Paring with spin fluctuations

A review of an interesting work observing the paring mechanism of an exotic superconductor.

Hattori et al. are able to correlate this field-angle-dependence of the magnetic fluctuations with another striking property of UCoGe, which is that its superconductivity is exceptionally sensitive to the direction of an applied magnetic field. When the magnetic field is perpendicular to the c axis the superconductivity is very robust, surviving to around 10 tesla; however, as the field direction is rotated towards the c axis, the critical field for destruction of superconductivity falls precipitously. An obvious interpretation of this behavior would be that the component of the applied field that is parallel to the c axis induces a large magnetic polarization, and the large internal field thus generated disrupts the paired electrons either through coupling to their spins or their orbital motion. This sort of physics is very well understood (indeed this is why ordinary superconductors don’t like magnetic fields) so it can be modeled quite accurately and, surprisingly, it doesn’t fit the measurements in UCoGe. Rather, Hattori et al. argue that their results are better explained if the magnetic field is disrupting not the pairs directly, but rather the underlying pairing mechanism. This, in particular, explains the striking parallel in the suppression of the magnetic fluctuations and the suppression of the superconductivity as the magnetic field is rotated towards the c axis. It is strong evidence that magnetic fluctuations are the ones doing the pairing.

A talk by P A Lee on SC and FM coexisting in oxide interface

http://videochannel.ust.hk/Watch.aspx?Section=Channels&Channel=2&SubType=All&View=Icon&Sort=Date&Page=1&Current=3&Mode=Play

Two pieces of work on cuprates

Just to highlight them here, because they seemingly represent something defying the cliche.
1. Electron-spin excitation coupling in an electron-doped copper oxide superconductor [Nphy, 7:719(2011)]

High-temperature (high-Tc) superconductivity in the copper oxides arises from electron or hole doping of their antiferromagnetic (AF) insulating parent compounds. The evolution of the AF phase with doping and its spatial coexistence with superconductivity are governed by the nature of charge and spin correlations, which provides clues to the mechanism of high-Tc superconductivity. Here we use neutron scattering and scanning tunnelling spectroscopy (STS) to study the evolution of the bosonic excitations in electron-doped superconductor Pr0:88LaCe0:12CuO4􀀀 with different transition temperatures (Tc) obtained through the oxygen annealing process.We find that spin excitations detected by neutron scattering have two distinct modes that evolve with Tc in a remarkably similar fashion to the low-energy electron tunnelling modes detected by STS. These results demonstrate that antiferromagnetism and superconductivity compete locally and coexist spatially on nanometre length scales, and the dominant electron–boson coupling at low energies originates from the electron-spin excitations.

2. Intense paramagnon excitations in a large family of high-temperature superconductors [Nphy 7:725(2011)]

In the search for the mechanism of high-temperature superconductivity, intense research has been focused on the evolution of the spin excitation spectrum on doping from the antiferromagnetic insulating to the superconducting state of the cuprates. Because of technical limitations, the experimental investigation of doped cuprates has been largely focused on low-energy excitations in a small range of momentum space. Here we use resonant inelastic X-ray scattering to show that a large family of superconductors, encompassing underdoped YBa2Cu4O8 and overdoped YBa2Cu3O7, exhibits damped spin excitations (paramagnons) with dispersions and spectral weights closely similar to those of magnons in undoped cuprates. The comprehensive experimental description of this surprisingly simple spectrum enables quantitative tests of magnetic Cooper pairing models. A numerical solution of the Eliashberg equations for the magnetic spectrum of YBa2Cu3O7 reproduces its superconducting transition temperature within a factor of two, a level of agreement comparable to that of Eliashberg theories of conventional superconductors.

New clue toward paramagnons as the glue

Certainly lots of doubts are over the magnetic fluctuations as the paring source of carriers in cuprate superconductors. A central issues concerns if there is sufficient paramagnons in the Sc region, since experiments have so far detected only a limited volume of such stuff. Now this gets changed due to this work [Nature Phys. 7, 725–730 (2011). ] reviewed below [http://www.nature.com/nphys/journal/v7/n9/full/nphys2077.html?WT.ec_id=NPHYS-201109]:

However, the observed excitations were restricted to a narrow window in both energy and momentum and furthermore carried relatively little spectral weight, posing a challenge to theoretical ideas about magnetic fluctuations being the source of Cooper pairing in these superconductors. Some researchers have suggested that the experimental limitations inherent in neutron scattering were partially responsible for this state of affairs — and only now has a breakthrough occurred.

