Conference dinner, evening of Thursday 12th August

Piers Coleman

The organizers decided we should get out of the lecture theatre, so on the last evening of the conference arranged a conference dinner. This dinner took place on the sea-front right beside the Adriatico guest house, where we ate nice sea food and drank wine, grappa and limoncello (some more than others!)

Piers started the proceedings by announcing that he wouldn't make a speech, but would instead haphazardly pick individuals out of the crowd to do so.

Aharon Kapitulnik proposing that someone make a toast

Andriy Chubukov and Sam Carr

First up was Paul Canfield, who was pleased to be here, and commented upon the romantic lifestyle of theorists. Aharon Kapitulnik agrees with Paul. Ilya Eremin gave a toast to the bloggers, and Laura Greene sang to us. We then had Zlatko Tesanovich, of the 'old generation' reminiscing about the first time he came to this conference in the 80's, and Natasha Perkins urging the 'old generation' (supervisors) to send the 'new generation' (students) to conferences.

Much fun was had by all. This is the life!

Zlatko Tesanovic

Raphael Fernandes and Paul Canfield

L-R: Foreground Meigan Aronson, Natasha Perkins, Andrei Chubukov, Background Yu Lu, Piers Coleman, Silke Paschen and Hanna Kapitulnik

Hide Takagi

Andy Schofield

Piers Coleman

Akira FURUSAKI (RIKEN) - Unconventional orders in frustrated ferromagnetic spin chains

Akira starts by thanking his collaborators for this work:
Toshiya Hikihara (Hokkaido Univ.)
Tsutomu Momoi (RIKEN)
Masahiro Sato (RIKEN)
Shunsuke Furukawa (Toronto)

And the work presented is published in these references:
PRB 78, 144404 (2008)
PRB 79, 060406 (2009)
PRB 81, 094430 (2010)

Introduction

We have the very general problem of the search for new states of matter in quantum spin systems. Geometric frustration suppresses conventional magnetic order, leaving two possibilities:
--No order at all (spin liquids, spinons, etc...) This was the topic of the previous seminar.
--Exotic unconventional orders (spin nematic, etc...) which will be the subject of this talk.

As a theorist, the strategy is to taken a simple minimal model, (in this case, essentially 1D), and solve it without any uncontrolled approximations.

Plan for talk:
--introduction to J1-J2 spin chain in magnetic field
--vector chiral order
--nematic and multipolar orders
--XXZ anisotropy (as an alternative to magnetic field)

Introduction to J1-J2 spin chain in magnetic field

H = J1 \sum_i S_i S_{i+1} + J2 \sum_i S_i S_{i+2} + h \sum_i S_i

This Hamiltonian can be viewed in two different ways: firstly as a spin chain with nearest neighbor (J1) and next-nearest-neighbor (J2) couplings, and a magnetic field h. Alternatively, one can consider the even sites on one leg of a 2-leg zig-zag ladder, and the odd sites on the other leg.

If J2>0 (anti-ferromagnetic AFM), then we get frustration, whether or not J1 is >0 (ferromagnetic - FM) or <0 (AFM). In this talk we will mainly consider J1<0 (FM), although later on we will also consider the other case. The J1-J2 model is a theorists simplification of reality, but there seems to be a pretty good experimental realization: a spin-1/2 edge-sharing Cu-oxide chain - where the nn is FM, but nnn is AFM due to presence of oxygens As specific examples of this, LiCuVO4, LiCu2O2, etc... different materials will have different ratios of J1/J2.  

More specific example: LiCuV04 J1=-1.6 meV, J2=5.6 meV
The phase diagram in mag field seems to show many different ordered phases (see Schrettle et al, 2007) This is one of the systems we will have in mind, and we will come back to it later.

J1-J2 model -- lets first discuss the classical limit, taking s as a classical variable.

