High Sensitivity Sensor
The shift of resonant frequency\(\Delta \omega_0\) \(\rightarrow\) measure differential magnetic torque \(\frac{\partial \tau}{\partial \theta}\) \(\rightarrow\) dHvA effect measurement \(\frac{1}{B_n}=\frac{2\pi e}{\hbar}(n+\gamma)\frac{1}{S(\alpha)}\rightarrow\) information about Fermi surface
Phase Lock Loop (PLL) Controlling scheme
Use phase lock loop (PLL) to detect frequency shift, increasing the resolution by ~ 3 orders of magnitude.
Result
TaAs sample
\[\frac{1}{B_n}=\frac{2\pi e}{\hbar}(n+\gamma)\frac{1}{S}\]
\(\gamma\approx 0\), Onsager phase trivial.
Lifshitz-Kosevich (LK) formula
\[R_T=\alpha\frac{𝑚_𝑒^∗\cdot T}{B} ∕ \sinh(\alpha\frac{𝑚_𝑒^∗\cdot T}{B})\]
Effective mass of the elections
\[m_e^* = (0.24\pm 0.27)m_e\]
CeRhIn5
The device was capable of detecting dHvA effect of \(\rm{CeRhIn_5}\), a heavy fermion superconductor, showing impressive sensitivity. The measurement result agrees with the reported values.
