In heavy fermion containing Ce, U etc get the competition between local and itinerant built into the atom itself.
Describes Kondo's theory of a single impurity in a metal with nice PPT images.
On the lattice: Local moments surrounded by conduction electrons. Moments screened by conduction electrons.
In momentum space this is describes as a band hybridization between a flat band and a dispersive conduction electron band. No symmetries are broken and there are no phase transitions.
Now turn to the hidden order in URu2Si2. A heavy fermion system with a phase transition but 27 years after the discovery no definitive information about the nature of the magnetic order.
question from Andy Schofield: Can you really have a Kondo effect for an Ising spin? Answer it is not truly an Ising spin there are other levels to worry about: OK
Impressive list of many theories offered to describe this. Emphasize that many of the theories have been ruled out and several more are on the way out.
Summary of major points to explain: Large entropy change at phase transition, small or absent magnetic ordered moment, proximity to antiferromagnetism.
New insights from STM: an effective measurement of the band structure. Hybridization develops at the hidden ordering transition. BCS development of the hybridization gap. This gap has also been seen in optical spectroscopy.
The experimental claim is that the Hybridization is the order parameter and it develops in a mean field fashion. Timusk points out that the data is not good enough to distinguish the critical exponent. There is agreement on this.
Then describe the Kyoto experiments revealing four fold symmetry breaking at the phase transition.
The absence of a transverse f-electron response indicates this is conduction electrons scattering off the hidden order. This leads to constraints on the spin dependent scattering t-matrix.
Now return to the giant Ising anisotropy. This is a generic feature of the non-Kramers ion.
Describe deHaas van Alpen data that show the carriers really are ideally Ising. The consequence is a Kramers index (-1)^2J. The Kramers index in this case must be -1.
This leads to the prediction that the hybridization operator must break double time reversal symmetry like a spinor.
Spinorial order parameter is also indicated by the proximity of the large moment antiferromagnetic phase. The nature of the multi phase diagram indicates that the order parameter of the hidden ordered phase and the AFM phase are relates by a simple rotation. This indicates that if the AFM order breaks time reversal symmetry then the hidden order must also.
Now discuss spinorial hybridization. In fluctuations from a non-Kramers doublet the fluctuations will also be to a doublet. Since the excited state is a doublet the hybridization operator must itself have spinor character.
hastacit means spear like and is associated with a rotation of the AFM phase. Now write a Landau Free energy that is to describe the behavior and phase diagram of the spinor field. This can produce the hidden order and by rotation the AFM order.
The theory predicts that the gap to longitudinal spin fluctuations should vanish at the first order phase transition between the HO and AFM phases.
The Landau theory also is able to describe the non-linear susceptibility and it's anisotropy. This is another aspect of URu2Si2 that had remained for many years since the discovery of the effect by Ramirez.
Now back to the microscopic theory. The Non-Kramers Gamma 5 doublet is relevant here. This is a magnetic non-Kramers doublet. It has a quadropolar moment and so is not exactly an Ising spin. This may address the previous comment about how one can have a Kondo effect for an Ising spin.
Now to the board! Write down two hybridization terms; Valence fluctuations terms. Now user Slave boson mean field theory. A Scwinger Boson representing the excited doublet. This is simultaneously a slave and a Schwinger Boson.
Develop the hybridization term which has gamma6 and gamma7 components. Develop a hidden order ansatz. The interchannel hybridization is staggered whereas the intra channel hybridization is uniform.
With the mean field hamiltonian can apply all the usual machinery and extract the results.
One is that there must be a magnetic moment that must be in the basal plane. The magnitude is about 0.01 muB and is an upper bound on what can be seen. There is no large f-electron moment.
The xy anisotropy should appear below TN.
Now address comparison to experimental results: There is generally consistency:
no large moments
hybridization gap is the order parameter
Ising quasi-particles
Broken tetragonal symmetry
inelastic neutron scattering is a pseudo goldstone mode.
predict longitudinal spin fluctuations that should vanish across the phase transition
resonant nematicity
Things to be done: How to generate superconductivity from the hastatic state.
Are there other examples of hastatic order.
In the hidden ordered phase: Kapitulnik says there is no Kerr effect in the hidden ordered phase but there is in the superconducting phase.
Fernandez: What would be the elastic data across the hidden ordered phase transition. Answer this should be looked at in new better samples.
Flint states that if the mixed valency is 20% then the transverse moment in the hidden ordered phase should be 0.01 muB.
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