In this case, we find that when -4 < J1/J2 < 4 (dominant n.n. AFM) gives the Neel state. Now, lets apply the magnetic field, still within the classical limit: in the helical state, we find the magnetic field leads to canting of spins forming an `umbrella' structure, before they eventually enter the FM phase at some critical h. This helical `umbrella' phase has a U(1) symmetry of overall rotation around the applied field, as well as a Z_2 (vector) chirality degree of freedom, related to the vector chiral operator (S_l x S_{l+1})^z. This chiral vector is a measure of which way around the spiral you are going. In 1D, the U(1) symmetry cannot be broken giving no helical long range order, however the Z_2 symmetry can be broken, giving long range order of vector chirality. Note it is very important to have the magnetic field breaking the SU(2) symmetry down to U(1) [see Kolezhuk & Vekua (2005)]. However, this breaking of SU(2) down to U(1) could also be done via easy-plane anisotropy (XXZ) [Nersesyan, Gogolin and Essler (1998)]. Question (Piers): Why can't we have this order without the magnetic field? Answer: One could get power law correlations functions, but not long range order. However, magnetic field may be infinitesimal. We will come back to this near the end. Lets look more closely at spin-nematic order:

Vector chirality: (S_l x S_{l+1})^z is antisymmetric p-type nematic [Chandra and Coleman (1991)]

But it is also possible to have symmetric products: i.e. n-type nematic order, which is in fact quadrupolar order with an order parameter Ql^-- = s_l^- s_l+1^-. In the classical picture, one sees that making a rotation of pi on the spins doesn't change Q - it is a director. It can also be related to bound states of magnons.

We can also look at operators for bounds states of higher numbers of magnons, e.g. 3-magnon, etc... These are multipolar orders. Back to the J1-J2 model, and we see the phase diagram in magnetic field (h>0): it is a very rich phase diagram, including a number of these multipolar orders such as anti-ferro-triatic, antiferro-nematic, nematic (IC) and vector chiral phases. We will now discuss aspects of this in more detail.

In the limit J1/J2-> 0, we can bosonize by taking two AF chains + weak J1 coupling (this is thinking in the zig-zag ladder picture). The spin operators represented in terms of the bosonic fields as smooth+staggered parts in the usual way. Taking all of the relevant inter-chain coupling terms gives us a nasty looking sine-Gordon like model with two cosines- but this has already been discussed in the literature by Nersesyan, Gogolin and Essler (1998). Depending on which cosine is the most relevant (which in turn depends on the scaling dimensions, which in turn depends on some non-trivial combination of the microscopic parameters), can find either vector chiral order, or nematic order.

In the Vector Chiral phase, find the vector chiral order parameter has long range order. This corresponds to a phase with alternating orbital spin currents in the zig-zag picture, - but note however that there is no net spin current flow. On the other hand, the spin-spin correlation functions have an incommensurate power-law decay. This is a quantum counterpart of the classical helical state.

This field-theory (for J1/J2->0) can be supplemented with DMRG (which is essentially numerically exact) - calculation of correlation functions here agrees with the analytic results.


Now, let us look at energy epectrum of magnon excitations at saturation field (h=hc). Can compute 1 magnon, 2 magnon, etc... and find depending on ration J1/J2 that 2 magnon, 3 magnon, etc... bound states may have the lowest energy state. This will lead us to multipolar order.

How can we write an effective theory for multi-polar Tomonaga-Luttinger (TL) liquids? Treat the p-magnon bound-state as a hard-core boson (with some extra residual interaction), then use Haldane's hydrodynamic approach (bosonization of bosons, [Haldane 1980]). This allows easy calculation of certain correlation functions, e.g. power law decays of bound magnons, as well as of SzSz correlation functions. However, depending on the Luttinger Liquid (LL) parameter (which depends in complicated way on microscopic parameters as usual), can find which of these correlation functions is the dominant one, giving both SDW phase, or nematic phase. Note that these `phases', unlike the Z2 chiral order, correspond to no broken symmetries however, and simply label the dominant correlation function in quasi-LRO.

DMRG results also confirm existence of these phases (nematic, triatic, SDW2 and SDW3), and clarifies positions of phase boundaries, which are not always reliably obtained within the field theory.

How to detect nematic, triatic etc... order?
One way is to look at dynamical spin structure factors, or in the NMR relaxation rate.

We then see a load of plots of these quantities in different phases, which I'm not sure I can describe in words. Do we have any photos of this slide?


Back to LiCuVO4
We know the ratio J1/J2, so can identify the experimentally determined phases with those of the theoretical phase diagram.

Question (Andrey): How well are the phases really understood experimentally?
Answer: Not well, but there is some evidence for the spiral order (I missed exactly what this evidence is).

