Bernhard Keimer (MPI FKF Stuttgart): Neutron studies of the cuprates

Bernhard begins by stating that most of his talk will be spent on the YBa2CuO6+x systems

Outline:
- survey of spin dynamics in cuprates
- aspects of the electronic nematic phase
- universal picture of spin dynamics in cuprates

last 15 mins will be on BaFeCoAs2
- comparison to YBaCuO
- electronic liquid crystal phase?

The next few minutes are spent on the question why to look at YBCO. Reasons: 1) high homogeneity, no phase separation, low disorder consistent with quantum oscillations] 2) possibility to create detwinned single crystals which allows to discriminate between 1D and 2D magnetism

Next slide leads the blogger to appreciate the efforts done to obtain the experimental data - 150-200 individually detwinned crystals (no secondary phases) oriented together, and prepared for each doping level which ranges from 6.35 to 6.6 oxygen content (YBCO6.35 to YBCO6.6)

Then Keimer shows a generic phase diagram of cuprates, commensurate AF, paramagnetic, and "pseudogap" phases as well as d-wave SC with an objective in mind to look on all these phases with neutrons, 6.35 is a special point as quantum oscialltions are done recently at this level.

Now comes the data: (magnetic part of) INS response at the AFM wave vector vs omega. Two main features: Bragg (quasi-elastic) peak and inelastic incommensurate spin excitations.

We first concentrate on the quasi-elastic peaks:
large anisotropy along a and b directions, fitted perfectly with uniaxial incommensurate modulation - "spin density wave". Quotation is because Keimer distinguishes between the amplitude modulation (usual SDW) or tranverse modulation (spiral magnetic excitations) - analysis is not yet finished bu the latter is more likely. Incommensurability parameter \delta is systematically lower than in LSCO, non-zero offset in delta versus - p (doping) relation is also observed. Remarkably it is approximately concident with the onset of Tc curve on the phase diagram.

Critical comparison with muSR data comes next: muSR sees static IC magnetic order with a lifetime \geq 1 microseconds, disappears above 2-5 K. The quasielastic peak seen in neutrons is consistent with that but the temperatures are different, the peak diappears above 40K. What helps? - To improve the resolution ( we now move to spin-echo spectroscopy with a resalution of 1 \mu eV as compared to 100\mu eV in usual triple axis spectroscopy) . The narrowing of the quasielastic peak to the experimental resolution at 5K (onset of the real SDW transition) compares well with muSR data. Piers raises an issue on the temp. dependence of the linewidth and whether Bernhard is able to say on the power law of this dependence (looks quadratic), Reply: the quality of the data is not enough to say definitely at present.

The conclusion of the data presented to far: incommensurate SDW transition at T=0 is a feature below the superconducting dome on the underdoped side - consistency with quantum oscillation measurements.

The next remark concerns the bahavior of the quasielastic incommensurate peaks which enhance in presence of the magnetic field showing strengthening of the SDW phase. This is overall qualitative agreement with a theory argument by Mooon and Sachdev phase diagram, PRB 2009, and Demler et al PRL 2001.

The fact that small pockets in quantum oscillations are seen at higher doping where INS sees no sign of SDW is interpreted in view of much smaller magnetic fields used in INS as compared to quantum oscillation measurements.

Now we move to the incommensurate response and the nematic phase - higher doping on the underdoped side, no quasielastic peaks (no SDW) but there is still an incommensurate response. A peculiar feature of this part of the phase diagram is spontaneous onset of incommensurability in the INS spectra upon cooling below 150K. The main fact is that orientational symmetry is broken without and static magnetic order and the translational symmetry is still preserved.

From a theory perspective it looks as electronic analog of nematic liquid crystal. (Fradkin, Kivelson). Possible routes towards nematicity includes Pomeranchuk instability, (Hallboth and Metzner PRL 2000, Yamase and Kohno, JPSJ 2000). Again worth to say that the onset of the nematicity is seen in INS. This is consistent with a resistivity anisotropy along a and b directions found by Ando et al at similar temperatures. Kapitulnik comments on the temp dependence of the resistivity at 200K and its consistency with his measurements (Kerr effect) and INS.

Next slide shows the q-map of the spin excitations with elliptic shape (broken orientation symmetry), analysis shows that the data can be described in terms of (nematic) order which occurs around 150K and is doping dependent (150K - O6.45, 175K-O6.5, 200K - O6.6).
Again the data are consistent with the Nernst effect except for a slight discrepancy with regard to the onset temperature.

Interesting remark on the onset of superconducting instability deep inside the nematic phase: based on the the c-axis optical conductivity data and the formation of the Josephson plasmon mode which is referred to the onset of phase incoherent superconductivity in a bilayer.
The nematic transition coincides with the onset of phase-incoherent superconductivity within bilayer unit. Kapitulnik and McKenzie comment on the similar measurements in BSSCO where simialar results have been found. Nevidomoskii raises a technical question of how the points on the phase diagram coincide with the original data of the optical conductivity and the observation of the plasmon peaks. Reply concerns with the coupling of the plasmon mode to the c-axis phonons and the anomaly associated with that. Lu raises an issue whether incommensurate SDWs are spiral or amplitude, the reply is that it is mostly likely spiral.

Now we see the spin excitations - nearly gapless, hour-glass type dispersion. However, in contrast to the previous talks the blogger heard, here there are two (or even three?!) types of the hour-glass (or sometime called X-shape) dispersion on the phase diagram: "open hour glass" - never closes at pi,pi point (undoped LSCO or underdoped YBCO (6.45)). signature of coexisting nematic phase with low-Tc superconductivity which gaps the low energy part of the "hour-glass"-shape.

Spin excitations in the d-wav SC in YBCO reveal a resonance mode with closed "hour-glass" shape below Tc [well understood within RPA type theories, see Eremin et al., PRL (2005)]. transforms into open "hour-glass" shape above Tc.
Next slide discusses the role of Zn impurities which according to Keimer restore IC-SDW, evidence for nearby QCP.

Summary: spin dynamics in cuprates uncovers: (a) spin wave excitations (AF), (b) paramagnons (overdoped phase), gappless open hour-glass (underdoped, pseudogap), gapped open hour-glass (pseudogap+SC), closed hour-glass (d-SC) phase

Then Keimer briefly flashes the new data on the high-energy excitations as measured by resonant inelastic x-ray scattering: sharp signatures of the dispersive spin excitations in the strongly overdoped cuprates (lie exactly on the same curve as in the underdoped cuprates, consistent with the same energy scale in the whole family of cuprates.

NOW ferropnictides: BaKFeAs crystals, quick flash of the resonant spin excitations below Tc, signature of sign-changing order parameter. anisotropy of the spin excitation along (pi,pi). Is that a signature of the nematic phase? The answer is no as the in-plane anisotropy of the data is well described within RPA and the band structure calculations, Inosov et al, arxiv:1007.3722v2.

Questions: blogger raises an issue of the nematicity in BCFA and cuprates and in particular whether the LDA-based calculations were done for the spin excitations also in YBCO.
Raphael raises a concern on the use of nematic order in applictaion to the pnictides. His statment is that the Ising nematic order in pncitides is magnetic in origin thus will not yield an electronic anisotropy. Reply: Keimer agrees but raises an issue of the electron nematic in the doped samples and not in the undoped magnetically ordered ferropnictides.