The vibrating sample magnetometer has become a widely used instrument for determining magnetic properties of a large variety of materials: diamagnetics, paramagnetics, ferromagnetics, ferromagnetics and antiferromagnetics. This experimental technique was invented in 1956 by Simon Foner, a scientist of the MIT. EGG Princeton Applied Research (EGG PAR) was the world leader company that started the commercialisation of this magnetometers in the sixties.

It has a flexible design and combines high sensitivity with easy of sample mounting and exchange. Samples may be interchange rapidly even at any operating temperature. Measurements of magnetic moments as small as 5x10-5 emu are possible in magnetic fields from zero to 9 Tesla (or higher). Maximum applied fields of 2-3 Tesla or 9 Tesla are reached using conventional laboratory electromagnets and superconducting solenoids, respectively. Vibrating sample magnetometers normally operate over a temperature range of 2.0 to 1050 K. Powders, bulk and thin films can be measured and studied.

Principle. If a sample of any material is placed in a uniform magnetic field, created between the poles of a electromagnet, a dipole moment will be induced. If the sample vibrates with sinusoidal motion a sinusoidal electrical signal can be induced in suitable placed pick-up coils. The signal has the same frequency of vibration and its amplitude will be proportional to the magnetic moment, amplitude, and relative position with respect to the pick-up coils system.
Fig. 1 shows the vibrating sample magnetometer block diagram.

The sample is fixed to a small sample holder located at the end of a sample rod mounted in a electromechanical transducer. The transducer is driven by a power amplifier which itself is driven by an oscillator at a frequency of 90 Hertz. So, the sample vibrates along the Z axis perpendicular to the magnetizing field. The latter induced a signal in the pick-up coil system that is fed to a differential amplifier. The output of the differential amplifier is subsequently fed into a tuned amplifier and an internal lock-in amplifier that receives a reference signal supplied by the oscillator. The output of this lock-in amplifier, or the output of the magnetometer itself, is a DC signal proportional to the magnetic moment of the sample being studied. The electromechanical transducer can move along X, Y and Z directions in order to find the saddle point (which Calibration of the vibrating sample magnetometer is done by measuring the signal of a pure Ni standard of known the saturation magnetic moment placed in the saddle point.

The basic instrument includes the electromechanical system and the electronic system (including a personal computer), while the costumer should select the electromagnet or superconducting coil system with the appropriate bipolar power supply. Laboratory electromagnets or superconducting coils of various maximum field strengths may be used. For ultra-high magnetic fields a cryogen-free magnets can be also used. For the characterization of soft magnetic materials a pair of Helmholtz coils may be also used. As accessories the costumer must also select a high temperature oven assembly and a liquid Helium cryostat.
Fig. 2 shows the vibrating sample magnetometer.

Technical specifications of VSM (typical figures).

Maximum sensitivity: 5x10-5 emu. Calibrated ranges from ? 100 to ? 0.01 emu full scale.
Stability of output signal: ? 0.05 % of full scale per day.
Absolute accuracy: better than 2 %
Angular variation of H: full 360o rotation ? 0.5o
Maximum sample size: 7 mm.
Operating temperature range: 2.0 K to 1050 K

Applications. Using a vibrating sample magnetometer one can measure the DC magnetic moment as a function of temperature, magnetic field, angle and time. So, it allows to perform susceptibility and magnetization studies. Some of the most common measurements done are: hysteresis loops, susceptibility or saturation magnetization as a function of temperature (thermomagnetic analysis), magnetization curves as a function as a function of angle (anisotropy), and magnetization as a function of time.