The Faraday force magnetometer allows measurements of the static magnetisation of small samples (some milligrams) at very low temperatures (down to 50 mK) and very high magnetic fields (up to 12 T). The force (F) acting on a specimen is proportional to its magnetization (M) times the externally applied gradient field (dB/dz ~ 10 T/m). The force on the sample can be measured by detecting the change in the capacity (C) between two metallic plates (see figure above from Ref. [1]).

$\begin{center} $\vec{F}=\left(\vec{M}\cdot\vec{\nabla}\right)\vec{B}$\\ $F$ = force; $M$ = magnetization; $H = B/\mu_{0}$ = magnetic field\\ \smallskip $|F|\sim\Delta C$\\ $C$ = capacity\\ \smallskip $d=\frac{\epsilon_{0}A}{C}$\\ $d$ = distance between the plates\\ \smallskip $M\sim\left(\frac{\partial{B}}{\partial{z}}\right)^{-1}(\Delta d)$\\ \end{center}$

Characteristics:
- Magnetic moment resolution close to 10 micro-emu.
- Temperature range: 0.04 < T < 5 K.
- Field range: -12 < B < 12 T.
- Sample space: disc of 0.6 cm diameter.

Images of the measuring cell. It is made of Cu alloy and has a diameter of few centimeters. The sample platform is made of Epoxy and suspended on 8 metallic wires.

[1] T. Sakakibara et al., Jpn. J. Appl. Phys. Vol. 33, Page 5067 (1994).


AC Susceptibility and de Haas van Alphen effect Contact: Dr. Manuel Brando

To measure the AC susceptibility of small samples (few milligrams) at very low temperatures, a special modulation coil has been built (cf. black cylinder in the picture). It matches exactly the inner hole of the 20 T superconducting magnet and both are located at the bottom of a 4He-dewar in helium bath at 4.2 K.
The sample is positioned in the center of a tiny pick-up coil at the very bottom of an Oxford-Instrument Kelvinox-400 cryostat. The lower part of this cryostat has a long and thin cold finger that can be inserted into the modulation coil (cf. white rod in the figure). The pick-up coil can be rotated mechanically from the top of the cryostat to align the magnetic field with one of the sample crystallographic axes.
The magnitude of the modulated external magnetic field (Bac) can be varied between 5 and 11 micro-Tesla with frequency (f) extending over several decades, usually 1 < f < 1000 Hz.
With the same setup it is possible to measure the de Haas van Alphen effect. In this case, higher currents in the main coil are needed. Since the main coil is immersed in the helium bath, currents as high as 0.5 A (rms) can be applied to achieve magnetic fields of about 5.4 mT [2].

$\begin{center} The AC susceptibility $\chi_{ac} = dM/dH$ can be derived from\\ the complex susceptibility $\chi' + i\chi ''$:\\ \medskip $B_{ext} = B_{dc} + B_{ac}$\\ \smallskip $B_{ac} = B_{0}cos(\omega t)~with~f = \omega / 2\pi$\\ \smallskip $\chi'(T,B) = \frac{1}{\pi B_{0}}\int_{0}^{2\pi} M(\omega t) cos(\omega t) d(\omega t)$\\ \smallskip $\chi''(T,B) = \frac{1}{\pi B_{0}}\int_{0}^{2\pi} M(\omega t) sin(\omega t) d(\omega t)$\\ \smallskip where~M~is~the~sample~magnetization. \end{center}$ .

Characteristics:
- Modulation field 4 < Bac < 11 micro-T
- Temperature range 0.02 < T < 5 K
- External magnetic field -20 < Bdc < +20 T
- Sensitivity close to 0.1 micro-emu

[2] Tanja Westerkamp, PhD Thesis, University of Dresden (2009).

Last modified on April 7, 2011

Print version

Top

Imprint