Finding a quantum phase transition, part 1

I am going to try to get the post frequency back up now that some tasks are getting off the to-do list....

Last year, we found what seems to be a previously undiscovered quantum phase transition, and I think it's kind of a fun example of how this kind of science gets done, with a few take-away lessons for students.  The paper itself is here.

My colleague Jun Lou and I had been interested in low-dimensional materials with interesting magnetic properties for a while (back before it was cool, as the hipsters say).  The 2d materials craze continues, and a number of these are expected to have magnetic ordering of various kinds.  For example, even down to atomically thin single layers, Cr₂Ge₂Te₆ is a ferromagnetic insulator (see here), as is CrI₃ (see here).  The 2d material VS₂ had been predicted to be a ferromagnet in the single-layer limit.  

In the pursuit of VS₂, Prof. Lou's student Jiangtan Yuan found that the vanadium-sulphur phase diagram is rather finicky, and we ended up with a variety of crystals of V₅S₈ with thicknesses down to about 10 nm (a few unit cells).  

[Lesson 1:  Just because they're not the samples you want doesn't mean that they're uninteresting.]   

It turns out that V₅S₈  had been investigated in bulk form (that is, mm-cm sized crystals) rather heavily by several Japanese groups starting in the mid-1970s.  They discovered and figured out quite a bit.  Using typical x-ray methods they found the material's structure:  It's better to think of V₅S₈  as V_0.25VS₂.  There are VS₂ layers with an ordered arrangement of vanadium atoms intercalated in the interlayer space.  By measuring electrical conduction, they found that the system as a whole is metallic.   Using neutron scattering, they showed that there are unpaired 3d electrons that are localized to those intercalated vanadium atoms, and that those local magnetic moments order antiferromagnetically below a Neel temperature of 32 K in the bulk.  The moments like to align (antialign) along a direction close to perpendicular to the VS₂ layers, as shown in the top panel of the figure.   (Antiferromagnetism can be tough to detect, as it does not produce the big stray magnetic fields that we all associate with ferromagnetism. )

If a large magnetic field is applied perpendicular to the layers, the spins that are anti-aligned become very energetically unfavored.  It becomes energetically favorable for the spins to find some way to avoid antialignment but still keep the antiferromagnetism.  The result is a spin-flop transition, when the moments keep their antiferromagnetism but flop down toward the plane, as in the lower panel of the figure.  What's particularly nice in this system is that this ends up producing a kink in the electrical resistance vs. magnetic field that is a clear, unambiguous signature of the spin flop, and therefore a way of spotting antiferromagnetism electrically. 

My student Will Hardy figured out how to make reliable electrical contact to the little, thin V₅S₈ crystals (not a trivial task), and we found the physics described above.  However, we also stumbled on a mystery that I'll leave you as a cliff-hanger until the next post:  Just below the Neel temperature, we didn't just find the spin-flop kink.  Instead, we found hysteresis in the magnetoresistance, over an extremely narrow temperature range, as shown here.

[Lesson 2:  New kinds of samples can make "old" materials young again.]

[Lesson 3:  Don't explore too coarsely.  We could easily have missed that entire ~ 2.5 K temperature window when you can see the hysteresis with our magnetic field range.] 

Tune in next time for the rest of the story....