤✐❧❡ ❢✉❧❧ ❧✐♥❡. ❛0❡ ❝❛❧❝✉❧❛❡❞ ❤❛♥❦. ♦ ❤❡

❛♥❛❧②✐❝❛❧ ♠♦❞❡❧.✳ ❇❧❛❝❦ ♦♣❡♥ ❝✐0❝❧❡. ❛0❡ ❞❛❛ ❢0♦♠ ❤❡ ❜❡♥❝❤♠❛0❦ .❛*❡

✇❤✐❧❡ ❤❡ 0❡❞ ♦♥❡. ❝♦00❡.♣♦♥❞ ♦ ❤❡ ❡①♣❡0✐♠❡♥❛❧ ❡J✉✐❜✐❛①✐❛❧ .❛❡ ✭✇✐*❤

σ ≃ 0.78 ●L❛✮✳ ❚❤❡ ❜❧✉❡ ❝✐0❝❧❡. ❛0❡ ♠❡❛.✉0❡♠❡♥*. ❝♦♠✐♥❣ ❢0♦♠ ✉♥✐❛①✲

✐❛❧ ❜❡♥❞✐♥❣ ✇✐❤ ❛ ✉♥✐❛①✐❛❧ .0❡.. ✭ σ

_xx

≃ 0.75 ●L❛✮ ❝♦♠♣❛0❛❜❧❡ ♦ ❤❡

❡J✉✐❜✐❛①✐❛❧ σ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻

✻✳✷✳✶ ❛✮ ❚②♣✐❝❛❧ ❇▲❙ .♣❡❝0❛ ♦❢ ❤❡ ✷✺✵ ♥♠✲❈❋❇ ✜❧♠. ❛♥♥❡❛❧❡❞ ❛* ❞✐✛❡0❡♥*

❡♠♣❡0❛✉0❡ ♦❜❛✐♥❡❞ ✇✐❤ ❛♥ ✐♥❝✐❞❡♥* ❛♥❣❧❡ ξ = 65 ➦✳ ❜✮ ❋0❡J✉❡♥❝② ✈❛0✐✲

❛✐♦♥. ♦❢ ❤❡ ❘❛②❧❡✐❣❤ ❛♥❞ ♦❢ ❤❡ ✜0. ❙❡③❛✇❛ ♠♦❞❡. ❛. ❢✉♥❝✐♦♥ ♦❢ ❤❡

❛♥♥❡❛❧✐♥❣ ❡♠♣❡0❛✉0❡✳ ❝✲❞✮ ❨♦✉♥❣✬. ♠♦❞✉❧✉. Y ✭❝✮ ❛♥❞ L♦✐.♦♥✬. 0❛*✐♦

ν ✭❞✮ ✈❛0✐❛✐♦♥. ❛. ❢✉♥❝✐♦♥ ♦❢ ❤❡ ❛♥♥❡❛❧✐♥❣ ❡♠♣❡0❛*✉0❡✳ ❚❤❡ ❧✐♥❡. ✐♥

✜❣✉0❡. ❜✮✱ ❝✮ ❛♥❞ ❞✮ ❛0❡ ❣✉✐❞❡❞ ❢♦0 *❤❡ ❡②❡.✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼

✻✳✷✳✷ ❛✮ ❚②♣✐❝❛❧ 0❡.♦♥❛♥❝❡ ✜❡❧❞ ❛♥❣✉❧❛0 ❞❡♣❡♥❞❡♥❝✐❡. ♦❢ ❤❡ ❛. ❞❡♣♦.✐❡❞ ❛♥❞ ❛♥✲

♥❡❛❧❡❞ ✜❧♠. ✭✶✵✵➦❈✱ ✸✵✵➦❈ ❛♥❞ ✸✺✵➦❈✮✳ ❜✮ ❊✈♦❧✉✐♦♥ ♦❢ ❤❡ ✐♥✐✐❛❧ ❛♥✐.♦0♦♣②

✜❡❧❞ H

_u

❛. ❢✉♥❝✐♦♥ ♦❢ ❤❡ ❛♥♥❡❛❧✐♥❣ ❡♠♣❡0❛✉0❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽

