Silke Paschen (Vienna): Exploring heavy fermion quantum criticality in the extreme 3D limit

Silke Paschen (TU, Vienna)
Exploring heavy fermion quantum criticality in the extreme 3D limit
Blogged by Andy Schofield

The point will be to show how experiments Ce₃Pd₂₀Si₆ (abreviated as CPS) reveal a new three dimensional (i.e. cubic) quantum critical system. This is not a superconducting system.



Introduction: The rising volume of the Fermi sea is illustrated with a cartoon from Piers Coleman's News and Views paper in Nature Materials, 11 185 (2012). The first heavy fermion system was CeAl3 [PRL, 35, 1779 (1975)] which has a mass enhancement of 1600 of a free electron. The Kadowaki-Woods ratio [SSC, 58 507 (1986)] unified the Fermi liquid response of many materials in the heavy fermion class. However subsequently materials of similar structure and composition started to show non-Fermi liquid response: eg Y doped U₂Pd₃ with C/T ~ log T. It then appeared that many of the bad-actors were close to a magnetic phase transition thereby anchoring non-Fermi liquid behaviour to quantum critical points formed by doping or other control parameters: CeCu_6-xAu_x (doping), YbRh₂Si₂ (magnetic field tuned), CeIn_3-xSn_x (doping PRL 2006), CeRhIn5 (Nature 2006).

Routes to magnetism in HF materials: Two views - either a spin-density wave instability of the heavy fermi liquid, or the breakdown of the Kondo effect and formation of order from local moments. The model for the latter case (particularly for CeCu_6-xAu_x) relied on two dimensionality.
Question: Is the SDW transition Stoner like? Yes
How could we distinguish between these two views. Coleman proposed Hall effect measurements for that to see the large heavy fermion fermi surface to magnetically ordered state with small fermi volume at the kondo breakdown scenario. YRS (YbRh₂Si₂) saw some support for this in the Hall effect, and with time this has improved.

The cross-over in the Hall sharpens in a fashion linear with T to infinitely sharp at T=0 (which will be tested with Silke's new adiabtic demag fridge so watch this space!). Cleanliness was once an issue (since the blogger proposed an alternative scenario which predicted an effect scaling with scattering) but the observed effect did not change with sample quality.
A more complete list of possible scenarios was then presented:

• Kondo breakdown
• A Lifshitz/Topogical transition
• Valence transition
• Quantum tricritical point
• Weak-field breakdown of Boltzmann transport

Now we have a new cubic material: Ce₃Pd₂₀Si₆ which has a Curie-Weiss susceptibility at high temperature, then seems to show a transition at about T_Q ~ 0.55K (quadrupolar ordering??) and then further Neel ordering at 0.25K as seen in specific heat and susceptibility. Crystal fields are analysed - there are 2 Ce sites with different crystal fields. The phase transitions are split apart in B field T_N goes down and T_Q goes up.

The non-Fermi liquid properties are as follows: Between the 2 phase transitions we see C/T = - Log T and the electrical resistivity is linear in T in a certain range. The Hall effect is then studied as a function of field which suggests two distinct regimes in terms of the slopes. The Neel ordering is now clearly seen in magnetotransport, but there is an additional line which is not associated with the magnetic ordering except at T=0 but goes off in a different direction with field and crosses the T_Q point with no effect - strikingly reminiscent of YRS with the sharpening feature as T to some power. This is in contrast to that seen at the Neel transition feature.
Question (from AJS): Are there a range of disordered systems? No - very hard to make.
Silke then made reference to a theoretical phase diagram (T=0) of the range of phases present (small vol and large vol fermi surfaces with magnetic order - either local or SDW - and paramagnetism). A picture due to Qimiao Si. Silke then placed YRS on that phase diagram.
Question (from PC): Is there an evidence for a line between multiple phases or could it be a tetracritical point? The Ir and Co doping suggest that it is a line but still basically open.
Silke claimed CPS is a transition between small and large volumes magnetic phase transitions so is a different point on the phase diagram with dimensionality being the "tuning parameter" that changes where the material is placed on the phase diagram (Custers et al Nat. Mat 2012). Matsuda's group in Kyoto work on MBE materials grown might be able to test this notion out. CeRhIn5 work shortly to be published is also suggestive of two phases.

So in summary: Seen physics in CPS very remeniscent of YRS but with the possibility that 3D materials are placed in a different point on the phase diagram.

Question (Collin Broholm): Did you consider the detailed shape of the phase boundaries under field so moving at fixed T could skim the top of the phase boundary? We avoided that part of the phase diagram.
Question (Nakatsuji):  What are the P phases on the phase diagram - are they seen? Paramagnetic regions - and we have looked in the Ge doped YRS where we do seem to see that as a non-Fermi liquid phase. Is it seen in transport only? Well T scale is very low and resistivity is the only probe we can currently use down there.

What a lovely talk!