CONDENSED MATTER PHYSICS: High-Temperature Superconductors and Magnetic Materials.

Interest in superconductors was reinforced in 1987 when a superconductor with a transition temperature as high as 92 K was discovered. It is a material that has the approximate formula Yba₂Cu₃O_6.5 and is often called YBCO because it contains yttrium, barium, copper and oxygen.

The transition temperature in T_c/K (without any magnetic field present) for YBCO compared with some other metals are as follows: 1.20 for aluminium (Al), 4.15 for mercury (Hg), 7.19 for lead (Pb), 9.26 for Niobium (Nb), 23.2 for Niobium-Germanium (Nb₃Ge), 93 for YBCO and 125 for TI₂Ba₂Ca₂Cu₃O₁₆. Further materials with high transition temperatures have been discovered since then and, like YBCO, they are compounds with imprecise ratios of elements.

These ‘high-temperature’ superconductors are likely to be more useful than the low-temperature superconductors. In particular, their transition temperature is above that of liquid nitrogen, which is relatively cheap and can be used to cool the superconductor, (in which the vapour is that of liquid nitrogen).

Unfortunately, it has so far proved difficult to make these high-temperature superconducting compounds in bulk form with tensile strength. It may be some years before useful superconductors at room temperature are finally made. Currently, transition temperatures up to 135 K have been achieved and even higher if pressure is applied to the superconductor.

MAGNETIC MATERIALS

Usually, when magnetic fields are connected with moving charges (electrons) within a wire and a current is passed through the wire, the associated magnetic field round the wire can be detected. But many atoms themselves have so called magnetic moments. That is, they behave rather like very small bar magnets. As in a current carrying wire, the magnetic field which is detected in a ferromagnetic material must arise from moving charges: in the material, the field arises from the motion of certain unpaired outer electrons in its atoms.

Whereas many atoms have magnetic moments, once these atoms are in combination as ions or molecules, the magnetic moments usually combine and cancel. It is only the atoms of certain elements, such as iron, nickel and cobalt (transition elements) that have magnetic moments which align in such a way as to maintain the magnetism in the bulk material. These are called ferromagnetic materials.

To form a permanent magnet from ferromagnetic material, the magnetic moments of its atoms are lined up in the same direction by inserting the specimen into a solenoid. Current through the turns of the solenoid is gradually increased and the magnetic field along the axis of the solenoid increases in proportion.

The magnetization of a specimen follows the magnetizing current, but not always linearly. Starting from zero magnetization, the magnetization curve follows AB (as is shown in the diagram below); when at B the specimen has reached magnetic saturation. At this stage, all the atoms with magnetic moments have become aligned with the magnetic field. If the current in the solenoid is now decreased, the magnetization in the specimen also decreases, but lags, following curve BC. When the current through the solenoid is zero and the magnetizing field is also zero, there remains a residual value of the magnetic induction at C called the remanence. This means that the material remains partly magnetized.

The current in the solenoid can now be reversed. The reverse magnetic field from the solenoid must reach a particular value, the coercivity, at D before the field in the specimen has been eliminated. At this stage, the magnetic moments of the atoms in the material will be randomly aligned. Alternatively, the magnetic moments may be aligned within domains, but the domains will then be randomly aligned. Further increase in the reverse magnetic field now starts to produce a reverse magnetization in the specimen that ultimately saturates at E.

As the current cycle continues, the field in the specimen follows the outside loop BDEGB. The area enclosed within the loop represents the energy lost (ultimately heating the magnet). If this area is small, then the specimen consists of a soft magnetic material. If the area within the loop is large and coercivity is large, then it is a hard magnetic material. This makes sense as it needs a large amount of reverse current to drive a material into its reverse magnetization.

A good analogue model of what is happening can be demonstrated in two dimensions using a grid of magnetized needles. The model grid is placed between large magnetizing loops (Helmholtz coils). Initially the directions of all the little magnets average out and there is no preferred direction as in the figure (a) below. You may however notice that there are local regions where the magnets are lined up; these are analogous to the domains I have mentioned. There is a local internal magnetic field within each domain but the fields average out overall throughout the material. An external magnetizing field can now be applied (by passing a current through the Helmholtz coils) and the magnets start to line up. Domains switch gradually until there is the alignment shown in the figure (b) below. This means we have gone up the steep part of the loop starting from A. Notice that the magnets have aligned along a natural direction arising from the way the magnets have been arranged – in this case on a square grid. In single crystals a similar thing happens with the alignment of the magnetic moments of the atoms according to the structure. However, this preferred direction of magnetization is slightly mis-oriented with respect to the external field. The field strength must be increased significantly to pull all the little magnets into line with it. This corresponds to the flattening of the loop as we come towards position B. If we then reduce the magnetizing field, the little magnets gradually swing back to their preferred alignment. As the field is reduced to zero, magnets in some of the domains switch singly or in groups, but it needs a substantial reverse field to cause a large switching of the domains.

