Pascoal Pagliuso (Campinas, Brazil): Low symmetry structures and strong f-s(d-s) hybridization as key ingredients to find new unconventional superconductors

Pascoal began by introducing Campinas on the map.  There are many great beaches in Brazil, he told us, but Campinas is a great place to work, precisely because its far from the distractions of Brazil's beautiful beaches!  He also introduced the facilities at the Campinas lab - from the synchrotron - the fabulous sample growing facilities and their unique ESR setup with four different wavebands. The synchrotron is the only in South America, and it is a great facility for magnetic X-ray scattering, and they have used it extensively for characterization of magnetic order.






Outline

1. Review of structurally related physical properites of HFS families - the role fo CEF tetragonal symmetry

2. CeRhIn5 doped with La and Sn

3. Cd-doped Ce2(RH,Ir) In8

4. Possible relationship with the Fe-based Sc

5. New ideas for new materials.

Review of Properties

Next he introduced the family of compounds - from cubic CeIn3, to CeMIn5 to Ce2MIn8.  There are several sc in this families (six) - what makes them special?   If you consider related materials, including Ce2PdIn8, CePt2In7 and Pu(Co,Rh)Ga5 you have even more sc, but Pascual will keep with the simple
structures of this family.

Pascoal introduced the phase diagram.  For Co - Tc is max far from magnetic order. There is a linear increase of Tc as you go from Ir to Co.  Same with Ce2Rh1-xIrxIn8 - the difference is that the Ir compound is a spin glass and the range of SC is much smaller.

When you apply pressure you suppress AF and then get sc in CeRhIrIn5 and CeRhIn5.

CeRhIn5 orders AFM with Ce moments in the plane and spiral order along c-axis. Pressure suppresses TN and induces SC.  Ce2RhIn8 also orders, but with a commensurate structure.

Next he showed the susceptibility of CeMIn5 - with the anisotropy - c-axis is the magnetic easy axis.  Another interesting feature of the data, is that Tc is a linear function of c/a.  The evolution of the c-axis susceptibility and Tc struck his group as interesting.

There are three interactions to consider - RKKY, crystal field  and the Kondo scale.  This is what he is now going to discuss, showing a detailed series of experiments designed to explore the link between each of these variables and the crystal field structure of these compounds.

Begin by going back to discuss the rare-earths. Most have valence of 3+, incomplete f-shells.  Chemically alike.  4f orbitals are partially shielded by the external orbitals so that spin orbit effects are strong.  Lets turn to their g-factors

Ce S=1/2, L=3, J=5/2
Pd, S=1, L = 5, J = 5  Non Kramers ion. No spin, but sometimes non-Kramers doublets.
Gd L=0, J= 7/2  pure spin ion: ideal for a control atom with minimal crystal field effects - this will be important later.

He introduced crystal symmetries for these systems.

Why are Ce and Yb special?  Becuase Ce is f¹, wherea.s Yb is f¹³ with one hole. Those states are close to the fermi energy so that fs hybridization is strong. They are different from the other rare earths in this regard, he said.

But they also have a competition between RKKY and Kondo.  Showed the Doniach scenario, so that when J is small, RKKY dominates, but once T_K becomes larger, Kondo
compensated state develops with a large FS. SC often develops at the transition from the magnet to the heavy fermi liquid.

Next he introduces the tetragonal crystal fields -

Gamma 6 -  +-1/2

Gamma 7 +- mixture between
a|5/2> + b |3/2> and by tuning the admixture you can tune the anisotropy.

Separating out the interactions

So how can we separate all the interactions using material science?  If I track the magnetic properties of all the Gd I am probing the dependence of exchange with M.  Gd Rh-Ir all have the same Neel temperature (T_N) - this is not affected by either M or going from 115 to 218. This tells you that RKKY is determined by the nearest neighbor interactions - and this is important.

