MAGNETIC MEASURING TECHNIQUES

The purpose of this Technical Note is to review the primary techniques for measuring the magnetic properties of materials, including the basic physical principles underlying each method, as well as some of their relative advantages and disadvantages. The types of instruments covered here will be those suitable for weakly magnetic materials and/or very small quantities of more strongly magnetic material: the Faraday force balance, the vibrating sample magnetometer (VSM), the AC Susceptometer and SQUID magnetometers/systems.

While they are all often called “Susceptometers,” all these instruments can also be called “Magnetometers” since fundamentally their output response is most directly related to the magnetic moment (total magnetization) of the sample, M. The total moment M is related to the volume magnetic susceptibility cv, sample volume B, and external magnetizing field H by

M = cv * H * V (1)
Equivalently, we may express this in terms of the mass susceptibility cm, and the total sample mass m

M = cm * H * V (2)

The instruments detect this magnetization by one of two fundamental methods. In force methods (Faraday, AFM) the magnetization produces a force on the sample which is measured directly. In induction methods (VSM, AC, SQUID) the magnetization is made to induce a current or voltage on a nearby sensing coil.

Before moving on to a discussion of each technique, something should be said about units for magnetic quantities. In both CGS electromagnet units and Systeme Internationale (SI) units, the volume magnetic susceptibility is a dimensionless quantity. However, in CGS cv is usually expressed in “units of emu/cm3.” An “emu” is not truly a unit – it is more a reminder that one is working in CGS electromagnet units. Numerically, the volume susceptibility in SI units is 4p times larger than the CGS value, i.e.
cv (SI) = 4 p cv (emu/cm3)

The “unit” for magnetic moment in CGS is also called an “emu”, but it is not the same as an “emu of susceptibility”. Indeed, a unit analysis of equations (1) and (2) shows an apparent imbalance of units:

M(emu) = cv (emu/cm3) * H(oe) * V (cm3)
M(emu) = cm (emu/gm) * H(oe) * m (gm)

Therefore some scientists write CGS susceptibility as emu/cm3 * oe or emu/gm*oe.

In SI units there is no comparable confusion, but the units are less familiar to most scientists, and the scales for volume and mass are inconveniently large. In SI equations (1) and (2) become

M(Tesla * meter3) = cv (dimensionless) * H(T) - V(m3)


THE FARADAY BALANCE AND THE ALTERNATING FORCE MAGNETOMETER (AFM)

While the Faraday balance is a standard tool for precision studies on weakly magnetic materials, its basic idea is the same as when a child learns which objects are “magnetic” by testing whether they can be picked up with a toy magnet. When a sample with magnetic moment M is placed in a magnetic field gradient dH/dx, it will experience a force, F or magnitude

F = M * dH/dx
= m * M(emu) = cm * H * dH/dx (3)

In the Faraday method the primary magnetizing field, H, is usually produced by a horizontal electromagnet. The field gradient is made to be along the vertical direction, so that the magnetic force will add to (or subtract from) the sample’s weight, and can be detected with a sensitive microbalance.

The two main sub-types of Faraday systems differ only by the manner in which the field gradient is produced. One method uses specially shaped pole caps on the electromagnet. The design of these caps produces a region in space over which he “force function,” H * dH/dx, is constant, so that the force on a sample in this region is directly proportional to c . With this method, the main field and the field gradient are not independent, but increase together as the current in the electromagnet is increased. This means that the susceptibility sensitivity of the instrument varies as the square of the applied field, and the moment sensitivity is linear with the applied field.

The second variant of Faraday systems adds a separate set of coils to the electromagnet to produce the field gradient, so that the primary field H and the gradient dH/dx can be varied independently. If the gradient coils are driven with a bipolar power supply, the force on the sample can be made to change sign. If the gradient coils are excited with a low frequency sine or square wave (typically < 1 Hz), the force can be detected using phase-sensitive (lock-in) techniques for added noise rejection. This configuration is sometimes called an Alternating Force Magnetometer (AFM).

In addition to greater expense, the major drawback to separate gradient coils is that the maximum gradients they produce are typically only one-tenth as large as the maximum gradient from shaped pole pieces. Thus at high applied fields (&Mac197; 10 KGauss) the pole cap system is about 10 times more sensitive, while at low fields (&Mac197; 100 gauss) the situation is reversed. The fact that the moment sensitivity of the shaped pole cap system goes to zero at zero applied field limits the utility of this configuration for studying permanent moments or hysteresis curves.

The sensitivity of the Faraday method can be quite good, since the microbalance can measure weight changes as small as 0.1 microgram. Equating the gravitational force on 0.1 microgram to the magnetic force (equation (3)) to compute the minimum detectable moment, we get

&Mac198;Mmin = (10-7)g)(980 cm/sec2)
________________________
(dH/dx)max

For the pole cap system, the maximum gradient is typically &Mac197; 2,000 oe/cm, so the moment sensitivity is theoretically &Mac197; 5 x 10-8 emu. For gradient coil systems, the maximum gradient is typically &Mac197; 200 oe/cm, so the theoretical moment sensitivity is 5 x 10-7 emu. While this theoretical sensitivity is what is quoted in some manufacturer’s specifications, actual performance may be significantly worse due to turbulence and drag forces on the sample from any gas surrounding the sample for temperature control.

A principle advantage of either variant of the Faraday technique is the fact that the system contains a sensitive microbalance. This provides a direct and accurate reading of the sample mass, and eliminates the need for a separate mass determination as required for all the induction methods (a measurement

which can easily limit the several precision and reproducibility of the data). In addition, the microbalance allows many of the functions and benefits of a dedicated thermogravimetric analyzer. For example, the variation of the magnetic properties of high Tc superconductors with oxygen content can be studied in situ by monitoring the mass of oxygen lost upon bake-out under vacuum. Studies can also be made as a function of in situ reactions with introduced gases.