A hard material is suitable for a permanent magnet where we want it to be difficult to reverse the direction of magnetization. It is difficult to alter the magnetization within the domains. A soft material, that gives little opposition to change of magnetization so that energy loss is small, is suitable for a transformer core. Steel cannot be easily magnetized and is a hard magnetic material; iron can be easily magnetized and is soft.

Looking at the curves again and choosing a particular magnetizing current, you will see that it has two possible maximum values of magnetization for the specimen. (This is apart from high current in the solenoid, when the magnetization has saturated.) Which value applies in practice depends on whether we are increasing or decreasing the current in the solenoid, since the value of the specimen’s magnetization depends on its previous magnetization history, shown as the path taken on the magnetizing current-magnetization graph. And so we say that the value for the specimen is path dependent, a property called hysteresis.

When an electromagnet is used to make measurements or obtain data such as magnetic resonance in a varying magnetic field, the hysteresis is kept small. This is done by using a very soft magnetic material, when the solenoid current-magnetization variation will be close to a single curve. Then, the energy loss within the magnetic material during the cycle is negligible.

Low energy loss is particularly necessary in transformer cores and so these are usually made from iron (with about 3 per cent silicon). However, iron has a low electrical resistivity so that it is necessary to make the core from laminated sheets to prevent eddy currents. The eddy currents arise from electromagnetic induction; the higher the frequency of operation of the transtormer, the larger is the induced e.m.f. setting up the eddy currents. If one can use a soft magnetic material that is also insulating then lamination becomes unnecessary. Ceramics such as ferrite ceramics can be used but usually only when the transformers are small. Metallic glasses have been developed that are easy to magnetize in all directions.

If a magnetic material is heated sufficiently there is enough energy to overcome the interaction between the magnetic moments of the atoms so the material is no longer capable of magnetization. The temperature at which this occurs is called the curie temperature. In the model of magnetic needles, a similar effect can be produced by inserting energy through shaking.

CONCLUSION

In these series of my post on Condensed matter physics, I mentioned the following:

• When atoms come close together, electron energy levels split and spread out to form energy bands
• Conduction in a metal occurs because electrons can move among partially occupied energy levels of the conduction band.
• Insulators cannot conduct electricity because they have a filled valence band and an empty conduction band separated by a large energy gap.
• A pure semiconductor has a small energy gap between valence and conduction bands, and so electrons can be thermally excited into the conduction band at finite temperature, leaving an equal number of holes in the valence band.
• Semiconductors can be doped with donor and acceptor impurities to produce n-type and p-type Semiconductors respectively.
• The electrical conductivity of a metal decreases with temperature, whereas that of an intrinsic semiconductor increases with temperature.
• The Hall effect can be used to find the type and number of carriers in an extrinsic semiconductor.
• Semiconductor lasers are small and efficient.
• Lasers depend on population inversion achieved by pumping.
• Superconductors require the temperature to be below a critical value, in order to have negligible resistance.
• Superconductors exclude magnetic field; this is the meissner effect.
• Soft and hard magnetic materials exhibit hysteresis loops, with small and large enclosed areas respectively.

REFERENCES

https://phys.org/news/2019-05-scientists-highest-temperature-superconductor.html
https://www.technologyreview.com/2018/12/10/138748/the-record-for-high-temperature-superconductivity-has-been-smashed-again/
https://www.sciencealert.com/physicists-have-officially-smashed-the-record-for-high-temperature-superconductivity
https://www.sciencedirect.com/topics/materials-science/high-temperature-superconductors
https://courses.lumenlearning.com/physics/chapter/34-6-high-temperature-superconductors/
https://en.wikipedia.org/wiki/High-temperature_superconductivity#:~:text=High%2Dtemperature%20superconductors%20
http://labman.phys.utk.edu/phys222core/modules/m4/magnetic%20materials.html
https://www.nature.com/subjects/magnetic-materials
https://en.wikipedia.org/wiki/Magnet
http://www.irm.umn.edu/hg2m/hg2m_b/hg2m_b.html