Question (blogger): What about inter-chain couplings in this material?
Answer: We didn't really study that, although they must of course be important to give real phase transitions. There is a recent paper (unfortunately I missed the authors) which address inter-chain couplings in nematic type phases.

AFM J1-J2 model

Now, lets look at a slight variation of the model, where all couplings are AFM (but still in a magnetic field). As references, see Okunishi & Tonegawa (2003); McCuolloch et al (2008); Okunishi (2008); Hikihara, Momoi, Furusaki and Kawamura (2010).

We now have a picture comparing the phase diagrams for J1<0>0 ... hopefully we can add this picture to the blog as it is rather too complicated to describe in real time...
We learn that this phase diagram was obtained mostly by numerics.

XXZ J1-J2 model

Another variation of the model: the case of no magnetic field, but breaking the SU(2) symmetry down to U(1) by XXZ easy-plane anisotropy.

Many previous studies of AF J1-J2 case with anistropy \Delta - showing regions of gapless chiral order. However, (more recent work), if J1 is FM, find much larger region (in phase space) of the gapless chiral order. For more details, see Furukawa, Sato and Onoda arXiv:1003.3940. We are running out of time during the talk however, and there is no time to discuss this more fully.






 

Summary:
--We study the spin-1/2 frustrated FM J1-J2 spin chain in a magnetic field.
--Many interesting `phases' seen, including conventional SDW forms, but also nematic and multipolar phases, as well as a vector chiral phase.

Question time!!

Question (Andrey): what happens in isotropic chain in zero field - there seems to be an accumulation point of many transitions?
Answer: this is an open question - some recent numerics seem to show a dimerized state, but it could be different to that seen in the anisotropic phase. This is such an unstable point, it's hard to say.

Comment (Shura): As long as SU(2) is unbroken, there is no room for phases with local currents (as the SU(2) cannot be spontaneously broken). So what happens? Seems we don't really know. This is either unfortunately or fortunately (depending on your point of view) an open question.

Question (Piers): Any hope for this physics to be seen in non-1D systems?
Answer: Maybe LiCuVO4 (note: this was also mentioned briefly within the main body of the talk, but the blogger missed it)
Comment (Chubukov): This is essentially 1D physics - any real material will be quasi-1D, and there will be a critical inter-chain coupling where this physics is killed.

Andrey Chubukov with Blogger, Sam Carr.

Yuji MATSUDA (Kyoto University): Elementary excitations in a 2D candidate quantum spin liquid

Lecture Notes

OUTLINE:
- Introduction
- A possible qu. SL on 2D triangulat lattice:
* kappa-(BEDT-TTF)2 Cu2(CN)3 (ET)
* EtMe3Sb[Pd(dmit)2]2
- Conclusions

Introduction

Exotic spin states have been proposed in the past: liquid, ice, chiral...
Quantum spin liquid (QSL) is a state that does not break any simple symmetry (lattice or spin-roationslal).

QSL - proposed in 1973 by PW.Anderson (strong qu. fluctuations deny LRO even at T=0)

1D: QSL is firmly established (S=1.2, e=0)
2D: classical - kagome
quantum: fluctuations lift the degeneracy of the ground state, so that QSL may disappear

Exp-tal candidates:

• triangular lattice of 3-He atoms
• BEDT salts (triangular lattice)
• kagome lattice: ZnCu3(OH)6Cl2

2D triangular lattice
Possible ground states:

• three sublattice Neel state (120 degree state)
• Valence bond solid (VBS) : breaks lattice symmetry, LRO of singlets
• RVB: resonating configuration of spin singlets. See Fazekas and Anderson, Philos. Mag. 30, 423 (1974)

Neel order even at T=0 (see D. Huse at al.)

Key questions:

• How can we identify a QSL in the experiments?
  
• What is the elem excitation of QSL in 2D triang. lattice?
• Does a QSL host exotic excitations? (gapped or gapless, magnetic or non-magnetic? localized or itinerant)

A wide range of exp-tal probes: NMR, muSR, \chi, torque, Cv, thermal conductivity...

