Satoru NAKATSUJI: Quantum criticality and spin liquid in Kondo Lattices (YbAlB4, Pr2Ir2O7)

Satoru begins by presenting the classic Doniach type phase diagram (of course in a its more "modern" form) showing a quantum critical point between the magnetism and Fermi liquid. The question is whether the magnetic order can be suppressed using geometric frustration for the f-electron system. This could reveal a quantum spin-liquid. Here the case to be presented is Pr2Ir2O7. The alternative is to use the itinerant electrons to weaken the order (perhaps by mediating a feromagnetic interaction) and this is the case in YbAlB4 where a chiral spin-liquid is stabilized.

Time reversal symmetry is fundamental in physics and can be broken say with magnetic dipole order. It can also be broken without dipolar order via a chiral spin state (where there is a net S.S x S around a plaquette) as proposed in the curpates in the distant past. It is difficult to detect this order, but the Hall effect may provide a signal. The anomalous Hall effect (AHE) in a ferromagnet would be an example (with a contribution proportional to the magnetization). However a chiral state would also give a contribution to the Hall effect because the Berry phase accumulates as electrons move in the presence of chirality. Here you get a Hall effect without M or B.

Pr2Ir2O7: (S. Nakatsuji, PRL 96, 2006) has Pr3+ 4f2 localized Ising moments in a pyrochlore lattice of corner sharing tetrahedra. It is highly frustrated with no order down to 0.3K much less than the Heisenberg scale of 2K. The Ir4+ 5d5 provide the conduction electrons. Piers asks about the crystal fields and in response to Satoru's comment, Paul Canfield: asks about the point symmetry and worries about the declared doublet groundstate since this is non Kramers. Satoru parks the question about the evidence for a magnetic doublet. The pyrochlore lattice has the ice rules physics (2 moments in, 2 moments out on each tetrahedra along the local 111; direction of a tetrahedra) with the residual entropy classically. Evidence that this is the case in the Pr2Ir2O7 is the magnetic anisotropy which is consistent and neutrons. There is also a metamagnetic transition only for B fields along 111 which is when the system switches to a 3in 1 out state. S-W Cheong: says why is there no magnetization plateaux then? The numbers seems to match expectations. The claim is that there are ferromagnetic correlations with a Jff of 1.4K as seen as a peak in the specific heat. Chi3 has a steep negative increase and saturates to a large negative value. Andriy: why negative? The explanation comes in the form of the M(H) curve being convex not concave (which seems like a restatement of the facts to me). Normally you would expect spin freezing at around 1.4K but this does not happen.

Below 1.5K there is an enhancement and hysteresis in rho_xy between zero field cold and field cooled. Yet muSR shows no freezing of the moments down to 20mK. Field is along [111] and current along [110]. There is also a remnant Hall effect when B is returned to zero, though no evidence in the magnetization of a net moment. So this points to a spontaneous breaking of time reversal symmetry (TRS) at 1.5K. S-W Cheong as a question and demands to see the next slide(!). He means previous of course to much amusement. Is it really a zero field state on domain related state? Answer: domains are being alligned which need to be trained by the field. Paul asks about a specific heat signature. Answer: there is a peak but no jump.
There is anisotropy in this hysteresis effect: largest with B//[111] and smallest with B//[100]. So the 3-in, 1-out state may be stabalized not only at B>B_c but also may have some overlap with the groundstate.

Zero field quantum criticality in beta YbAlB4

We now turn to the second material which may show a spin-liquid groundstate. In beta YbAlB4 the Yb ions are organized into a honeycomb lattice which is slightly stretched and the B ions form a lattice of 5 and 7 fold coordinated rings. Here the ordered magnetism is suppressed apparently by the enhanced hybridization of the local moments with the conduction electron sea. Hard X-ray XPS reveals that this is ain intermediate valence compound with Yb averaging 2.75 rather than either 3+ or 2+.

Application of pressure enhances the hybrization as seen in the resistivities. The evidence for quantum criticality comes from the magnetic Gruniesen parameter which diverges but with two distinct power-laws. T^{-1.5} for 0.4K < t="0.">300). The critical field is quite anisotropic and seems to be paramagnetically limited. SdH oscillations are seen '(mean free path of order 1 micron) anbd show a 3D Fermi surface, and a mass of 30m. It is a combination of 2D cylinders and 1D sheets. A surprising thing is that X-ray PES shows that Yb3+ and Yb2+ coexists (roughly 2.75) . This mixed valence would normally yield a Pauli paramgnetic suscpetibility because of the screening/itinerancy. However in this material you actually see shows 1/T. Paul says, no it does not look like 1/T. Coleman says: is there one or two regions of Curie-Weiss. Answer: there are two. Resistivity exponent (rho ~ T^2) colour maps suggest a quantum critical point at B=0. Moreover it is a rare example of M diverging as a quantum critical point is approached. With interesting power laws. Rafael Fernandes asks is there something in the specific heat? Answer: yes but wait.... The interesting thing is that there is scaling of the magnetization (dM/dT) at B< f="B^\alpha" b="0". Oh no... it looks like my attempt to put in the scaling form as deleted the rest of my blog....help. Is there anyway of recovering it? Here is my attempt to recall the other later aspects of the blog and the questions.

Yuri Grin and Satoru Nakatsuji discusss alpha and beta YAlB4

There was a nice experimental contrast with the alpha phase of this material which differs by having a chequerboard arrangement of the distortions in the honeycomb lattice. It seems to be a Fermi liquid. So the claim is that this (ie the beta material) system is right on the border (within 1 gauss) of a quantum critical point. This seems an unlikely fine tuning so Satoru offered an argument that this is part of a quantum critical phase where magnetism has become a spin liquid. The mechanism was argued to be ferromagnetic interactions effectively frustrating the system.
Question time (apologies to those I have not remembered)
Amy Briffa and Rafael Fernandes: both asked about the evidence for the first material being chiral as opposed to a ferromagnet. The fact that there is no hysteresis in the magnetization but only in the Hall precludes ferromagnetism. There is no microscopic signature yet of the chirality - just the Hall anomaly.
Juri and Thamizhavel: both asked about the growth conditions of the alpha and beta phases. They can be discriminated by colour and morphology from the flux. However, why such similar materials emerge in pure form from a flux did not seem to be understood.