(a) Tuning RKKY without Xtal fields or Kondo: the case of Gd

How do we tune JRRKY?   As we go from 218, 115 103 Gd systems, same T_N and same magnetic structures (1/2, 0, 1/2) and spins in the ab-plane -> same JRKKY.

Q Canfield asks clarification - usually in a magnetically ordered state you have some magnetostriction.
A Pascoal says yes there is, but it does not reduce the symmetry.  Grenado, Serrano PRB (2004), PRB (2006).

(b) Turning on Xtal fields, but without Kondo: the case of Nd.

Now lets turn on the xtal fields by going to the Nd compounds.  As you go from Nd In3, Nd2RhIn8, Nd RhIn4, Nd2IrIn8, Nd IrIn8, there is a reduction of the amount of entropy associated with the transition (did I get this right?) - and the T_N goes up - larger Gamma 8 CEF splitting leads to a larger T_N.

Summarizing 103-115-218 -  as the anisotropy increases,  Nd increases T_N, Nd T_N goes up, Tb goes up, Gd stays the same (no crystal field effects) but Ce goes down.  Is the difference Kondo? : " I don't think so".

Paul Canfield  points out that the Gd T_N does actually go down weakly.
PP says yes, but only by 10%.

Now summarizing the magnetic order, Nd spins lie along the c-axis, Tb along c-axis also, but Gd and Ce order in plane (as does Sm).  When the  moment is along c-axis, T_N increases with tetragonal asymmetry, but when the moments lie in the  ab plane, T_N decreases with tetragonal asymmetry.

Here work with theorists comes in.  Garcia and Miranda (J. Appl. Phys. 99, 08P703 (2006); doi:10.1063/1.2176109, R. Lora-Serrano et al, Phys. Rev. B 79, 024422 (2009)) made a crystal field model with

H=B₂₀ O₂₀ +B₄₀ O₄₀ + B₄₄ O₄₄.

As you turn on B₂₀, for Ce, moment goes to plane, Nd tends to go along the c-axis.   No Kondo in the model.

Rafael Fernandes - what is the difference between the two cases?
PP - you just change the J.


Piers Coleman  asks - is there a simple way to understand this?
PP: - for Ce, Gamma 7 has a higher tendancy to have g-anisotropy in the plane. Nd tends to have c-axis Ising anisotropy in this structure.

Going on he shows T_N versus the Jz^2 in this model.  You do this for 5/2 and 9/2, as a function of Jz^2 anisotropy.  For J= 5/2, T_N goes down as the Jz^2 goes up, whereas for 9/2 and 6, T_N goes up.  Ce has the frustrated property that it has a larger C-axis susceptibility, but this suppresses T_N.

You may remember this is exactly what you saw experimentally.  T_N went down with Ising symmetry, but an increase in T_N for the large J systems.

But to be sure, the group used neutron scattering to track the evolution of the xtal ield ground-state. As you go from In to 115 Rh - Ir - Co you are increasing the 3/2 part of the xtal fields. Recently confirmed by Severing. Co is more Ising like - Rh is less Ising like and has larger T_N.

Rh - Ir - Co  Ising symmetry increasing, T_N going down.

All of this is going on without any effect of Kondo.

Increasing the xy anisotropy drives TN below the Kondo temperature, leading to SC.

Next he introduces a scenario - lets assume they have comparable TRKKY and T_K - it is anisotropy that is tuning T_N down through T_K with increasing g-anisotropy.

2. CeRhIn5 doped with La and Sn

OK. Lets now consider the Kondo effect influence.  For this, the group used dilution expts.  They choose samples with the same T_N=2.8K.  One is CeRhIn-Sn, one is Ce-LaRhIn5. Now apply pressure and for the Sn and La one, you get SC, but the critical pressures are different.  For La need higher pressure to find superconductivity.   From that data, you construct a phase diagram . Can clearly see that the Sn occurs at lower pressure, whereas La shifts SC to a higher pressure. Yet they started at the same T_N, so it must be the tuning of something else.