In Nature Physics, Le Tacon and colleagues² report the application to various copper oxides of an alternative technique to map magnetic excitations: resonant inelastic X-ray scattering (RIXS)³. Here, an electron is transferred, by a high-energy photon, from a deep core level into an unoccupied low-energy state; subsequently, an electron from a different low-energy state fills the core hole and emits a high-energy photon. Thus, a net excitation is generated in a low-energy band, the energy and momentum of which can be measured by examining the scattered photon.

Among the advantages of RIXS, compared with neutron scattering, is the large cross-section for the scattering of photons (which eliminates the need for large samples) and the possibility to probe essentially the entire Brillouin zone. There are disadvantages as well: in contrast to neutron scattering, the cross-section is not simply related to a dynamic susceptibility, which complicates the data analysis, and the energy resolution is at present limited to about 100 meV (it's far below 1 meV in state-of-the-art neutron-scattering experiments). Despite these limitations, the past decade has seen exciting progress in RIXS³ such that investigations of elementary spin excitations have now become feasible.

Le Tacon et al.² have investigated magnetic excitations using RIXS in a family of copper-oxide materials, covering a range of hole dopings from the undoped insulator to the slightly overdoped superconductor. In all doped materials, they identified damped spin excitations with high intensity over a large part of momentum space. These excitations, in both their overall dispersion and their intensity, seem to show surprisingly little variation with doping.

These findings are important for a number of reasons. First, together with similar recent experiments^{3, 4, 5}, they establish RIXS as a powerful tool for the investigation of complex correlated-electron materials. Second, they show that previous neutron-scattering studies have indeed missed a significant part of the spectral weight of spin fluctuations in copper oxides. This implies that theories of electron pairing based on the exchange of magnetic fluctuations can be considered on safer ground. In fact, Le Tacon et al. provide a sample calculation of a superconducting critical temperature (T_c), in which they use the measured spin-fluctuation spectrum and electronic bands as input and obtain a T_c value comparable to the experimental one.

Third, and perhaps most importantly, their data indicate that key features of the spin fluctuations in doped copper oxides are strikingly similar to that of their undoped counterparts (Fig. 1): at the elevated energies probed by RIXS, the only significant effect of doping is an energy broadening of the excitations, probably arising from damping due to electron-hole excitations. (One should note that the present energy resolution of RIXS is insufficient to resolve fine structures on scales below 100 meV; therefore the similarity of doped and undoped spectra refers to gross features, and the details may well differ.)

All organic molecule spin valve

I remember in my previous entry I mentioned a spin filtering effect of DNA molecules. Here comes another molecule with similar effect and can operate as a spin valve at low temperatures[http://www.nature.com/nmat/journal/v10/n7/full/nmat3061.html?WT.ec_id=NMAT-201107].

Now, writing in Nature Materials, Urdampilleta and co-workers¹ report that a single-walled carbon nanotube decorated with magnetic molecules can act in just the same way as a conventional spin valve, albeit only at low temperature.
...............
How is it possible for a single molecule to perform as efficiently as 10 nm of iron? The key is the ability of a chemical bond to modify the magnetic properties of a surface, which has been studied under the suggestive name of 'spinterface science'⁵. It has already been shown that an attached molecule can alter the spin-polarization of the electrons emerging from a magnetic surface^{6, 7}; the experiments of Urdampilleta and co-workers now prove the opposite effect — namely that a magnetic molecule can alter the spin polarization of the current flowing in a non-magnetic material. Two particular features make this possible. First, the magnetic centre must be sufficiently close to the conduction channel. In this respect, the case of bis-phthalocyaninato-terbium(III) is rather peculiar, because the Tb³⁺ ion (Tb³⁺ carries a total angular momentum, J = 6) is sandwiched between two phthalocyanine ligands, and it is at least 1 nm away from the nanotube — too far to transfer any magnetic information. However, there is a second source of spin in this molecule, namely a S = 1/2 radical delocalized over the two phthalocyanine ligands. These are likely to participate in the bond and help to spin-polarize the electron current. Second, the conduction channel must be sufficiently sensitive to the local magnetic moment. All the atoms in a single-walled carbon nanotube reside on the surface, so that a surface modification results in an alteration of the entire electronic structure. It is an extreme surface sensitivity that makes this spin valve work.