A powerful probe: Thermal conductivity.
- kappa = kappa_spin + kappa_phonon
- kappa_spin = C*v*l = specific heat * velocity of excitations * mean-free-path
E.g. - Sr2CuO3 (1D Heisenberg). kappa/T goes to 0 as T goes to 0 (gapped SL).
Signatures measurable in experiment:

• If gapless SL: kappa/T would have finite value at T=0; otherwise the value is 0.
  
• Field dependence of k_spin talls you if excitations are magnetic
  
• localized or itinerant? - from the magnitude of the mean free path

3-He atoms on triangular lattice: "4/7 phase": gapless down to T~J/300, where J~3mK (Masutomi PRL 92, 025301 (2004)).

Example 1: kappa-(BEDT-TTF)2Cu2(CN)3:
2D triangular lattice of BEDT-TTF molecules (with S=1/2 per two molecules), seperated by the layers of anions, like Cu2(CN)3.

Experimental observations:

• NMR: no internal magn. field
• \chi(T): J ~ 250K from high-T expansion of susceptibility
• mu-SR: no spin rotation, i.e. no magnetic order down to 20mK (~J/10^5)
• specific heat: Cv/T non-zero, i.e. gapless. subtrating Schottky anomaly (in other BEDT salts, it shows a gap)
• thermal conductivity: gapped by \Delta ~ 0.5K
• muSR: relaxation curve below 300mK, indication microscopic separation between gapped and (magnetic) gapless regions - see T.Goto et al.
  
• NMR 1/T1 shows stretched exponential with \alpha less than 0.5
• thermal expansion: lattice anomaly at ~6K (Manna et al., PRL'2010) - is it a structural transition involving charge degrees of freedom?
  
• frequency-dependent dielectric constant
  

Summary: genuine features of a QSL masked by inhomogeneity.

Example 2: Recently found material: EtMe3Sb[Pd(dmit)2]2
Nearly triangular lattice of EtMe3Sb units (S=1/2 per two neighbouring units). t'/t~ 0.93 (close to triangular lattice).
As a function of t'/t, different compounds in this family show a variety of phases, including AFM, charge insulator, QSL.

Experiments (Yamashita et al, Science'2010, and others):

• magnetic susceptibility measured down to 5K (and disappears below, meaning there is a spin-gap to excitation - see a Comment to this post below)
  
• magnetic torque down to T=0.3K
• no LRO down to T=0.3K (from 13C NMR)
  
• ZF mu-SR: no magnetic order down to ~J/10^5. See Ishi et al. Itou et al, Nat. Phys. (2010)
• no change in zero-field vs. field cooled (answer to the question from the audience)
  
• NMR 1/T1 shows stretched exponential with alpha that changes between 0.5 and 1 with a minimum at ~1K: sign of inhomogeneity
• specific heat after Schottky subtraction: - gapless in EtMe3Sb (dmit-131) with finite C/T at T=0 (as opposed to non-magnetic Et2Me2Sb (dmit-221) with only phonon contribution C~T^3)
• thermal conductivity: gapless, since kappa/T=0.19 W/K^2m shows finite value in dmit-131 (i.e. gapless) as opposed to zero value in the spin-singlet analogue dmit-221.
• excitations are itinerant: mean free path estimates ~1.2 micro-meter (~10^3 larger than interspin distance)
  

Question from S.-W. Cheong: how come phonons do not scatter on spin excitations?
A: irrelevant, since phonon mean-free path is comparable to the sample size at these low temperatures.

Question from P. Coleman: could you dope the sample with impurities to see how \kappa/T changes?
A: We know that the mean free path of the excitations is very long, much longer than the distance between the spins. Hence, we do not expect any scattering off impurities.

Note: QSL apparently conducts heat very well - like brass of a 5-yen coin (LOL :-)
Field-dependence of elementary excitations:
H larger 1K: linear increase in kappa_spin
H smaller 1K: spin-gap like behaviour (H_gap ~ 2 T) Interpreted as coexistence of non-magnetic gapless excitations and spin-gap like excitations that couple to magnetic field.
C.f. R.Singh and D.Huse (2007): S=1/2 on kagome lattice showing gapped excitations

Wilson ratio R~1.2 - similar to metals (!)
Is there symmetry breaking in the QSL?
NMR shows a peak in 1/(T1T) around T~1K suggesting a phase transition (to what ?)

