suppl. mat. for magnon wf law
TRANSCRIPT
Suppl. Mat. for magnon WF law
Kouki Nakata
All the responsibilities rest with Kouki Nakata
K
−
Charge
Heat
Thermal Conductivity 𝑲 ≈ 𝑳𝟐𝟐 for Fermions
Seebeck & Peltier
WF law （Low temp.）
?
Electron = Fermion Magnon = Boson Textbook by Ashcroft & Mermin
Lorenz number =
= =
=
? ?
?
−
Magnon
Heat
Thermal Conductivity 𝑲 ≠ 𝑳𝟐𝟐 for Magnons Nakata, Simon, and Loss, Phys. Rev. B 92, 134425 (2015)
Seebeck & Peltier
WF law （Low temp.）
?
?
Electron = Fermion Magnon = Boson Textbook by Ashcroft & Mermin
Lorenz number =
= =
=
K
? ?
−
Magnon
Heat
Thermal Conductivity 𝑲 ≠ 𝑳𝟐𝟐 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
!
𝐈𝑄 = 𝐿21𝜵𝐵∗ − 𝐿22𝜵𝑇 = −(𝐿22 − 𝐿21𝐿12/𝐿11)𝜵𝑇
Thermal conductivity 𝑲: 𝐈𝑄 ≡ −𝐾 ∙ 𝜵𝑇 with !
𝐈m = 0
K Note:
K
⓪Thermal gradient 𝜵𝑇