Nesting not so holy in pnictides

This [Phys. Rev. B 83, 220504 (2011)] might be call theories solely based on nesting into question !

Despite intense study, researchers have not yet uncovered the secrets behind the peculiar properties of iron-based (pnictide) superconductors. Many theories that try to explain the driving mechanism of superconductivity in these materials suggest it is tied to so-called nesting of the electron and hole Fermi surfaces. This geometric feature of the Fermi surface, where one portion of the surface maps to another if it is translated by a suitable reciprocal-lattice vector, is common to the structure of many families of pnictides. Nesting often implies the existence of collective electron behavior, so if it is present in the host materials of the pnictides, it would have significant implications for their properties.

In a Rapid Communication appearing in Physical Review B, Brendan Arnold at the University of Bristol, UK, and colleagues use the de Haas-van Alphen effect, where electrons and holes orbit the extrema of the Fermi surface in response to a magnetic field, to map out the electron and hole Fermi surface sheets of BaFe₂P₂, the parent material of an important family of pnictide materials. Besides providing highly detailed information about the geometry of the Fermi surfaces, they find, rather surprisingly, that the nesting present in the superconducting doped compounds BaFe₂(As_1-xP_x)₂ persists in BaFe₂P₂, which is not superconducting. This finding agrees with a growing list of experiments that conclude nesting does not play a dominant role in the development of superconductivity, at least in one family of pnictide compounds. – Alex Klironomos

Delocalization of Cooper pairs by doping ?

This is definitely a very wonderful step forward. Have not read it yet, but eager to tomorrow.
http://www.nature.com/nature/journal/v472/n7344/pdf/nature09998.pdf

Spins coupled to a mechanical resonator

Employing the spin-phonon coupling, they argued that, a tiny magnet welded with a torsional mechanical oscillator can be described by a spin-boson model [PRL, 106:147203(2011)]. What interests me is actually this, is it possible to filter spins using magnetoptical coupling schemes ? Especially, what is the implication for the DNA filtering effects that were reported earlier in this blog. See also the review [Phyics, 4:28(2011)].

Electrons take on diverse jobs in a compound

It was reported that two species of electrons in the same compound were found carrying superconductivity and anti-ferromagnetism, respectively. These two have different mass, one very light while the other quite heavy. This compound has quasi-3D stacked structure, nearly isomorphic to pnictide superconductors. I feel this is funny and many other rich phenomena might happen. "We found that the ZrCuSiAs-type crystal CeNi0:8Bi2 with a layered structure composed of alternate stacking of ½CeNixBið1Þ þ and Bið2Þ exhibits a superconductive transition at 4 K. The conductivities, magnetic susceptibilities, and heat capacities measurements indicate the presence of two types of carriers with notable different masses, i.e., a light electron responsible for superconductivity and a heavy electron interacting with the Ce 4f electron. This observation suggests that 6p electrons of Bi(2) forming the square net and electrons in CeNixBið1Þ layers primarily correspond to the light and heavy electrons, respectively."[PRL, 106:057002(2011)]

More oscillations in cuprate superconductors

http://www.nature.com/nphys/journal/v7/n3/full/nphys1930.html?WT.ec_id=NPHYS-201103

Since its discovery almost 25 years ago, high-temperature superconductivity has led to a wealth of new theoretical ideas and deepened our understanding of complex condensed-matter systems. At the same time, the study of cuprates has been the driving force for tremendous innovations in the experimental methodology of condensed-matter physics, with methods ranging from photoemission, scanning microscopy, optics and neutron scattering to, in the past few years, quantum oscillations. As reported in Nature Physics¹, measurements by Brad Ramshaw et al. of quantum oscillations in the underdoped high-temperature superconductor YBa₂Cu₃O_6.59 typifies these advances in a number of striking ways. First, the samples studied are the result of two decades of intensive development leading to unique levels of purity that would previously have been unimaginable in such complex oxides. Second, the measurements take place in pulsed magnetic fields that reach both a magnitude of field and a quality of signal-to-noise ratio far beyond what could formerly be achieved. And third, the latest innovation of 'genetic algorithms' allows consistent parameters to be extracted from a large data set of quantum oscillations as a function of field direction and temperature. The authors obtain, among other things, a value of the g-factor of the charge carriers near 2, showing that they are surprisingly like free electrons. This result has profound implications for the nature of the ground state that gives rise to these oscillations.