Theories on QSL
- Hubbard model on triangular lattice for intermediate U strength.
- Heisenbeg model suggest QSL for J'/J between 0.6 and 0.8.
- ring exchange theory: suggests QSL (Misguich et al), but excitations are gapped
- O. Motrunich (2003), S. Lee and P.A. Lee (2005), Lee, Lee and Senthil (2007) suggest a spinon Fermi surface, however that would predict a large Hall angle kappa_xy/kappa_xx, which the exp-t does not see.
- algebraic spin liquid: Wen PRB (2002)
- gapless boson

Conclusions:

1. kappa-(BEDT-TTF)2 Cu2(CN)3 (ET)
   
   
   • controversial gap vs. gapless spin excitations
   • problems with homogeneity
     
2. EtMe3Sb[Pd(dmit)2]2

• a homogeneous system
• specific heat and \kappa/T shows unambiguous(?) gapless excitations
• very long mean free path - itinerant spin excitations
  
• dual nature of spin excitations (gapless at H=0, and gapped when field is applied)
  
• Wilson ratio ~ 1.2 (like in metals)
  
• Symmetry breaking in QSL?

QUESTIONS:
Q:Chubukov: Anyone did dHvA?
A: we plan it in near future

Q: S-W. Cheong. Your story is based on T below 0.3K which is not too far from the phonon peak. Are you sure of your power-law fitting?
A: Yes, we are sure.

Q: P. Coleman. kappa/T shows a peak at ~0.6K - where does it come from?
A: This is a low-lying phonon peak.

Q. Silke Paschen: Can you exclude the possibility of coupling to phonons?
A: these are very itinerant excitations

Q: Keimer: Some spin chain systems also have long m.f.p., is it therefore so unusual to see long m.f.p. in this triangular-lattice system?
A: Experimentally, you're quite right. However there are still debates on this subject.

Laura Greene (Illinois): Point contact spectroscopy of strongly-correlated electron materials

Laura Greene was asked by the organizers to give an overview of her approach for developing new families of superconducting materials.

This research is a part of a much larger program to develop better practical superconductors (higher Jc and Hc2) that is being funded by the DOE as an Energy Frontier Research Center (EFRC). This program started about one year ago, so only some general guiding principles were presented by Laura, with a few specific examples of systems that they have started work on. The six strategies for their search for new SCs are to look for materials with:

1) Reduced Dimensionality
2) Transition Metal and other large U ions
3) Light atoms
4) Tunability
5) Charged and Multivalent ions
6) Low dielectric constant

In addition one would hope to combine some of these criteria with systems that have competing phases (as has been the case for cuprates and Fe-based SCs). I will not go into much detail on Laura’s discussion of the positives and negatives of each of these six strategies, since many of these have been discussed in the literature in the past. As was pointed out by Paul Canfield, and agreed to by Laura, the particular list of strategies is not so important. What is important, if such a search is to be successful, is that many groups go ahead and start synthesizing new materials based upon their own ideas of where to search. As history has shown, most discoveries of new superconductors have been based upon empirical methods with a lot of serendipity.

In agreement with Paul, Laura mentioned that there are now five other groups in the USA that are being supported by the Air Force to search for new superconductors. This is unprecedented support for such an activity in the USA. In addition, the Air Force and ICAM would like to encourage collaboration in this endeavor with scientists from other countries. Laura and Rick Greene have formed a working group of international scientists interested in such a collaboration (first meeting was at the SCES conference in July). However, it will take time and more discussions to see if, and how, such collaboration can be actually be made to work.

One strategy that was extensively discussed was #2 above, where the Illinois group feels that having a parent compound that is a Mott insulator that can be doped is a very promising approach to higher Tc materials. Questions about this were raised by many in the audience. In particular, Meigan Aronson asked if being near any metal-insulator phase boundary might not be a good approach. Laura agreed.

Some specific materials for the EFRC search were mentioned by Laura. These are:

1) Doping of BiOCuS, a system on the verge of a FM instability
2) Doping of Fe2La2O3E2 (E= S, Se), a material known to be a Mott insulator (although no evidence for this was presented).

In addition the Illinois group is trying to make artificial quantum materials using Jim Eckstein’s layer by layer MBE method. The exact systems to be tried were not specified.

