Vibrating-sample magnetometer

Working principle

Vibrating Sample Magnetometry is based on the physical principle of electromagnetic induction: A sample with magnetic moment ${\displaystyle \mu }$ is placed in a homogeneous magnetic field ${\displaystyle \mathbf {B} }$. The sample is vibrated in the field with position ${\displaystyle z(t)}$, which causes a change in the magnetic flux

${\displaystyle \Phi =\int _{A}\mathbf {B} \cdot d\mathbf {A} =\mu _{0}\int _{A}\mathbf {\mu } \cdot d\mathbf {A} }$

in a sensing coil with cross-sectional area ${\displaystyle \mathbf {A} }$, ${\displaystyle \mu _{0}}$ is the vacuum permeability. According to Faraday's law of induction, the change in the magnetic flux is proportional to an induced electric voltage

${\displaystyle U_{\mathrm {ind} }={\frac {d\Phi }{dt}}={\frac {dz}{dt}}{\frac {d\Phi }{dz}}}$.

The first factor ${\displaystyle {\frac {dz}{dt}}}$ is directly dependent on the device and is thus known to the experimenter. The second factor is proportional to ${\displaystyle \mu }$. Factors of proportionality are determined through calibration of the setup.

Because ${\displaystyle U_{\mathrm {ind} }\propto \mu }$ with all further factors either determined from the device or through calibration, a measurement of the induced voltage directly yields the magnetic moment of the sample.^[5]

Parts of a typical VSM setup

• Actively cooled electromagnet/power supply
• Amplifier
• Control Chassis
• Meter
• Computer interface
• Sensor coils
• Vibration exciter with sample holder
• Hall probe (optional)

Sample Operating Procedure

Source:^[6]

1. Mounting the sample in the sample holder
2. Turning on the VSM system
3. Run the computer software to initialize the system
4. Calibrate the system
5. Optimize the system for M^[6]
6. Calibrate the Lock-In Amplifier
7. Take measurements and record data

Conditions for VSM to be effective

1. Magnetic field must be strong enough to fully saturate the samples (or else inaccurate measurements will be taken)
2. Magnetic field must be uniform across the sample space (otherwise the addition of field gradients^[7][9] will induce force that alter the vibration once again leading to inaccurate results