After the thanks for Doreen and the bloggers.
Paul Canfield stands up to make a point. In general there seem to be two classes of material.
(1) The old style: MgB2, RNi2B2C, Nb3Ge
They are relatively easy to make and doing stuff to them makes them worse superconductors. They are ordered and reveal their superconducting state easily.
(2) New style: FeAs CuO
These are harder to make and generally need to be doped from a parent (host state) to make them superconductors to remove some other state.
Paul says we know so little that it does not matter what the rational is, as long as we are looking we will find stuff. But, what would be useful to the experimentalists ("animals invited to this paradise") from the theorists is what sort of host materials should we be looking at to reduce the size of the phase space. The hosts will probably be non superconducting.
Laura Greene: well Philip^2 and Si have pointed to Mott insulators as being a good starting point. Also, theorists don't always help because they don't understand stuff that we do about the compounds and so have a simplistic view of the changes that really take place on doping.
Piers Coleman: this is just the start of a better collaboration between the materials and the theorists. It was great to have Juri. But here is an issue: theorists live mainly in momentum space but the chemistry lies in real space. Here perhaps heavy fermions have something to offer.
Andrey Chubukov: Plot Tc against Hubbard U/W then "obviously Tc goes up from the small U/W limit, it must also go down at large U/W. What seems surprising is that Tc is rather flat in the intermediate region with Tc ~ 0.02E_F (Piers says it is not true in heavy fermions). This means Tc ~200K max.
And at this point your blogger must leave for his flight...so over to Sam.
Rick Green: Question to Andrey: what about pressure, which seems to increase superconductivity?
Andrey: Well, the top won't be perfectly flat, and this is a very schematic picture.
Andrey: This was about Tc in the absence of competing orders. Of course, when there is competing order the picture changes. But just to emphasize again, the numbers are quite interesting - that Tc always comes out about 2% of the Fermi energy.
Question: What about dimensionality? Should we stick to 2D systems, or maybe try and move elsewhere?
Andrey: In fact, this picture is quite general in the generic shape; but the more dimensions, the more factors of 2pi and the more small pieces of BZ you have to worry about, so the numbers come out smaller.
Piers: What about condensation entropy? Never seen it go about about 1/3 log 2. That's another way of thinking of these limits.
---
Piers: Now that we've finished scientific questions, what about organization issues. Should we have less talks (seems to be a general consensus that the number of talks is actually quite good). What about more people - many more people could fit in this lecture theatre.
Laura Greene: I'd like to see many more young people.
Piers + Andrey: A lot of this is a question of money - we have to look into getting more funding.
Andriy: What about holding it in the Adriatico lecture hall, rather than this one in the main building? Seems to be general consensus that main building is better.
Well, that's the end!!! Two weeks have gone by very quickly. Ciao tutti.
Physicists met at the International Center for Theoretical Physics to discuss the challenges of understanding and designing strongly correlated electron materials - novel kinds of order, magnetism and superconductivity. The meeting was funded by the ICTP, the NSF, the ESF, ICAM and RIKEN.
Friday, August 13, 2010
Pascoal Pagliuso (Campinas, Brazil): Low symmetry structures and strong f-s(d-s) hybridization as key ingredients to find new unconventional superconductors
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.
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.
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.
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 TK becomes larger, Kondo
compensated state develops with a large FS. SC often develops at the transition from the magnet to the heavy fermi liquid.
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 (TN) - 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 TN 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 TN goes up - larger Gamma 8 CEF splitting leads to a larger TN.
Paul Canfield points out that the Gd TN 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, TN increases with tetragonal asymmetry, but when the moments lie in the ab plane, TN decreases with tetragonal asymmetry.
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 TN 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, TN goes down as the Jz^2 goes up, whereas for 9/2 and 6, TN goes up. Ce has the frustrated property that it has a larger C-axis susceptibility, but this suppresses TN.
You may remember this is exactly what you saw experimentally. TN went down with Ising symmetry, but an increase in TN 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 TN.
Rh - Ir - Co Ising symmetry increasing, TN going down.
All of this is going on without any effect of Kondo.
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| Increasing the xy anisotropy drives TN below the Kondo temperature, leading to SC. |
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 TN=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 TN, so it must be the tuning of something else.
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 TN 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 TN.
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 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.
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
T. Hanaguri (RIKEN) : Landau level spectroscopy of helical Dirac fermions in a topological insulator Bi2Se3
--Why are we doing STM?