The last 5 minutes of Laura’s talk were a very quick summary of her point contact spectroscopy (PCS) studies of correlated SCs, namely CoInCe5 and Fe (Se,Te). Her very interesting and nice work on the 115 material is published and the Fe (Se, Te) study is on the arXives. In 115, this work shows that the pairing symmetry is d-wave. However, this technique cannot easily tell about an s+- order parameter, as strongly suggested by other experiments in the Fe-based SCs . However, she is thinking about how to do this with PCS.

[Blogged by Rick Greene (no relation)]

P. Canfield (Ames): What we have learned from BaFeTMAs studies: empirical rule to tell theory

Lecture Notes

Paul starts his talk by a very short introduction to the discoveries of iron-based superconductors including the works by Kamihara et al. in 1111 compound, and Rotter et al. in 122 system.
To him the most important discovery in iron-based superconductors is that you can introduce superconductivity by disorder and not only by doping.

Next slides are sort of philosophical discussion where an important part of it is an argument that one has to think prior of doing measurements.

On the next slide Paul introduced the tool how the single crystalline samples were grown out of flux (slow cooling of a melt in a self flux - blogger cannot believe he is able to write these words). Easy and difficult examples, among them CeSb. Few more slides on the beauty of growing the ternary compounds, like RCu2Ge2 can be grown out of ternary in the same way. Similar growth techniques have been applied to the AFe2As2 families of compounds.

Now the top statement: "Within 14 hours of hearing about superconductivity in K doped BaFe2As2 compounds they had grown first single crystals out of a Sc-rich quaternary melt! Beautiful pictures of the single crystals on the millimeter paper.

A substitution of K for Ba or Sr in the 122 materials is difficult BUT they can be grown out of a FeAs melt. By shifting from one transition metal to another one can change the solvent. Using the elemental analysis one is able to determine the composition of each batch used.

Generally a lot of information can be place into and extracted from phase diagram. At the same time it is often difficult out of a single measurement techniques and the more experimental methods that provide consistent information is needed and the likely they are to be accurate.

Next Paul moves to the transport: Important point on the analysis of the resistivity, it can be used to learn about the superconducting state especially rho (H,T) in a field. One has , however, remember about the effect of the local moments. rho_0 increases with increased disorder. Resistivity also helps to identify multiple transitions, sensitive to the changes of the FS (identification of the density wave transition. - double hump)

Now next slides: Magnetic susceptibility: used for determining Curie-Weiss or antiferromagnetic transition , maximum in chi only gives rough estimate to it. It is better to take d\chi/dt which has often the sam temp dep. as the specific heat. BTW d\rho/dT shows similar temp dependence near T_N. But life can be complicated especially in case of multiple transitions. Example is given for the cascade of the transitions between 6 and 5 K in HoNi2B2C.

We are back to FeAs systems: combined structural and AFM transitions, nicely seen from susceptibility and resistivity data. Neutron and X-ray scattering data: clear separation between stuctural and the magnetic in BaFeCoAs systems. Remarkable, one also finds a competion of AF and SC in the coexistence region, even the re-entrant behavior. Theoretical explanation by Fernandes and Schmalian in favor of s+- superconductivity [PRB 81 (2010)]. Comment by Andrey follows to the understanding in the audience that the re-entrant bahavior we do not see on the slide, Paul has to update his slide.

Again "philosophical" break:

to experimentalists: for the phase diagram, carefully state what is your criterion?,
to theorists: many data have to be taken with a skepticism.

Bak to iron-based superconductors: Ni and Cu doping suppresses the upper transition similar to Co, whereas Ni stabilizes SC; Cu substitution does not show SC for T>2K. Next comes the phase diagrams BaFeNiAs and BaFeCuAs, the latter shows very weak SC. What is with Cu, is it a poison? Answer: No, adding Cu to the existing BaFeCoAs composition does not affect SC actually. Instead crucial is to ave the right doping range! Examples: For Co doping, e =x, Ni doping e =2x and for Cu e=3x. This tells us that there is a doping (e) which supports superconductivity. Thus suppression of AF/ST helps to uncover SC and no scaling of the SC on the underdoped side of the phase diagram.