✻✳✷✳✸ ❙❛✉0❛✐♦♥ ♠❛❣♥❡✐③❛✐♦♥ M

s

✲❛✮ ❛♥❞ ♠❛❣♥❡♦.0✐❝✐♦♥ ❝♦❡✣❝✐❡♥ λ✲❜✮ ✈❛0✐✲

❛✐♦♥. ❛. ❢✉♥❝✐♦♥ ❤❡ ❛♥♥❡❛❧✐♥❣ ❡♠♣❡0❛✉0❡✳ ❝✮ ❊✈♦❧✉✐♦♥ ♦❢ *❤❡ ♥♦0♠❛❧✲

✐③❡❞ ✈❛❧✉❡ ♦❢ ❤❡ ❨♦✉♥❣✬. ♠♦❞✉❧✉. Y ✱ ❤❡ L♦✐..♦♥✬. 0❛✐♦ ν ✱ ❤❡ ✐♥✐*✐❛❧

❛♥✐.♦*0♦♣② ✜❡❧❞ H

u

❛♥❞ ❤❡ ♠❛❣♥❡♦.0✐❝✐♦♥ ❝♦❡✣❝✐❡♥* λ ❛. ❢✉♥❝*✐♦♥ ♦❢

❤❡ ❛♥♥❡❛❧✐♥❣ ❡♠♣❡0❛✉0❡✳ ■♥ ❛❧❧ ❣0❛♣❤.✱ ❧✐♥❡. ❛0❡ ❣✉✐❞❡ ❢♦0 ❤❡ ❡②❡.✳ ✳ ✳ ✶✵✾

✻✳✷✳✹ L❤♦♦❣0❛♣❤② ♦❢ ❤0❡❡ ❈❋❇ .❛♠♣❧❡. ❛♥♥❡❛❧❡❞ ❛* ❞✐✛❡0❡♥* ❡♠♣❡0❛✉0❡

✭✶✵✵➦❈✱ ✷✵✵➦❈ ❛♥❞ ✸✵✵➦❈✮ .❤♦✇✐♥❣ ✐♥❝0❡❛.✐♥❣ ❝②❧✐♥❞0✐❝❛❧ ❜❡♥❞✐♥❣ ✇✐*❤

❛♥♥❡❛❧✐♥❣ ❡♠♣❡0❛✉0❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾

✼✳✶✳✶ ❜✮ ❙✇❡❡♣ ✜❡❧❞ ❋▼❘ ❡①♣❡0✐♠❡♥✱ ❤❡ ❞0✐✈✐♥❣ ❢0❡J✉❡♥❝② ✐. ❝♦♥.❛♥ ❛♥❞ *❤❡

0❡.♦♥❛♥❝❡ ✐. ♣0♦❜❡❞ ❜② .✇❡❡♣✐♥❣ ❤❡ ❛♣♣❧✐❡❞ ♠❛❣♥❡✐❝ ✜❡❧❞ ❛0♦✉♥❞ *❤❡ 0❡.✲

♦♥❛♥❝❡ ✜❡❧❞✳ ❉✉0✐♥❣ ❤✐. .❝❛♥✱ ❛ J✉❛.✐✲.❛✐❝ 0♦❛✐♦♥ ♦❢ ❤❡ ♠❛❣♥❡✐③❛✐♦♥

♦❝❝✉0.✳ ❜✮ ❙✇❡❡♣ ❢0❡J✉❡♥❝② ❋▼❘ ❡①♣❡0✐♠❡♥✱ ❤❡ ❛♣♣❧✐❡❞ ♠❛❣♥❡*✐❝ ✜❡❧❞

✐. ✜①❡❞ ❛♥❞ ❤❡ 0❡.♦♥❛♥❝❡ ✐. ♣0♦❜❡❞ ❜② .❝❛♥♥✐♥❣ ❤❡ ❞0✐✈✐♥❣ ❢0❡J✉❡♥❝②✳

❉✉0✐♥❣ ❤✐. .❝❛♥✱ ❤❡ ♠❛❣♥❡✐③❛✐♦♥ ❞✐.0✐❜✉✐♦♥ ✐. ♥♦* ♣❡0*✉❜❡❞✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹

