这是一份liverpool利物浦大学PHYS486的成功案例

Allowing for anisotropic d-spin HF coupling, we then take
$$
\mathcal{H}{d s}=\sum{\beta=x, y, z} A_{d \beta} I_{\beta} S_{\beta} \text { with } \chi_{d \beta}=\frac{N_{A} g_{\beta} \mu_{B}\left\langle S_{\beta}\right\rangle}{H}
$$
The d-spin shift coefficient is then defined as
$$
\alpha_{d \beta}=\frac{K_{d \beta}}{\chi_{d \beta}}=\frac{A_{d \beta}}{N_{A} \gamma \hbar_{\beta} \mu_{B}}
$$
For ordinary $3 \mathrm{~d}$ metals we shall take $g_{\beta} \sim 2$, whereupon $\chi_{d \beta}$ becomes isotropic. However, these definitions carry over into the discussion of cuprates in Chap. 3 , where there is evidence for substantial g-shifts. We also note here that the HF coefficient can be quoted as simply $A_{d \beta}$ in energy units, as $A_{d \beta} / \hbar$ in units of $s^{-1}$, as $A_{d \beta} / \gamma \hbar$ in $\mathrm{kG} / \mathrm{spin}$, or as $A_{d \beta} / \gamma \hbar_{\beta}$ in units of $k G / \mu_{B}$. Although it may be somewhat confusing, one finds all of these units in use in the high- $T_{c}$. literature. The d-spin HF field is also known as the core-polarization HF field (hence $A_{d} \rightarrow A_{c p}$ ), which we now discuss.

PHYS486 COURSE NOTES ：

$$
K_{\beta}(T)=\frac{2 C_{\beta}}{\hbar \gamma_{17} g_{\beta} \mu_{B} N_{A}} \chi_{s \beta}(T)=\alpha_{17 \beta} \chi_{s \beta}(T)
$$
where $\alpha_{17 \beta}$ is the shift coefficient and $\chi_{s \beta}(T)=-g_{\beta} \mu_{B} N_{A}\left(S_{j \beta}\right\rangle / H$ is the molar susceptibility $\left(\left\langle S_{j \beta}\right\rangle<0\right.$ is independent of $\left.\mathrm{j}\right)$ of a $\mathrm{Cu}(2)$ site.

In practice the shift coefficient is determined experimentally by dividing a measured spin-paramagnetic shift by a “best estimate” of the corresponding molar susceptibility. The tensor $C_{\beta}$ has the units of energy, so what we will tabulate is the quantity
$$
C_{\beta}^{\prime}=N_{A} \mu_{B} \alpha_{17 \beta} / 2=C_{\beta} / \hbar \gamma_{17} g_{\beta},
$$