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Suppl. Mat. for magnon WF law
Kouki Nakata
All the responsibilities rest with Kouki Nakata
K
−
Charge
Heat
Thermal Conductivity 𝑲 ≈ 𝑳 𝟐𝟐
for Fermions
Seebeck &
Peltier
WF law
(Low temp.)
?
Electron = Fermion Magnon = BosonTextbook by
Ashcroft & Mermin
Lorenz
number =
= =
=
? ?
?
−
Magnon
Heat
Thermal Conductivity 𝑲 ≠ 𝑳 𝟐𝟐
for Magnons
Nakata, Simon, and Loss, Phys. Rev. B 92, 134425 (2015)
Seebeck &
Peltier
WF law
(Low temp.)
?
?
Electron = Fermion Magnon = BosonTextbook by
Ashcroft & Mermin
Lorenz
number =
= =
=
K
? ?
−
Magnon
Heat
Thermal Conductivity 𝑲 ≠ 𝑳 𝟐𝟐
for Magnons
Nakata, Simon, and Loss, Phys. Rev. B 92, 134425 (2015)
Textbook by Ashcroft & Mermin Eq. (13.56): K is measured under conditions of no quasi-particle current
①Magnons flow 𝐈m = −𝐿12
𝜵𝑇  ②Magnon accumulation: Magnetization gradient 𝜵𝐵
③Counter current 𝐈m = 𝐿11 𝜵𝐵  ④A new quasi-equilibrium state 𝐈m = 0 in 𝜵𝐵∗: Measured
𝐈m = 𝐿11 𝜵𝐵 − 𝐿12 𝜵𝑇 = 0  𝜵𝐵∗ =
𝐿12
𝐿11 𝜵𝑇
!
𝐈 𝑄 = 𝐿21
𝜵𝐵∗
− 𝐿22
𝜵𝑇 = −(𝐿22
− 𝐿21
𝐿12
/𝐿11
)𝜵𝑇
Thermal conductivity 𝑲: 𝐈 𝑄 ≡ −𝐾 ∙ 𝜵𝑇 with
!
𝐈m = 0
KNote:
K
⓪Thermal gradient 𝜵𝑇

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Suppl. Mat. for magnon WF law

  • 1. Suppl. Mat. for magnon WF law Kouki Nakata All the responsibilities rest with Kouki Nakata
  • 2. K − Charge Heat Thermal Conductivity 𝑲 ≈ 𝑳 𝟐𝟐 for Fermions Seebeck & Peltier WF law (Low temp.) ? Electron = Fermion Magnon = BosonTextbook by Ashcroft & Mermin Lorenz number = = = = ? ? ?
  • 3. − Magnon Heat Thermal Conductivity 𝑲 ≠ 𝑳 𝟐𝟐 for Magnons Nakata, Simon, and Loss, Phys. Rev. B 92, 134425 (2015) Seebeck & Peltier WF law (Low temp.) ? ? Electron = Fermion Magnon = BosonTextbook by Ashcroft & Mermin Lorenz number = = = = K ? ?
  • 4. − Magnon Heat Thermal Conductivity 𝑲 ≠ 𝑳 𝟐𝟐 for Magnons Nakata, Simon, and Loss, Phys. Rev. B 92, 134425 (2015) Textbook by Ashcroft & Mermin Eq. (13.56): K is measured under conditions of no quasi-particle current ①Magnons flow 𝐈m = −𝐿12 𝜵𝑇  ②Magnon accumulation: Magnetization gradient 𝜵𝐵 ③Counter current 𝐈m = 𝐿11 𝜵𝐵  ④A new quasi-equilibrium state 𝐈m = 0 in 𝜵𝐵∗: Measured 𝐈m = 𝐿11 𝜵𝐵 − 𝐿12 𝜵𝑇 = 0  𝜵𝐵∗ = 𝐿12 𝐿11 𝜵𝑇 ! 𝐈 𝑄 = 𝐿21 𝜵𝐵∗ − 𝐿22 𝜵𝑇 = −(𝐿22 − 𝐿21 𝐿12 /𝐿11 )𝜵𝑇 Thermal conductivity 𝑲: 𝐈 𝑄 ≡ −𝐾 ∙ 𝜵𝑇 with ! 𝐈m = 0 KNote: K ⓪Thermal gradient 𝜵𝑇