Meigan Aronson (Stony Brook and Brookhaven NL) Geometric Frustration and Quantum Criticality in Heavy Fermion Compounds

Meigan began with a short introduction about the formation of quantum critical points.  She emphasized how in  wide variety of compounds, heavy fermions, organics, arsenides, quantum critical points play an organizing role. We've come to know that if we are such a QCP, that we will see unusual critical phenomena - C/T ~ log(T), chi ~ T^(1 + lambda), chi'' ~ f(E/T).   Yet if we are away from the QCP - Fermi liquid, C/T~ gamma_0, chi~ chi_0, rho~ A T^2, m*/m ~ 1/T_F.   This reveals that one has an underlying electronic state with Landau quasiparticles.

In some, not all, she said, as we come towards the QCP, we often see that the effective mass m*/m diverges - a phenomenon that is associated with the break-down of the Fermi liquid at the QCP.

One picture that has emerged, there is a transition from a small to a large Fermi surface.   g the tuning parmeter. When g< g_c, one has a small Fermi surface, but when g > g_c, a large Fermi surface, in which the localized spin is absorbed into the large Fermi surface.

Meigan discussed how it now appears, that the localization delocalization transition may sometimes separate from the magnetic ordering QCP, leaving open the possibility of an intermediate phase that she called a "spin liquid".

The sequence at T=0 would then be

   metallic AFM ---------metallic "spin liquid" ----large fermi surface Fermi liquid.

This then motivates a search for new materials in which geometric frustration is important.

Meigan reviewed the Kondo effect.  T>>TK, localized moments decoupled from conduction electrons - f-electrons excluded from the small Fermi surface.  T<

1/T ---> chi_0
spectral function T< TK develops a Kondo resonance. eg inverse photoemission shows formation of Kondo resonance in CeNi2

Once one goes to the Kondo lattice, there is, she said, the potential for magnetic order, with a TN ~ J'~ J^2. This requires that TN> TK.  But if TN < JK, get a large FS Fermi liquid.  From this (Doniach) perspective, we expect a QCP separating the small FS AFM from the large FS Fermi liquid.

At this point, Meigan introduced the concept of the Shastry Sutherland Kondo lattice.  This model has the Hamiltonian

H =  J * sum over nearest neigbor bonds + J' * sum over diagonal bonds.

Intrinsic QCP at J'/J ~ 0.7, and for J' bigger than this point, a "spin liquid" develops. (Dimer fluid).

Q: (Schofield) why did you call it a liquid, rather than a solid?
A: What I meant is that you have local dimers, with no magnetic order.

Meigan then introduced the combined global phase diagram that combines the two ideas, frustration and Kondo effect.

Q: (Raphael Fernandes)  you showed a phase diagram where TK goes to zero - yet here it has a finite value at the quantum critical point.
A: The scale that you are refering to, is really T*, the delocalization scale - its relation to the Kondo temperature is complicated.  Here the quantity we are using is the single ion Kondo temperature.

Q: (Andrey Chubukov) can the Fermi liquid just go into a Fermi liquid with no major change in FS.
A: It could go either way. Localizing transition or spin density wave. (Blogger liberally interpreted Meigan's answer).

So that inbetween the small FS spin liquid and the large FS Fermi liquid, there should be a phase transition.

Some discussion with Paul Canfield about what it means to have a small or large Fermi surface.

Blogger: Piers Coleman

Blogger mentions work of Sachdev Senthil and Vojta - if you have an odd no of spins per unit cell - will donate a non-integral amount of electrons per spin, and there is definitively a difference between small and large FS.

Megian intrdouces the Shastry Sutherland mateiral SrCu2(BO3)2. This is a spin gap material with gap appearing that is seen in thermodynamics.  The hallmark of  a SS lattice is the presence of lattices in the

magnetization. Once the triplet becomes the ground-state, the possibility of AFM emerges - as you increase the field, a larger and larger no of the dimers will enter the AFM. You don't just see a smooth increase in magnetization - dimer triplets crystallize into SDW with long range AF order - these are incompressible leading to plateaux in the magnetization M(H).  The SDW co-exists with gaples, intinerant "superfluid' = triplets and singlets, and this leads to a rounding of the plateaux.




R2T2X Compounds

So Meigan's system takes us to the next level - the inclusion of conduction electrons.  She introduced the R2T2X compounds. These 221 compounds contain a frustrated rare earth layer separated by a transition metal TX layer.  These systems are interesting because there is the possibilty of Kondo physics, for a wide variety of compounds.   She introduced a huge list of Ce 221 compounds. Many are AFM ordered. Others are valence fluctuating.

