Hi Adam,

I have used tiny neodymium magnets in the past, they have relative smaller volume, lighter weight and higher performance than other magnetic systems. However, I never used them bellow 77 K (liquid nitrogen), as I were working with high temperature superconductivity.

As you probably know, ferromagnetic materials work well at low temperatures with the exception of hard ferrite. You have to take measures to avoid exposing it to external magnetic fields while cooled down. Basically, the magnetic coercivity decreases as temperature decreases, making it vulnerable to partial or total demagnetisation. In the case of neodymium, there is a spin reorientation transition near 135 K, which weakens magnetisation.

Alternatively, you could use a samarium-cobalt magnet. They have relatively weaker remanent magnetization compared to neodymium, but the coercivity increases as temperature decreases. They are reported to operate well at cryogenic temperatures, all the way down to 2 K.

I can see you still have two problems: (i) stabilise the magnet on top of the sample, for which I'd recommend a sample larger than the magnet, and (ii) the superconductor transition of your lead sample is known (~7K) for zero magnetic field, but as you know, in the presence of a magnetic field that transition temperature will be lower. Therefore, you would end up seeing levitation at a lower temperature than the zero field cooling (ZFC) transition. For that reason, I'd recommend to use a nonmagetic separator to avoid exposing the sample to the most intense field, in the surface of the magnet. Indeed, the separator should be thinner than the distance at which the magnet levitate, otherwise you will not see levitation.

hope it helps.

regards,

Claro.

Dear Adam, the suggestions given above by Claro are very interesting but I'm curious about how you will see the levitation... Are you planning to perform the experiment in a transparent cryostat? If your cryostat is not transparent or the visual observation of the experiment is difficult, I suggest you make a small winding of isolated copper wire and then glue it below your lead sheet. So, in the normal state, the magnetic lines of the magnet will pass through the sheet causing a constant magnetic flux in the copper winding. In this way, during the superconducting transition of your lead sheet, the magnetic flux in the copper winding will suddenly change to zero due to the Meissner effect generating an electrical pulse in the copper winding that can be observed (or even recorded) by using an oscilloscope or voltmeter...

Thanks for the suggestion Walter, but I have a transparent window in my cryostat so seeing levitation shouldn't be a problem.

Dear Adam, I have never seen levitating lead, keep us updated when you try. But bear in mind that the critical field for lead is quite low and it will not become superconducting when it's close to a NdFeB (or SmCo) magnet. I would rather try to suspend the Pb piece on a thread and apply the magnetic field from outside with a coil or large magnet (if your cryostat is not too big), the Pb piece should deflect away from the magnet (much more than when in normal state). You can also try a magnet or coil inside the cryostat, but then you have less control of your experiment. Also, Cu coil will heat up your cryostat quickly if you pass sizable current through it... Good luck!

Hi. I should add an important remark.

In a type II superconductor, the magnetic field partially penetrates the sample in the form of vortices, once the first critical field (Hc1) has been exceeded. These vortices are pinned by defects in the sample. Thus, such pinning effect confers stability to a levitating magnet on top of the sample.

However, lead is a type I superconductor. Vortices cannot exist in lead. Therefore, the magnet requires another form of stabilisation. For example, a concave shape of the lead foil gives the levitation stability and prevents the magnet from sliding on the side.

If the magnet were placed above a nonmagnetic separator, which is itself on top of a flat lead foil, the magnet would jump to the side but not levitate.

Do we call it \textit{gedankenexperiment}?

If I skim both threads it seems like you just want to demonstrate flux exclusion.  A very sensitive way to see flux exclusion is by magnetic susceptibility. You will see a strong diamagnetic signal below Tc.  A clever way of checking this, with a very small field, is to use your Pb sample as an inductor in an oscillator circuit.  You can measure a frequency shift very sensitively.  For more details see Varmazis and Strongin Phys. Rev. B 10, 1885 (1974).  

You have the answers for the permanent magnets (that you can buy on internet).

To improve the stability of the levitation, you can give a slightly concave shape to the lead plate, so that the magnet will stay in the center of it.

Measuring the resistance of a niobium coil (it is easier to get Nb wire than Pb) is spectacular too, and you can make a light switched on, in series with the Nb coil  when this one  becomes superconducting.

You can also measure the mutual inductance of two coils (primary + secondary) in the center of which you have put your lead sample. In that case you have better to ajust the mutual inductance to "zero" before cooling down to see the superconducting transition. To get a zero "mutual inductance" you can construct the secondary coil in two pick-up parts (positive and negative) which are compensated, and put the sample in one of the pick-up parts. More sophisticated, you can move the lead sample from one pick-up coil to the other, and measure the mutual inductance, then the diamagnetism.