Now comes a comparison of Rh-doped and Co-doped samples: one again finds identical phase diagrams [change of lattice parameters is not sensitive for SC, Piers this is a remark goes directly to your post] . Phase diagram shows that there is a nice scaling of SC with doping (roughly linear behavior)

How do we understand the scaling Tc vs e? answers come from TEP (thermoelectric power) and Hall coefficient measurements. Observe a dramatic change in TEP over the whole temp. range measured as X from 0.02 to 0.024, the low temp. Hall coefficient changes for the same x values. The same results for Cu except the change are at e~0.025. This is consistent with the idea that there is a change in the band structure or Fermi surface of Bafe2As2. And indeed you see this also in ARPES (refers to Kaminski's data), change of the size of the hole pocket [Gamma pocket disappears].

Similar phase diagrams with pressure: doping and pressure changes the structural transition in the same way and reveal the same dome of SC. Example: BaFeRuAs the changes in the unit cell dimensions and volume are remarkably similar for Ru and Rh. On the other hand the phase diagrams are very different. Now again Ru doping resemble to tuning with pressure The right change of the c-axis parameter may catch the salient physics.

Effect of pressure can increase Tc dramatically on the underdoped side but does little on the increase of Tc on the overdoped side. Main role of pressure is to get rid of structural transition and to reveal the dome of superconductivity.

Summary:

1) structural and AFM transitions are suppressed in a similar manner by many TM elements and scales roughly with x

2) there is a region of e which supports sc

3) the sc dome scales will with e doping on the overdoped thetragonal phase

4) the onset of the sc dome on the underdoped depends on how quickly the suppression of AF occurs.

Open questions


-Cu affects Tc 3 times faster than anything else. Cu3+ is difficult to imagine, what is this: band filling, scattering, ... ?

- the dramatic change in TEP with Co dopin into BAFeAs is remarkable, comparable to Yb-based materials, what is the difference between them?

Questuins:
blogger: what about the data which says that there is a magic correspondance of Tc and magic angle of the tetrahedra [see the post]. Reply: it seems that we do not find this relation and I doubt it is correct.

Chubukov asks about the interrelation of magnetism and Cu and whether the statement from the talk might be that superconductivity exists independent on magnetism it simply depends on the killing of the AF order. Reply: to be more precise it is more exactly to say that it reduces the size of distortion and/or ordered moment or change fluctuation spectrum.

Buechner slightly disagrees that disorder does nothing to SC [see F. Hammerath et al., PRB 81, 140504 (2010) ] Reply: indeed this is an important remark

Bernd Buechner (Dresden): Nanoscale inhomogeneities in underdoped pnictide superconductors

Bernd started his talk by introducing the iron pnictides and showing their crystal structures; during his talk he will mainly focus on the 1111 and 111 compounds. He states that these two different families have considerably distinct properties.

Phase diagram of La-1111

Bernd presents the phase diagram of La-1111, showing resistivity data. The spin-density wave state (SDW) is suppressed with doping, together with the orthorhombic phase. A superconducting dome (SC) develops for intermediary doping levels. Showing data of thermal expansion, magnetization, NMR and resistivity, Bernd explains that in these materials there is a strong link between electronic, structural and magnetic degrees of freedom.

Q (Paul Canfield): Are these polycrystals?
A: Yes.

Now he is presenting detailed temperature dependence of the thermal expansion for different doping levels (F doping on the O site). He also presents mu-SR measurements for different doping, comparing to neutron diffraction data. These data show a very sharp boundary between the SDW and the SC states, indicating a first-order transition, he says.

Comparing to the phase diagram of other 1111 compounds, Bernd poses the question: is the coexistence between SDW and SC intrinsic? He explores in details the phase diagram of the Ce-1111, which seems to present a quantum critical point where both SDW and SC transition lines meet at zero temperature.

Q (Piers Coleman): What happens to the Ce moments in the SC state?
A: Do not find evidence of magnetic order inside the SC phase.

Q (Paul Canfield): How do you evaluate the amount of F doping?
A: WDS measurements.

Bernd presents the phase diagram of electron and hole doped Ba-122 compounds, calling attention to the region of coexistence between SC and SDW and to the relationship between magnetic and structural phase transitions.

Nernst effect

Bernd explains that, in one-band metals, the Nernst signal is zero (Sondheimer cancellation), whereas in multi-band metals, it is expected to be very small. In superconductors, the Nernst signal can be large due to vortex flow, and further enhanced due to vortex fluctuation. Bernd recalls data of Nernst effect in the cuprates and their relation to the pseudogap phase.