--Some technical aspects of STS/STM
--Why STM/STS on topological insulator
--Landau level spectroscopy on topological insulator
Strategy to find exotic phenomena
One way we search for exotic phenomena is to build up "boring" electrons to find new emergent macroscopic phenomena.
Alternatively, lets break down "boring" materials, analyze them thoroughly to find quantum structure and interference around impurities and otherwise microscopic properties that show it wasn't as "boring" as we thought.
Background to STM
- STM is a tool to explore the electronic states - measures the local density of states (LDOS), and can make topographical scans of material surfaces.
- At any certain point, can measure current as function of bias, and to a good approximation, the LDOS of the material is given by dI/dV.
- At any fixed bias, can then scan the surface, to get a "topograph conductance" map - this is spectroscopic imaging STM (SI-STM). Then can obtain these images at different biases, V (or in other words, energy, epsilon). Putting these together and taking a Fourier transform gives momentum space information.
Why is STM so powerful?
--Atomic spatial resolution: 0.1nm laterally and ~pm vertically giving very precise local information
--Momentum space accessible, from FT SI-STM (Fourier-Transform Spectroscopic Imaging Scanning Tunneling Microscopy)
--Very high energy resolution, as high as micro-eV
--can do experiments under a wide range of external conditions.
To get good results, one needs a few target specifications of the SI-STM machine:
--Ultra-high vacum (of order 10^-10 Torr), as the surface must be kept clean for a long time.
--High magnetic field >10T to control the spin and Landau orbits
--very low temperature <1k in order to reduce the thermal broadening [ Typical energy scales in materials we want to see: Mott gap ~ eV, Thermal 1K~0.1meV, SC gap (HTC) ~ 10meV, impurity resonances ~ 1meV, Zeeman energy ~ 0.06meV/T ] --variable temperature (in order to study phase transitions) Typical scans (of space and energy) will take of order 36 hours, and require even nm drift forbidden during this timescale. In RIKEN, have a multi-extreme STM, satisfying all of these requirements, including sub-pm noise. How small is sub-pm noise? 0.5pm/2cm = 0.1 micro meter / 4000m (height of Mt. Fuji) [bloggers note: wow! this is serious resolution!]
Now onto main topic of talk
published recently in: Hanaguri et al PRB 82, 081305(R) (2010)
Also see similar recent work in: Cheng et al PRL 105, 076801 (2010)
Introduction to Topological insulators: Topological insulators are (band) insulators with a robust gapless edge or surface state. How can this be true? Need a band structure with a specific "topology".
What about 3D case? [see e.g. Fu, Kane and Mele PRL 98, 106803 (2007)] In 2D, we have gapless edge states with linear dispersion. In 3D, this will map into gapless surface states with a linear dispersion - i.e. Dirac Fermions (with an added helical structure).
In fact, in solid state, one finds that Dirac cones are everywhere!
--Graphene [ see e.g. Castro Neto et al, RMP (2009) ]
--Organic conductors
--d-wave SC
--Surface states of 3D topological insulators (TI).
Usually, the Dirac cones come in pairs. However, in the TI, find an odd number of cones centered at time-reversal invariant momenta. This is due to the TR invariance, one of the conditions of a topological insulator. We also find that in the TI (unlike other cases) there is no spin degeneracy in the surface states. This is related to the spin-orbit coupling necessary to make this state.
Experimental verifications of 3D TI: First, Bi-Sb -- ARPES revealed an odd number of Dirac cones [ Hsieh et al, Nature 452, 970 (2008) ]
Since then, we have found some other cases:
--Bi2Se3 - single isotropic Dirac cone [Zhang et al, Nat. Phys. 5, 438 (2009) ]
--Bi2Te3 - which is anisotropic [ Chen et al, Science, 178 (2009) ]
An odd number of Dirac cones is good evidence for TI states. But what more can we do?
Next, spin-resolved ARPES revealed the helical spin structure.
So ARPES is great! There is a helical Dirac cone in these materials no doubt.
But what else can we do?
Let's look a little close at the helical spin-structure: one of the properties is that it gives suppressed back scattering. Now, scattering interference may generate electronic standing waves (QPI), which should detect this interesting scattering properties of the helical Dirac fermions.
The helical structure can be modeled by a multi-band model with spin-selection rules. Can also include certain FS distortions -- many of these have been calculated, and give nice agreement with QPI patterns.
What about Landau levels?
