Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons...

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Modelo de Stoner para o Ferromagnetismo metálico

Transcript of Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons...

Page 1: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this

Modelo de Stoner para o Ferromagnetismo metálico

Page 2: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this
Page 3: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this
Page 4: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this

Modelo de Stoner: Dependência com a Temperatura

Page 5: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this
Page 6: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this
Page 7: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this

Lei de Curie-Weiss

Page 8: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this

Magnetismo Localizado (Modelo de Heisenberg)

Interação de Troca

Acoplamento dipolar com campo externo

Hamiltoniano não linear → difícil diagonalização

Aproximação de campo médio:

Page 9: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this

Para um material ferromagnético, todos os spins têm valores médios idênticos:

Além disso:

Page 10: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this
Page 11: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this

Solução é equivalente ao caso de magnetismo metálico !!

Page 12: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this

Lei de Curie-Weiss (de novo !)

Page 13: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this

Antiferromagnetismo

Page 14: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this

Através de um tratamento similar ao caso ferromagnético:

M+ → 0 para

Page 15: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this

Para T > TN:

Lei de Curie-Weiss (de novo !)

Page 16: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this
Page 17: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this
Page 18: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this
Page 19: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this

Ondas de Spin

Page 20: Modelo de Stoner para o Ferromagnetismo metálico · edge of the d-band of majority spin electrons and the Fermi energy is known as the Stoner gap. In the bandstructure picture, this

Magnetização de uma amostra ferromagnética


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