Now Bernd is presenting Nernst data for the La-1111 pnictides. For undoped samples, they show a strong enhanced signal for T smaller than TN (Neel temperature). Additional thermopower and Hall measurements indicate the partial gapping of the Fermi surface in the SDW state. For optimally doped samples, the Nernst effect is still enhanced in the SC state, although no SDW order is present. For overdoped samples, the signal enhancement is very weak and practically disappears. Bernd relates these results to NMR data for intermediary doping samples, which indicate slowing down of spin fluctuations below 150K. He points out that this sample does not order magnetically, though.

Q (Zlatko Tesanovic): Is there a connection between the slowing down of spin fluctuations and a pseudogap state?
A: No direct evidence for the pseudogap.

Nuclear magnetic and quadrupole resonance

Bernd explains that NMR and NQR can be performed on As, due to its larger nuclear spin. NMR gives the spin susceptibility (static through Knight shift and dynamic through relaxation rate), while NQR gives the local charge distribution.

First, he shows Knight shift data on doped La-1111, from which he can extract the static susceptibility. Its main feature is that it grows with temperature, and this feature is present for various doping levels. He also finds a decrease of the relaxation rate in the normal state at high temperatures. Bernd explains that although the spin susceptibility is decreasing, the slow AFM spin fluctuations lead to the increase of the relaxation rate. He also points out that the non-constant relaxation rate indicates non-Fermi liquid behavior.

The temperature dependence of the relaxation rate in the SC state follows an unusual polynomial dependence, which suggests that disorder is important in order to be able to determine the SC gap symmetry.

Now, Bernd is presenting NQR data for undoped and optimally doped samples, which indicate one set of charge environment in each As site. However, the doping dependence is opposite to the one predicted by LDA. Bernd shows data on the underdoped region, which indicate the presence of two sets of charge environment, he says. The question he poses is: what is the length scale associated to these two coexisting charge environments? He presents more NMR relaxation rate data, which indicate that the coexistence of these electronic states is in the nanoscale, he says. Bernd discusses different possibilities for the nature of these two local coexisting orders, which could be due to charge and orbital order, for example.

Li-111 compounds

Bernd first shows ARPES data on these compounds, which do not indicate nesting features on the Fermi surface. He also points out the small size of one of the hole pockets at the gamma point (center of the Brillouin zone). He shows that, while LDA calculations predict nesting of the bands, the data do not show it. Bernd also points out that his group is now able to perform ARPES below 1K.

Q (Paul Canfield): asks if the compounds are stoichometric.
A: Yes.

Both ARPES and specific heat measurements presented by Bernd show evidence for two SC gaps in these 111 compounds, according to his analysis. He also discusses resistivity data, which show a not so large residual resistivity. Together with NQR data, he argues that his results indicate a very clean sample, specially when compared to other pnictide compounds.

Bernd now presents NQR relaxation rate data on the Li-111 compound. In the SC state, instead of the expected decrease in the relaxation rate, there is a significant increase. Turning on the magnetic field and performing NMR, Bernd finds that the increase in the relaxation rate below Tc disappears, and the usual behavior is recovered. Impurity effects and vortex contributions can be discarded as the cause for this unusual increase, Bernd argues.

He presents further raw NMR data, with the magnetic field along different directions. No change in the Knight shift is seen in the SC state (with H parallel to the a or b directions), and Bernd argues that this is an indication that no singlet pairs are formed below Tc. However, after changing the magnetic field direction, the data show the expected decrease in the Knight shift. Bernd argues that this is an indication that SC singlet pairs are not compatible to these observations.

Q (Ilya Eremin): Other group did not find this behavior in their Knight shift data.
A: They use powder, which is an important difference.

Bernd shows data on the line width of the NMR spectrum, which indicates the presence of spin fluctuations in the normal state, he says.

Discussion

Q (Andriy Nevidomsky): Why changing the field direction leads to decrease in the Knight shift?
A: A singlet component is induced by the magnetic field.

Q (Andrey Chubukov): Are low temperature data available for Li-111?
A: More data necessary, this is a work in progress.

Q (Takagi): Spin susceptibility anisotropy in the normal state?
A: Still more work necessary due to some issues with the surface.