She presented pictures of three single crystal compounds, Ce2Ge2Mg, Yb2Pt2Pb and Ce2Pt2Pb.
The first is magnetic, the second close to a QCP (but magnetic) and the third is a heavy fermion metal?
Ce221Mg  and Yb2Pt2Pb 221Pb are highly anisotropic, with moment lying in the plane of the  SS lattice.

She showed Schottky anomalies in the specific heat.  The Ce221 Mg and Yb221 show magnetic ordering peaks, but in the Ce221Pb, there is a smooth peak suggesting no magnetic order. It looks as if the Yb221 has an ordering state in which some percentage of the Yb states are in dimers.  Ce221 Mg - S= 0.49R at Tc suggesting that 93% of triplets - but in Yb 221, 77% triplets (0.4R) while Ce 221Pb 0.29R - 56% triplets.

Yb moments R log(2) = 0.68R
Yb triplets    1/2 R log(3) = 0.55 R

Canfield - I assume that further data will solidify the argument that the J'/J axis plays an important role.
Aronson - I agree with you - up to this point, I have not definitively shown that it is important.

Nevidomskyy - can you clarify the entropy.
Aronson - integration of C/T from T=0

Chubukov - what is the peak?
Aronson - would be the triplet-singlet excitation in an insulating SS magnet.

Magnetization of Ce2Ge2Mg - you cansee that lowering into the magnetic sate, one sees steps in the magnetization curve. Peaks in dB/dM that occur at M/Msaturation = 1/3, 4/9, 8/11 - exactly as in SrCu2(BO3)2. Perhaps most striking is the field scale - 14 tesla enough to get to 85% of saturation - but in Sr system, 33T gives 1/4 saturation magnetization, suggesting a much large interaction in the Sr case.

Also note that the steps are sharp in Ce2Ge2Mg, compared with the Sr221 system.

Takagi - question - the Strontium is Heisenberg - but this one is Ising like.
Aronson - Sr is also Ising out of plane - but ours are Ising like in the plane.
Takagi - but then you can't use a simple singlet-triplet picture.

Similar DB/dM for Yb2Pt2Pb- much more small index states, much more like Sr221, but broader and more hysteretic - much broader - so closer to melting in this case than in Ce221Mg.

Ce221Pb SDW completely absent - itinerant dimer triplets only.

Yb221 field-temperature phase diagram.  Actually, done using Hall sensor magnetometer - but you can see that the magnetization is highly structured.  The sharp peaks are the magnetization plateau. The highest temperature one is the analog of the Neel temperature - suppressed to zero at B~ 1T.Saw a lot of hysteresis beneath the neel dome - corresponding to strongly 1st order transitions. The upper transition does not show hysteresis, suggesting that it is second order.

TN/TN(B=0) vs B-BN/TN lines lie on top of one-another. Can place Ce2Pt2Pnb  and the other materials onto a single phase diagram.

Now turn to Ce2Pt2Pb.  Powelaw like divergence of magnetic susceptibility.
Heat capacity of Ce221Pb, has C/T ~ T^1.4.

C/T = large gamma_0 * T + C_o T^alpha

Ended talk presenting many materials on phase diagram.

Electronic structure very modified in Yb221 and Ce 221 - large resisitivity and collapsed anisotropy.   Still missing, evidence for Fermi liquid and spin liquid phases. Large to small Fermi surface transitions/crossovers.

Q how did you grow the crystals
A magnesium flux.

Q how close are these systems to perfect SS systems?
A one reason that they are not idealized - there are two SS bonds on one plane.  May also be important interplane interactions.  We haven't considered them yet?
Q what about dipolar interactions
A interesting question - typically, we don't think that the dipolar interactions are so important in HF compounds because they are metallic - screens out. But there might be short range interactions and these could contain dipole components?

Paul Canfield - possibility that there is a lot of disorder cerium. Do you single crystal x-ray refinements on the lanthanum or cerium.
Aronson - we don't have on La, but in Ce we do, and don't see signs of disorder in the X-ray refinement.

Silke Paschen.  Frustration diagram. I think you should allow the possibility of large FS magnetic order - consider extending the T* part of your diagram into the magnetically ordered phase.
Meigan - since we don't know anything about where the FS is small or large, will have to report back on it.
Paschen - maybe safer to put large FS on magnetic side.

Chubukov - you said there is anomalous T dependence of Sheat - can be magnetic, or electronic. Can you change magnetic field go away from critical point and measure whether T1/4 changes into T^2.
Aronson - yes - but we haven't yet.