Thank you all for your answers, they're all interesting and I feel I've already learned a lot from you. I tried the simplest experiment yesterday, but I didn't see any movement of the magnet whatsoever - I filmed it just to be sure but it really didn't budge. I attach a photo of my setup. The head of the cryostat is made of oxygen-free copper. Any ideas what I could improve, before I move on to Garrett's suggestion for susceptibility measurement?

Why do you put Indium, which is normal metal at 4.2K?

It's thickness can just hide the levitation

There are a few other possibilities :

1) You have not a 4.2K temperature for lead

2)When you cool both the lead and the magnet, since the field of the SmCo is much larger than the critical field of lead,  a large part of lead remains normal even at 4.2K (and don't expulse flux)

3) Try to approach the magnet from above, when the lead is cold. So that you can have levitation, before the lead goes to the normal state (or use a weaker and light magnet)

I did such experiments 50 years ago, with a large and concave lead plate.

It's much easier with YBCO ceramics

at Nitrogen temperature (and also at 4.2K of course)

Hi.

Nice picture. My first reactions are as follows:

(i) that indium foil is way too thin. Aim at least 5-10 mm or more separation.

(ii) use a thermal conductive paste between the lead and the cold finger, if you haven't don't that already. 

(iii) if you have access to machining equipment, you would want carve a sphere in the lead plate with a radius say 10 times that of the magnet and half the lead thickness deep, to confer some stability to the levitation. 

Would you restate where are you heading?

Hi Claro,

My final objective, as in the initial post is this: "I need to know if my piece of Pb is superconductive in my setup.". It's as simple as this. Firstly, I don't know if my lead is pure enough (it's this item: https://goo.gl/AyTLGK, they state 99.95% as purity) and secondly, I don't know how much I can trust the temperature reading. I'll be using the same piece of lead in a different experiment where I need it to be superconductive, in the same cryostat but with no magnets around.

(i) wow, that much? even if the thickness of the lead itself is 2mm and the magnet is 1mm thick?

(ii) I assume the system will eventually reach the steady state, right? It's a helium flow cryostat, I'm not worried about thermal contact, should I? But it definitely doesn't hurt to put some paste on there.

(iii) since I can constantly monitor it with a camera, isn't carving a concave shape overkill? I think I would see some movement anyway.

Thanks a lot for your help!

Adam

Hi Adam,

it's not so easy to observe Meissner effect. Even during my experiments wit very sensitive SQUID magnetometer in very weak magnetic fields the diamagnetic effect in pure type I superconductors was much less than predicted (simply a lot of flux got trapped in the superconductor). Your geometry (large demagnetization factor of the superconductor) won't help the flux lines to escape from the bulk superconductor.

Even the original Meissner and Ochsenfeld paper is very confusing about what was actually measured (see e.g. https://www.researchgate.net/publication/230995701_Meissner_and_Ochsenfeld_revisited). 

If you bring the magnet close to already superconducting piece of lead, it may levitate (see the third picture here: http://www.thefullwiki.org/Meissner_Effect), but that is just eddy currents in ideal conductor, not ideal diamagnetism.

Also, as mentioned many times earlier, the magnetic field of the magnet in contact with the lead is strong enough so that a substantial part of the lead around the magnet stays in normal state. Making the gap bigger won't help in your configuration, I'm afraid...

If you want to see some physical movement during the transition, I suggest an order of magnitude more sensitive arrangement: suspend the magnet on a long string so that it rests next to a bulk of lead (maybe in some distance). When the lead becomes superconductive you may hope to see some deflection of the magnet away from the bulk lead. If it does not repel, there is no chance to get it levitate...

Good luck!

btw. Nice cryostat! I wish I had one like that :-).

Article Meissner and Ochsenfeld revisited

Hi Adam,

only now I read your last post. Two additional comments:

1. If you just want to be able to tell whether the lead is superconductive, there are simpler ways than Meissner effect (the onset of ideal diamagnetism). I would put a piece of lead inside a coil of an LC tank circuit (you want to chose the right capacitors that work at helium temperatures) and observe changes of resonant frequency (or impedance around the resonant frequency - if you have something as fancy as this: https://www.testworld.com/used-electronic-test-equipment/keysight-agilent-lcr-impedance-testers/keysight-agilenthp-4284a-precision-lcr-meter-20-hz-1-mhz/).

2. Thermal contact is very important, because the lead absorbs lots of thermal radiation through the windows. I would just submerge it in the liquid helium to make sure. You may also attach some thermal probe. Any wires should be anchored to 4.2K!

Hi Adam. On a quick note, Zdenek suggestion about the pendulum inside the cryostat sounds promising: look for repulsion instead of levitation. It has the additional advantage of easily controlling distance between the magnet and the lead foil, thus decreasing the applied field while cooling. The magnetic induction in the magnet's surface can be near 1T. Regarding high thermal conductivity with the copper, I believe it's necessary. It adds thermal stability and cooling power. Good luck.