✼✳✷✳✶ ❛✮ ❙✇❡❡♣✲❢0❡J✉❡♥❝② ❋▼❘ .♣❡❝0❛ ♦❜❛✐♥❡❞ ❛❝❝♦0❞✐♥❣ ♦ ❤❡ *✇♦ ❝♦♥✜❣✲

✉0❛✐♦♥. ❞❡♣✐❝❡❞ ✐♥ ❜✮ ❛♥❞ ❝✮ ✇❤❡0❡ P

_in

❛♥❞ P

_out

❛0❡ ❤❡ ✐♥❥❡❝❡❞ ❛♥❞

*0❛♥.♠✐**❡❞ 0❛❞✐♦ ❢0❡J✉❡♥❝② ❝✉00❡♥✳ ❚❤❡ ♦♥❧② ❞✐✛❡0❡♥❝❡ ❝♦♠❡. ❢0♦♠ ❤❡

♣✉♠♣✐♥❣ ✜❡❧❞ ✭ ~h

rf

✮ ✇❤✐❝❤ ❡✐*❤❡0 ♣❛0❛❧❧❡❧ ✭0❡❞ .J✉❛0❡.✮ ♦0 ♣❡0♣❡♥❞✐❝✉❧❛0

✭❜❧✉❡ ❝✐0❝❧❡.✮ ♦ M ~ ❞✐0❡❝✐♦♥ ❣✐✈✐♥❣ 0✐.❡ ♦ ❤❡ ❤✐❣❤ ❛♥❞ ❧♦✇ .❡♥.✐✐✈✐✐❡.

❣❡♦♠❡0✐❡.✳ ❚❤❡ ✐♥.❡ .❤♦✇. ❛ ③♦♦♠ ♦❢ ❤❡ ♠❛0❦❡❞ ❛0❡❛✳ ◆♦❡ ❤❛ ❛ .❛✉0❛✐♥❣ ✜❡❧❞ ♦❢ ✺✵✵ ❖❡ ✇❛. ❛♣♣❧✐❡❞ ♦ ❡♥.✉0❡ ❛ ✉♥✐❢♦0♠ ♠❛❣♥❡✐③❛*✐♦♥

❞✐.0✐❜✉✐♦♥✳ ❚❤❡ .♦❧✐❞ ❧✐♥❡. .❤♦✇ ✜. ♦ ❤❡ ✜0. ❞❡0✐✈❛✐✈❡ ♦❢ ❤❡ .*❛♥❞❛0❞

▲♦0❡♥*③✐❛♥ ❝✉0✈❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺

①

Films minces magnétiques sur substrat flexible : Etude des effets magnéto-mécaniques par résonance ferromagnétique

HAL Id: tel-01730578

https://tel.archives-ouvertes.fr/tel-01730578

Submitted on 13 Mar 2018

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des effets magnéto-mécaniques par résonance ferromagnétique

Mouhamadou Gueye

To cite this version:

Mouhamadou Gueye. Films minces magnétiques sur substrat flexible : Etude des effets magnéto-

mécaniques par résonance ferromagnétique. Mechanics of materials [physics.class-ph]. Université

Sorbonne Paris Cité, 2017. English. �NNT : 2017USPCD007�. �tel-01730578�

T H E S E Doctorat de physique

TH ` ESE

pour obtenir le grade de docteur d´ elivr´ e par

l’Universit´ e Paris XIII

Sp´ ecialit´ e “Science des Mat´ eriaux”

pr´ esent´ ee par

Mouhamadou Gueye

soutenue le 27 Mars 2017

Magnetic thin films on flexible substrates:

magnetomechanical study by ferromagnetic resonance

Jury

Mme. Alexandra Mougin Rapporteur M. Vincent Repain Rapporteur M. Mohamed Belmeguenai Examinateur M. Manuel Bibes Examinateur M. Damien Faurie Examinateur M. Philippe Goudeau Examinateur M. Michel Viret Examinateur M. Fatih Zighem Examinateur