So putting this all together. Can calculate the negative pressure of La that decreases the Kondo coupling.  We know that Sn increases T_K, and from Tmax, can calculate the pressure effect of Sn.  Can drop all of them onto a single curve.  So the suppression fo the magnetisim has to be associated with an increasing T_K and a consequent crossover between localized and intinerant behavior of the Ce 4f.  Sn P* = P + 5kbar, La P* = P-2kbar. From these shifts, all fall on the same curve.

Canfield says equating this with pressure "is a sin in of itself".  Because the lattice pressure effects from physical pressure and substitution are different. But blogger did not follow the intricate discussion.



Canfield - when you are trying to compare with chemical pressure there are many parameters - it becomes ambiguous. La - changes size of Unit cell, hybridization - magnetic zero La will suppress T_N also.  Pascoal replied that they certainly accounted for this. He used Gd similar - same La Yt concentration - La distorts, Gd does not, so can show there is no affect of distortion in the T_N.

Monika Gazma: Does the La go in uniformly?
PP says mainly in the plane.
Monika Gazma- this will change hybridization a lot no?
PP - yes.
Monika Gazma- no change of lattice parameters with Sn
PP - no.

Main points again:

1 Ising like doublet.
2 Some sort of hybridization.















3. Cd-doped Ce2(RH,Ir) In8

Now Cd doping in 218 Rh, find that Cd tends to rotate the Ce moment into the plane (C. Adriano et al, PRB 81, 245115 (2010)). So Cd both tunes and changes the crystal fields.  So according to the ideas - Cd in plane - not good for SC, and applying pressure will not produce SC. This was confirmed by expt.  Pressure is also pushing spins into plane - even worst for SC.  Currently trying the converse with Sn and Ga - expect it will increase T_c, but experiment not done yet, nor direction of moment yet tracked.

Now to the Yb systems - why no SC?  YbRh2Si2 has a doublet in the plane from the anisotropy in the g-factor - - tends to favor AFM and this is why for PP, this compound will never be superconducting.
Now for YbAlB4, this is Ising like, but has larger susceptibility along c-axis.  This system has a very curious ESR signal - with a g that is larger along the c-axis.  Confirms this trend.

Meigan Aronson - But the Np compound is different - this is xy
PP -Np - probably  5f2 - different situation.

Paul Canfield - CeCu2si2?
PP - Ising like.

Ising doublets are good for SC.

4/5. Possible relationship with the Fe-based Sc and New ideas for new materials.

Speculative part- how can we apply this knowledge to the 3d systems?   Here I have a problem because 3d doesn't have the same kind of local anisotropies.  We know that 122 structure is good for Ce and good for iron. So why not try to use that comparison.  218 structure.  Likes it.

So shows Tc vs c/a.  FeAs systems lie at intermediate c/a. Same for the cuprates. What is interesting is that that the borocarbide has nice c/a, but low Tc.  MgB2 also doesn't lie on the curve.  Maybe here there is some connection.  I want to use to try to make new materials with SC and high anisotropy (c/a ratio).   Eg, 218 structure with c/a = 3.0. A2MB8  materials.  M - CuFe, Co, Ni, n, Ru, Re, Mo, A = La, Y, Ca, Sr, Ba, Mg, K,  B = Bi, Sb, Ge, Sn, In As.  Can also do with 122 and 214 c/a - 3/4. Trying to choose transition M's with a local moment - hoping for 2D magnetism that will drive SC.


Andriy Nevidomskyy - could you please repeat conclusion for YAlB4.
PP - just because it has a larger g out of plane from ESR - small - complication here - we are not directly probing the f-resonance, so we're not capturing all of the anisotropy.
Andriy Nevidomskyy  - how would you compare with alpha case?
PP - dont have any coupling to the f-electron - doesn't

Paul Canfield - the unspoken difficulty of a plot with this, is all the compounds that have Tc=0! It is a very highly selective data set.
PP - I don't want the ones with zero Tc, I want guidance about those