Neutron Star materials - If a neutron star stops spinning, What will be the characteristics of the materials in it?
As the title says, what if a neutron star stops spinning what will happen to the materials that the neutron star is made of?
Will they still be super dense?
Are they brittle? If they are, how strong is it?
How heavy those materials will be?
Here's the actual scenario: A certain blacksmith discovers a rock (technically a mine) that is so heavy that in fact, just a pebble of it took him and 3 of his sons to carry it.
Along that scenario, what I could actually do with that kind of denseness and if it can be worked with.
Or possible create a fabric so strong that it beats other metals in terms of armor properties
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Let's go more with the scenario you are describing, than the question you start out by asking (which appears to be only peripherally related).
Let's assume that a "pebble" is approximately 1 cm3 in size.
Let's also assume that one of these adult men can carry somewhere on the order of 75 kg.
Let's also ignore how four men are able to simultaneously hold on to an object that is 1 cm3 in size, which is going to be a serious challenge, but not unsolvable, in itself.
With these assumptions, we can estimate the pebble's weight to be on the order of $4 \times 75~\text{kg} = 300~\text{kg}$.
As a consequence, the density of the material is something like $300 \times 10^6 = 3 \times 10^8$ kg/m3 (because $\frac{\text{cm}^3}{\text{m}^3} = 10^6$).
Apparently, osmium is the densest naturally occuring element on Earth, at 22.59 g/cm3 = $2.259 \times 10^4$ kg/m3. A pebble-sized ball of osmium would weigh a few tens of grams.
For back-of-the-envelope calculations, it's common to just look at the exponent. Your material is $10^{8-4} = 10^4$ times as dense as osmium. The actual result is that the material these men found is somewhere around 13,000 times as dense as osmium, but this figure could easily be anywhere from 10,000 to 15,000 times depending on how strong these men are.
For comparison, as pointed out by Chinu, a neutron star has a density on the order of $10^{17}$ kg/m3 (actually, several times that; Wikipedia states $3.7 \times 10^{17}$ to $5.9 \times 10^{17}$ kg/m3), which is another nine orders of magnitude (a billion times) more dense than the material you envision. A pebble-sized portion of a neutron star, assuming it stayed together (which it wouldn't, as IndigoFenix already pointed out), would weigh not 300 kg, but more like 300,000,000,000 ($3 \times 10^{11}$) kg.
In conclusion, basically and unfortunately, this question is another example of a lack of sense of scale in space.
I agree with AndyD273: It would probably be better, and less likely to risk loss of suspension of disbelief, to just have these men come up with a super-strong alloy instead. You don't even have to name or describe the parts to such an alloy unless you want to (but if you do, beware of falling into the same trap again by misestimating things).
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Neutronium probably isn't the material that you want to use if you want to keep it even slightly plausible. It can't exist outside of a neutron star that has less than 2 solar masses squeezed into a 10 mile diameter. Anything less than that and the strong nuclear force would cause the outer layers to pop off, losing more mass, until it disintegrates into a cloud of neutron radiation.
But say you handwaved that part away.
Could you make armor out of it? No. It would be to heavy to move (like several earths heavy), and with so much gravity that anything in the vicinity around it would be pulled toward it, crushing down to a crusty patina on the surface.
Could you make a weapon out of it? Yes. Drop a chunk toward a planet and watch it shatter it's way through, and then the broken chunks would slowly form around the piece of neutronium.
Alternatives:
If you want an unbreakable armor, I'd personally suggest some super advanced alloy. Say they find a mysterious piece of metal, melt it down and combine it with other metals like iron to form something new.
Steel is an alloy of iron, carbon, and a few other metals depending on what properties you want it to have. By adding this mystery metal you could give it whatever properties you want.
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