Universit´ e Paris XIII

Laboratoire des Sciences des Proc´ ed´ es et des Mat´ eriaux (LSPM)

UPR CNRS 3407, 99 avenue J. B. Cl´ ement, 93430 Villetaneuse, France

T H E S E Doctorat de physique

TH ` ESE

pour obtenir le grade de docteur d´ elivr´ e par

l’Universit´ e Paris XIII

Sp´ ecialit´ e “Science des Mat´ eriaux”

pr´ esent´ ee par

Mouhamadou Gueye

soutenue le 27 Mars 2017

Magnetic thin films on flexible substrates:

magnetomechanical study by ferromagnetic resonance

Jury

Mme. Alexandra Mougin Rapporteur M. Vincent Repain Rapporteur M. Mohamed Belmeguenai Examinateur M. Manuel Bibes Examinateur M. Damien Faurie Examinateur M. Philippe Goudeau Examinateur M. Michel Viret Examinateur M. Fatih Zighem Examinateur

Universit´ e Paris XIII

Laboratoire des Sciences des Proc´ ed´ es et des Mat´ eriaux (LSPM)

UPR CNRS 3407, 99 avenue J. B. Cl´ ement, 93430 Villetaneuse, France

❆❝❦♥♦✇❧❡❞❣♠❡♥+, ①✐✐✐

■♥+0♦❞✉❝+✐♦♥ ✶

❇✐❜❧✐♦❣0❛♣❤② ✶✶

✶ ❋✉♥❞❛♠❡♥+❛❧ ❝♦♥❝❡♣+, ✐♥ ♠❛❣♥❡+✐,♠ ✶✸

✶✳✶ ▼❛❣♥❡'✐❝ ✐♥'❡*❛❝'✐♦♥, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸

✶✳✶✳✶ ▼❛❣♥❡'✐❝ ❞✐♣♦❧❛* ✐♥'❡*❛❝'✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸

✶✳✶✳✷ ❊①❝❤❛♥❣❡ ✐♥'❡*❛❝'✐♦♥, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹

✶✳✶✳✷✳✶ ❉✐*❡❝' ❡①❝❤❛♥❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹

✶✳✶✳✷✳✷ ■♥❞✐*❡❝' ❡①❝❤❛♥❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✶✳✷ ▼❛❣♥❡'✐❝ ❛♥✐,♦'*♦♣② ❡✛❡❝', ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✶✳✷✳✶ ▼❛❣♥❡'♦❝*②,'❛❧❧✐♥❡ ❛♥✐,♦'*♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✶✳✷✳✶✳✶ ❯♥✐❛①✐❛❧ ❛♥✐,♦'*♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✶✳✷✳✶✳✷ ❈✉❜✐❝ ❛♥✐,♦'*♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼

✶✳✷✳✷ ❙❤❛♣❡ ❛♥✐,♦'*♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✶✳✷✳✸ ▼❛❣♥❡'♦❡❧❛,'✐❝ ❛♥✐,♦'*♦♣② ❛♥❞ ♠❛❣♥❡'♦,'*✐❝'✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✶✳✸ ▼❛❣♥❡'✐③❛'✐♦♥ ❉②♥❛♠✐❝, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

✶✳✸✳✶ ▲❛♥❞❛✉ ▲✐❢,❝❤✐'③ ●✐❧❜❡*' ✭▲▲●✮ ❡K✉❛'✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

✶✳✸✳✷ ▼❛❣♥❡'✐❝ ,✉,❝❡♣'✐❜✐❧✐'② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

✶✳✸✳✷✳✶ ▲♦,,❧❡,, ▼❛❣♥❡'✐❝ ❙✉,❝❡♣'✐❜✐❧✐'② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

✶✳✸✳✷✳✷ ▲♦,,② ♠❛❣♥❡'✐❝ ,✉,❝❡♣'✐❜✐❧✐'② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻

✶✳✹ ❙♣✐♥ ✇❛✈❡, ♠♦❞❡, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

✶✳✹✳✶ ❯♥✐❢♦*♠ ♣*❡❝❡,,✐♦♥ ♠♦❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

✶✳✹✳✷ ▼❛❣♥❡'♦,'❛'✐❝ ,♣✐♥ ✇❛✈❡, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✶✳✹✳✸ ❙'❛♥❞✐♥❣ ,♣✐♥ ✇❛✈❡, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

✶✳✹✳✹ ❘❡❧❛①❛'✐♦♥ ♠❡❝❤❛♥✐,♠, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

✶✳✹✳✹✳✶ ■♥'*✐♥,✐❝ ♠❡❝❤❛♥✐,♠, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

✶✳✹✳✹✳✷ ❊①'*✐♥,✐❝ ♠❡❝❤❛♥✐,♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

❇✐❜❧✐♦❣0❛♣❤② ✸✻

✷ ▼❡❝❤❛♥✐❝❛❧ +❡,+✐♥❣ ✸✽

✷✳✶ ❇❛,✐❝, ✐♥ ❡❧❛,'✐❝✐'② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✷✳✶✳✶ ❙'*❡,, ❛♥❞ ❙'*❛✐♥, ✐♥ ,♦❧✐❞, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✷✳✶✳✷ ❊❧❛,'✐❝✐'② ✐♥ ,✐♥❣❧❡ ❝*②,'❛❧✿ '❤❡ ❝✉❜✐❝ ❝❛,❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

✷✳✷ ❊❧❛,'✐❝✐'② ✐♥ ♣♦❧②❝*②,'❛❧, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶

✐

✷✳✸ ❊①♣❡'✐♠❡♥+❛❧ ❞❡/✐❣♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✷✳✸✳✶ ❇❡♥❞✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✷✳✸✳✶✳✶ ❯♥✐❛①✐❛❧ ❇❡♥❞✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✷✳✸✳✶✳✷ ❊5✉✐❜✐❛①✐❛❧ ❜❡♥❞✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✶✳✷✳✶ ▼❛❣♥❡'♦❝②,'❛❧❧✐♥❡ ❛♥✐,♦'♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✶✳✷✳✸ ▼❛❣♥❡'♦❡❧❛,'✐❝ ❛♥✐,♦'♦♣② ❛♥❞ ♠❛❣♥❡'♦,'✐❝'✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✶✳✹✳✶ ❯♥✐❢♦♠ ♣❡❝❡,,✐♦♥ ♠♦❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

✷✳✶✳✶ ❙'❡,, ❛♥❞ ❙'❛✐♥, ✐♥ ,♦❧✐❞, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✺✳✷ ❘❡✐❞✉❛❧ ♠❛❣♥❡3✐❝ ❛♥✐♦3$♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵

✺✳✸ ❖$✐❣✐♥ ♦❢ 3❤❡ $❡✐❞✉❛❧ ♠❛❣♥❡3✐❝ ❛♥✐♦3$♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷

✻✳✶ ❆* ❞❡♣♦✐3❡❞ ✜❧♠✿ ❡❧❛3✐❝✱ ♠❛❣♥❡3✐❝ ❛♥❞ ♠❛❣♥❡3♦✲❡❧❛3✐❝ ♣$♦♣❡$3✐❡ ✳ ✳ ✳ ✳ ✾✾

✻✳✶✳✶ ❊❧❛3✐❝ ♣$♦♣❡$3✐❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵

✻✳✶✳✷ ▼❛❣♥❡3✐❝ ❛♥❞ ♠❛❣♥❡3♦✲❡❧❛3✐❝ ♣$♦♣❡$3✐❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶

✻✳✷✳✷ ▼❛❣♥❡3✐❝ ❛♥❞ ♠❛❣♥❡3♦✲❡❧❛3✐❝ ♣$♦♣❡$3✐❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽

✼✳✸ ❊①♣❡$✐♠❡♥3❛❧ $❡✉❧3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