national high magnetic field laboratory
PULSED FIELD FACILITY
the future
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WHY MEASURE MAGNETIZATION?
BASIC PRINCIPLES
COMPENSATED COILS
WINDING COILS FOR PULSED FIELD MAGNETOMETRY
COMPENSATED COILS EXAMPLES
MAGNETOMETRY SAMPLE REQUIREMENTS
EXAMPLES OF PULSED FIELD DATA
LITERATURE AND THE de HAAS van ALPHEN EFFECT
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Magnetometry
specialization and methods
A measurement of the magnetization (M or M) of a sample can be very informative indeed. To see why, let us list some important facts.
Magnetization...
1) is the magnetic moment per unit volume;
2) is a thermodynamic function of state;
3) is connected to other functions of state by fundamental, quantitative relationships;
4) may be calculated from theoretical models of the system with very few or no assumptions (unlike e.g. transport);
5) is related to magnetic field applied by an electromagnet (H) and the magnetic flux density (B) by
B = μ₀(H+M).
Another important parameter is the differential susceptibility:
χ = (dM/dH).
In measurements of both magnetization and susceptibility, we are helped by the fact that we use pulsed fields. Our pulsed magnets produce fields that change at rates of 100s to 1000s of Tesla per second (the figure to the left shows a typical pulse profile). A magnetic field that changes with time induces a voltage in a coil. This is the principle of our measurements.
why measure magnetization?
Most users of the pulsed-field facility wish to have a measurement of a sample’s magnetization that extends to as high a field as possible and that can be spliced onto their own low-field SQUID or PPMS/MPMS data. This is best done using a compensated, inductive, extraction magnetometer, the only type of pulsed-field magnetometer that can be reliably calibrated. In order to understand how such a magnetometer works, we need to look at the basic principles of the measurement, and the construction of the magnetometer. Some experiments (e.g. the de Haas-van Alphen effect) require only the susceptibility; we will return to such measurements later in this account.
Most magnetometers work by measuring the voltage induced in a coil containing the sample when it is exposed to a time-dependent magnetic field. As mentioned above, in the pulsed-field facility, we are fortunate that the magnets themselves provide this dB/dt without the need for an extra modulation coil. The illustration below shows a schematic, and the box indicates how this relates to electromagnetic theory, i.e. Maxwell’s Equations.
In practice, a single coil provides only a tiny signal due to the presence of even a very magnetic sample. Adding turns does not help; too much induced voltage is produced by the rest of the coil. To get useful data, we need a more cunningly-designed coil.
basic principles
compensated coils
Two concentric coils are wound in series, the inner one (green in the figures) being wound clockwise, the outer (red) counterclockwise (or vice-versa). The coils are designed to provide equal and opposite induced voltages, so that their combined induced voltage is zero in the absence of a sample. When a sample is introduced, any induced voltage will be due to the sample’s moment.
Whilst this sounds simple in theory, putting it all into practice requires further refinement, as the next sections show. But don’t worry- all of the difficult stuff is done by us before the user even gets here.
V = 0 for empty coil
V = α dM/dt when sample is
present; integrate to get M.
winding coils for pulsed field magnetometry
In winding the compensated coil, several things must be taken into account. First, pulsed-field magnets are usually quite compact (see figure to right); the cold bore is small (typically 7 mm in ³ He space). Hence, the coil must also be small. Second, the field changes rapidly; therefore the wire from which the coil is made must be small to avoid heating inside wire due to eddy currents.
A coil-winding machine for pulsed-field magnetometers is shown to the left. The wire used is 50 gauge (25 microns), dual coated, high-purity Cu (fragile!); sometimes, 56 gauge is used in smaller coils. As it is wound, the coil is painted with methyl ethyl ketone after each layer; this glues it together. The whole process is observed under a microscope. A typical recipe for a magnetometer coil is 1.5 mm bore with 1000 turns clockwise and about 500 turns counterclockwise. A coil and the mandrel used to wind it are shown in the inset (pen is for scale).
compensation I: benchtop compensation
Though designed carefully, the coil is not yet finished; if it is placed in a changing field, there will be an induced voltage. Therefore, turns are added or removed on the benchtop by hand. The steps are shown in the box next to the illustration.
The coil is placed on a wooden toothpick mounted on a G10 rod. The connecting wires are held accurately parallel (by black Apiezon “clay”) to prevent stray induced voltage. The coil is slid into second-hand pulsed magnet through which a large-amplitude AC current flows. The following steps are performed.