Another important advantage of the Faraday technique is its relative simplicity and the versatility of its components. The dewar structure for controlling sample temperatures does not need to contain any coils or sophisticated circuitry, and the magnetism of the construction materials is much less critical than for induction methods. Therefore, variable temperature capability can be less expensive, and it is easier to provide capabilities for operation at high temperatures or in the presence of reactive gases. It is also relatively easy to adapt the sample dewar and magnet for other measurements, such as measuring resistivity, critical current of superconductors, or Hall effect, whereas induction instruments are generally dedicated, single purpose devices.


VIBRATING SAMPLE MAGNETOMETER

The VSM uses an induction technique, and is widely used for characterizing ferromagnetic materials. In a VSM the sample is mounted on the end of a rigid rod attached to a mechanical resonator which oscillates the sample (usually in a vertical direction) at a fixed frequency. Surrounding the sample is a set of sensing coils. As the sample moves, its magnetization, M, alters the magnetic flux through the coils. This produces and AC voltage directly proportional to M, which can be amplified and detected using a lock-in amplifier. The external magnetizing field is usually provided by a horizontal electromagnet. The design of a VSM must ensure that the vibration of the sample produces no vibration of the sensing coils relative to the magnet, or large spurious signals would result. This problem is reduced if the magnet’s field is very homogeneous, and thus VSMs typically use large electromagnets with large pole piece diameters.

VSMs can easily measure permanent moments and hysteresis curves of ferromagnetic materials, and strongly paramagnetic salts. However, their moment sensitivity (typically 10-4 emu of moment with a 1 second time constant) is not really adequate for weakly magnetic systems or very small samples.




SQUID MAGNETOMETER/SUSCEPTOMETER

In a SQUID Susceptometer the magnetizing field is provided by a superconducting electromagnet. The sample is surrounded by a superconducting sensing coil, which is coupled through superconducting circuitry to the SQUID device. The magnetization of the sample changes the magnetic flux through the sensing coil, inducing a supercurrent which changes the flux through the SQUID, and therefore produces a change in the SQUID output signal. In essence, the SQUID Susceptometer is a special type of VSM which works at DC frequencies, with the SQUID device serving as a special type of VSM which works at DC frequencies, with the SQUID device serving as a very very low noise amplifier. The great sensitivity is of SQUIDs gives such systems a moment sensitivity of 10-8 emu or better, and this high sensitivity is often the reason for choosing a SQUID system. SQUID systems also can have excellent precision and reproducibility, which is important for sensitive inter-sample comparisons or when looking for very small variations with temperature, For certain applications the potential high field of superconducting magnets (>5 Tesla) and/or sample temperatures below 2K are also important advantages of liquid helium technology. Another unique capability of SQUID system is the study of kinetic phenomenon such as light-driven chemical reactions, where the millisecond response time of the instrument is a major benefit.

In addition to the expense and inconvenience of liquid helium there are certain other drawbacks and technical difficulties for SQUID systems which are not present in other Susceptometers, primarily due to its DC operation. Even a persistent-mode superconducting magnet will have some drift in field strength (typically 1 part in 107/hour) due to “flux creep” in Type II superconductors and relaxation of mechanical stress in the magnet windings. Since the SQUID can detect field changes of &Mac197;10-9 oe at the sample, for applied fields greater than a few hundred oe this magnet drift could produce large spurious signals. In high field systems this problem can be reduced by using a pair of oppositely-wound sensing coils (a first-derivative gradiometer configuration), or reduced further by using a (+1, -2, +1) set of coils (second-derivative gradiometer). In addition, a cylinder of superconductor is sometimes placed inside the magnet to help stabilize the field. A second problem is that the instrument is sensitive to changes in the magnetism of the construction materials near the sensing coils. Thirdly, the SQUID itself is strictly a differential device – it measures field changes but cannot determine a unique zero reading. or all three reasons, in SQUID systems the output reading when no sample is present is not zero, and this offset will change slowly with time and whenever the sample temperature or magnet current is changed. Therefore, it is also necessary to move the sample in and out of the sensing coil(s) to distinguish the true sample moment from the offset. Therefore and accurate and reproducible sample drive system is an important part of the measurement system and a major determinant of system performance.

Studies of magnetization vs. field strength are not as straight forward for SQUID systems, since data cannot be recorded continuously as the field is swept. Instead, the field must be varied in a series of discrete steps. For each field value the superconducting magnet must be cycled in and out out of its persistent superconducting mode. The superconducting path from the sensing coil(s) to the SQUID must be temporarily broken to prevent excessive current in this circuitry as the magnet field is changed, and then the sample moved in and out of the sensing coil(s) to make a measurement. In addition, for those systems using a cylindrical superconducting shield to stabilize the magnet, his shield must be warmed above its superconducting transition temperature each time the field is changed, followed by a significant time for cooling and restabilization. Finally, SQUID systems are often prone to noise from vibrations and microphonics since sub-Angstrom motions of the sensing coils in the large field of the magnet can produce detectable changes in total magnetic flux. For this reason SQUID systems often require some vibration isolation, and a shunt resistor is often placed across the SQUID input to cut off the high frequency response of the system.

With proper system design and good automation, these inherent difficulties of the SQUID systems can be overcome and can be largely hidden from the end user. However, these are the underlying reasons why SQUID systems are generally more complex and expensive than the other types.