Table 2 Non-vanishing components of transverse conductivity

From: Phonon-mediated spin transport in quantum paraelectric metals

i

j

α

\({\sigma }_{ij}^{\alpha }({{{\boldsymbol{q}}}})={[{\sigma }_{ji}^{\alpha }({{{\boldsymbol{q}}}})]}^{* }\)

x

y

x

χ0(−qxqz) + iκ0(−qxqz)

y

z

x

\({\chi }_{0}({q}_{y}^{2}-{q}_{z}^{2})+i{\kappa }_{0}({q}_{y}^{2}+{q}_{z}^{2})\)

z

x

x

χ0(qxqy) + iκ0(−qxqy)

x

y

y

χ0(qyqz) + iκ0(−qyqz)

y

z

y

χ0(−qxqy) + iκ0(−qxqy)

z

x

y

\({\chi }_{0}({q}_{z}^{2}-{q}_{x}^{2})+i{\kappa }_{0}({q}_{z}^{2}+{q}_{x}^{2})\)

x

y

z

\({\chi }_{0}({q}_{x}^{2}-{q}_{y}^{2})+i{\kappa }_{0}({q}_{x}^{2}+{q}_{y}^{2})\)

y

z

z

χ0(qxqz) + iκ0(−qxqz)

z

x

z

χ0(−qyqz) + iκ0(−qyqz)

  1. \({\sigma }_{ij}^{\alpha }({{{\boldsymbol{q}}}})\) for i, j, α = {x, y, z} denotes the spin conductivity, as defined in Eq. (17). Here, i denotes the spin current direction, j denotes the external electric field direction, and α denotes the spin quantization axis direction. q = (qx, qy, qz) denotes a wave vector of external electric fields. χ0 and κ0 are q-independent constants, as defined in Eqs. (19) and (20), respectively.
  2. * denotes complex conjugation.
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