1. The induced voltage and its phase are measured and compared with those in a loop with known area;
2: the outer layers of the coil are painted with GE varnish solvent;
3. turns are added or removed by hand;
4. this is repeated until the induced voltage corresponds to a fraction of a turn.
For magnetization measurements, the sample is placed inside an ampoule on a long thin rod that allows the ampoule to be slid in and out of the coil. Two shots of the pulsed magnet are then fired,
sample in;
sample out.
The integrated sample out signal is then subtracted from the integrated sample in signal to give M.
compensation III: sample in minus sample out
Though designed carefully, the coil is not yet finished; if it is placed in a changing field, there will be an induced voltage. Therefore, turns are added or removed on the benchtop by hand. The steps are shown in the box next to the illustration.
Though the coil is now nicely compensated at Room Temperature, it is of course mainly going to be used at cryogenic temperatures. Cooling causes contraction, and so the coil will go out of compensation. To deal with this, the coil is fixed to the probe (left, above) and then an additional, single-turn, coil (the compensation coil) is wound around the outside (see schematic above, right). A third, 10 turn coil is added to measure B inductively; the calibration procedure for this is described later.
When the probe is in use, the induced voltages from both the signal coil and the compensation coil are amplified. A fraction of the voltage from the compensation coil is then added to or subtracted from the signal coil voltage to null out any remaining induced voltage.
compensation II: electronic compensation
magnetometry sample requirements
As mentioned above, the sample sits in an ampoule that is mounted on the end of a long rod. This allows the ampoule to be slid in and out of the coil from above. The lower end of the rod is shown in the upper photo, whilst the lower photo shows the ampoule filled with a powder sample. The sample space in the ampoule is 4.5 mm long and 1 mm in diameter. For powder samples, best results are obtained if >2.0 mm of the ampoule is filled. Powder samples should be packed down tightly (pushing the powder in using the shank of a clean 1mm drill bit works well). Hold the powder in place using a plug of silicone vacuum grease on top; motion of a loosely-packed powder can cause noise. Single crystals work best if they fit the ampoule snugly. The crystal should be cut so that the long axis is the one that you want parallel to H. Again, us silicone grease to hold the sample in place. Smaller crystals can be stacked, and held together with suitable glue.
Ampoules can be mailed to you so that you can mount samples at your home institute before coming to LANL- email to get some.
jsingle@lanl.gov
examples of pulsed field M(H) data
Pulsed-field magnetometry data may be calibrated to give quantitative values of M (left-hand figure). Data are usually noise-free enough for accurate comparisons with theory (top right). For samples that require higher fields, the extraction magnetometer may be used in the 100 T multishot magnet (lower right).
literature
Some examples of pulsed-field magnetometry are give in the following papers, and references therein.
Manson et al., Angew. Chem. Int. Ed. 50, 1573 –1576 (2011).
Goddard et al., New J. Phys. 10, 083025 (2008).
Goddard et al., Phys. Rev. Lett. (2012)
susceptometry and the de Haas-van Alphen effect
Magnetic quantum oscillations provide the most accurate way of measuring the Fermi surface of a metallic sample. When observed in the magnetization, quantum oscillations are known as the de Haas-van Alphen effect. The frequencies of the oscillations give the cross-sections of the Fermi surface in plane perpendicular to B; their temperature dependence gives the effective mass.
The samples used for de Haas-van Alphen measurements are metallic and tend to have low resistivities; eddy-current heating is therefor an issue, and the sample cross-sectional area should be relatively small. The coils used are therefore smaller than those in the magnetometer, typically with a bore of 0.5 mm. There is no ampoule, and the sample is held directly in the coil using silicone grease; consequently, there is no sample-out shot. Oscillations are observed directly in the differential susceptibility.
Samples should be single crystals, cut so that the long axis is parallel to the axis of interest. The samples should be >1 mm long and their cross-section should be small enough to fit within a 0.5 mm hole. Flat samples (platelets) can sometimes be fixed to the end of the coil.
examples of pulsed field de Haas-van Alphen data
The oscillations are observed in the differential susceptibility (top figure). Fourier transforms are used to reveal the frequencies present (lower figure). Each frequency represents a cross-sectional area of the Fermi surface in a plane perpendicular to the applied field.