First, take some lessons from Graphene, [Castro Neto et al, RMP 81, 109 (2009) ]
--Find that the LL (Landau level) energies E_n are proportional to \sqrt{nB}
--Also find a B-independent LL with n=0. This gives a half-integer QHE, and furthermore the large gap due to this n=0 state means that the QHE can even be observed at room temperature. [Novoselov et al, Science 315, 1379 (2007)]
We should compare this to the conventional 2D electron gas where E_n proportional to (n+1/2)B.
In a topological insulator: this should be easier to look at than graphene as you see the Dirac fermions at the surface of a large bulk material. Furthermore, in graphene, you get factors of 4 (from 2 Dirac cones, and 2-fold spin degeneracy). But in a TI, there is a single Dirac cone may give rise to true half-integer QHE. In other words, the TI should be great to look at the ususual QHE properties of the Dirac cone.
But there is a little problem - an unavoidable bulk contribution in Bi2Se3. For example, compare band calculations [Zhang et al, Nat. Phys. 5, 438 (2009)] to ARPES data [Xia et al, Nat. Phys. 5, 398 (2009)] and find that the experimental system looks e-doped. This bulk contribution dominates for example magneto-transport. A surface probe is necessary to study the Dirac cone; but ARPES is not magnetic-field compatible. So lets do STM.
Experiment on Bi2Se3, crystals grown by Igarashi and Sasagawa (TIT). Bulk electron density in range 10^18 to 10^20 for two different samples.
Basic tunneling conductance against sample bias agrees nicely with ARPES results (including e-doping level).
Question: Why is there a sharp kink seen at 0 sample bias?
Answer: Don't know (although I didn't quite catch the slightly more extended answer)
Search for QPI : see almost nothing!!! QPI is very weak in single, isotropic and helical Dirac cone, as compatible with the theory of forbidden backscattering.
Now, LL spectroscopy: Increase B, and measure tunneling conductance against sample bias. We see clearly the development of the Landau levels, including the n=0 level at the Dirac point. E_n is definitely sub-linear in n, and is furthermore consistent with square root behavior of LL of single helical Dirac cone. [T. Hanaguri et al, PRB 82, 081305(R) (2010)].
However, as compared to the perfectly square root behavior seen in Graphene, we find in Bi2Se3 slight deviations from this. A short analysis shows us that in fact plotting E_n against sqrt(nB) is in fact an energy/momentum like relation - showing the slight bending away from linear behavior in the Dirac cones of Bi2Se3. This can be nicely compared to the dispersion seen in ARPES. This is new momentum-resolved spectroscopy using STM!
--missing n<0 LLs - maybe due to coupling with bulk band. --Enhanced amplitude of LL oscillations near E_F. This can be interpreted as an E-dependent QP lifetime. --Also find anomalous fine features near E_F. The fine structures shift in the same manner as LL's. --There is also an extra amplitude enhancement suddenly at |E|<~20meV. This is a new energy scale in the problem. [What is this energy scale?]
Summary
--Studied Helical Dirac fermions at surface of topological insulator.
--Clearly identified unusual LL structure expected for Dirac fermions
--Anomalous fine structures identified near E_F.
--Spectroscopic STM is now ready to explore exotic electronic phenomena.
Thursday, August 12, 2010
Conference dinner, evening of Thursday 12th August
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| Piers Coleman |
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.
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| Aharon Kapitulnik proposing that someone make a toast |
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| Andriy Chubukov and Sam Carr |
Much fun was had by all. This is the life!
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| Zlatko Tesanovic |
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| Raphael Fernandes and Paul Canfield |
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| L-R: Foreground Meigan Aronson, Natasha Perkins, Andrei Chubukov, Background Yu Lu, Piers Coleman, Silke Paschen and Hanna Kapitulnik |
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| Hide Takagi |
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| Andy Schofield |
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| Piers Coleman |
Akira FURUSAKI (RIKEN) - Unconventional orders in frustrated ferromagnetic spin chains
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.
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
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.
--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.
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| Andrey Chubukov with Blogger, Sam Carr. |
Yuji MATSUDA (Kyoto University): Elementary excitations in a 2D candidate quantum spin liquid
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)
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 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
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
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)
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:
- kappa-(BEDT-TTF)2 Cu2(CN)3 (ET)
- controversial gap vs. gapless spin excitations
- problems with homogeneity
- 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
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 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.
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
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.
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.
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.
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)
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.
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
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.
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.
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.
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.
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.
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