Single band or double band ?

It is frequently disputed in the field of cuprate superconductors that, the essential physics may be encapsulated more adequately by a single (let's call it d) or double (s-d) band model. Fairly speaking, throughout the whole span of this arena, from the early days till now, as initialized by Anderson and pushed by Zhang and Rice et al., the d-model has been at the center and unchallenged. This situation was further corroborated by the thinking that, the s-d model can be mapped onto the d-model rigorously [see Ref.1 for a review]. Nevertheless, this situation ha to change for two reasons: (1) the d-model can not address the intervening spin glass phase; (2) the d-model can hardly explain the checkerboard pattern observed at low doping.

Why cant the spin glass phase exist within the d-model ? Suppose one has a half-filled single-band Hubbard model. Now add an extra electron to it. What can this electron do ? It shall try to hop from one site to another. Due to Pauli's principle, to render this hopping, the electrons on the two sites must have their spins aligned parallel. This means that, this extra electron tends to align the already existing electrons. On the other hand, the already existing electrons also try to hop and require their neighbors anti-parallel. And these two effects cancel exactly, because the two electrons on the same site have exactly the same hopping amplitude.

Obviously, in the s-d model, the effects don't cancel. This is where the difference gets in.

[1]SPIN POLARONS AND HIGH-Tc SUPERCONDUCTIVITY, A. L. Chernyshev†,* and R. F. Wood Solid State Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831;

Magnetic fluctuations at high energies in parent La2CuO4

The LCO is a quasi-2D anti-ferromagnetic insulator which can be doped into a superconductor. Seemingly simple, its 2D magnetic behaviors have recently displayed some new features, which were published in a PRL days ago [PRL 105, 247001 (2010)]. They used INS as the probes. They found some unusual traits with the zone corner fluctuations with momenta around (pi,0). The dispersion around this point is much broader and with long tail in comparison with, let's say, the (pi/2, pi/2) region. Moreover, significant spectral weight were disclosed over there. The authors proposed spinon as the cause of the broad peak: a magnon decays into spinons mostly at zone corners. The decay shortens its life time and increases the peak width.

Pinwheel magnetic structure

Solid black lines are magnetic exchange interactions with three different strengths. The ellipses show the main spin correlations of the pinwheel valence-bond solid state found by Matan and co-workers in Rb₂Cu₃SnF₁₂. Spin singlets form between spin pairs linked by the dominant exchange interactions.


[Nature Physics Volume:6 ,Pages:837–838 Year published: 2010]

Molecules filtering spins

Using STM with a magnetic tip can be used to probe the magnetic feature of a surface. The tunneling current shall be sensitive to the alignment (collimation) between the spin orientation of the surface and that of the tip. If the tunneling, as is usually the case, is non-magnetic, then parallel alignment yield a bigger current. A very valuable aspect of STM is that this device probes the local properties of a material. This makes it especially useful in investigating defects or impurities of a surface. Now these authors [Phys. Rev. Lett. 105, 066601 (2010)] came to examine what will happen to the signal if the electrons tunnel from the Fe surface into the tip through a single organic molecule with Beneze rings. The result is this: this molecule allows more spin-up electrons to pass. So, it works as a selective valve, which may be tailored to specific applications that needs manipulate spin current. This phenomenon was predicted 3 years ago in Ref.[3], where the computation was implemented in the aid of DFT. However, it may prove more elucidating if a simple model description is prescribed.
For convenience, some references are attested on this subject:

1. Atodiresei, N. et al. Phys. Rev. Lett. 105, 066601 (2010).
2. Brede, J. et al. Phys. Rev. Lett. 105, 047204 (2010).
3. Rocha, A. R. & Sanvito, S. J. Appl. Phys. 101, 09B102 (2007).
4. Barraud, C. et al. Nature Phys. 6, 615–620 (2010).
5. Sanvito, S. Nature Phys. 6, 562–564 (2010).
6. Cinchetti, M. et al. Nature Mater. 8, 115–119 (2009).
7. Drew, A. J. et al. Nature Mater. 8, 109–114 (2009).
8. Szulczewski, G., Sanvito, S. & Coey, J. M. D. Nature Mater. 8, 693–695 (2009)

Thermal Hall effect of magnons

Thermal Hall Effects refer to a class of phenomena in which thermal current carried by elementary excitations of a material is deflected by applying magnetic field. Magnons, as magnetic excitations have been predicted to show such behaviors when both magnetic field and temperature gradient are present. This has been just observed in Lu2V2O7, whose V element is magnetic and magnetic ordering occurs below about 100K[1].

[1]Science 329, 297 (2010)

The Hall effect usually occurs in conductors when the Lorentz force acts on a charge current in the presence of a perpendicular magnetic field. Neutral quasi-particles such as phonons and spins can, however, carry heat current and potentially exhibit the thermal Hall effect without resorting to the Lorentz force. We report experimental evidence for the anomalous thermal Hall effect caused by spin excitations (magnons) in an insulating ferromagnet with a pyrochlore lattice structure. Our theoretical analysis indicates that the propagation of the spin waves is
influenced by the Dzyaloshinskii-Moriya spin-orbit interaction, which plays the role of the vector potential, much as in the intrinsic anomalous Hall effect in metallic ferromagnets.

Microscopic phase separation in thin films

Matter can exist in various phases. These phases are frequently found separated by interfaces, if they can coexist. For example, liquid H2O can not be mixed uniformly with gas H2O, due to their differing densities. Thus, phase separation is a very common phenomena that are encountered every day. Of course, there may also exist systems that exhibit multiple coexisting phases without spatial phase boundaries. One example is multiferroics: BiFeO3 is at the same time an anti-ferromagnet and an ferroelectric, without electrical polarization aliened from magnetic one. They are both homogeneously distributed in the entire sample.

Phase separation can happen on not only large scales, but also on small ones. Examples include multi-domain crystal, in which down magnetization regions are spaced from up magnetization regions by domain walls. Such multi-domain structure is due to long range interactions. Short-range interactions are usually not supposed to raise multi-domain structures. Another example is pnictide superconductors, in which some authors claimed evidences of coexistence of superconductivity and AFM, spatially divorced.

Here[1], the author studied phase separation in thin films of magnese substrated upon STO. Strain caused at the interface is found of important role. The phases are complex and rich.

[1]Science 329, 190 (2010)

Covalency makes a smaller form factor !

Theories involving highly energetic spin fluctuations are among the leading contenders for explaining high-temperature superconductivity in the cuprates¹. These theories could be tested by inelastic neutron scattering (INS), as a change in the magnetic scattering intensity that marks the entry into the superconducting state provides a precise quantitative measure of the spin-interaction energy involved in the superconductivity^{2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. However, the absolute intensities of spin fluctuations measured in neutron scattering experiments vary widely, and are usually much smaller than expected from fundamental sum rules, resulting in 'missing' INS intensity^{2, 3, 4, 5, 12, 13}. Here, we solve this problem by studying magnetic excitations in the one-dimensional related compound, Sr₂CuO₃, for which an exact theory of the dynamical spin response has recently been developed. In this case, the missing INS intensity can be unambiguously identified and associated with the strongly covalent nature of magnetic orbitals. We find that whereas the energies of spin excitations in Sr₂CuO₃ are well described by the nearest-neighbour spin-1/2 Heisenberg Hamiltonian, the corresponding magnetic INS intensities are modified markedly by the strong 2p–3d hybridization of Cu and O states. Hence, the ionic picture of magnetism, where spins reside on the atomic-like 3d orbitals of Cu²⁺ ions, fails markedly in the cuprates.

A recent high Tc model seems promising in solving the underestimated INS intensity. This model explicitly covers the spin-spin interaction between the spin of O holes and the spin of Cu holes. Such interaction effectively makes a smaller scattering form factor, which may give a good fit into observations. Details to be worked out !

[1]Nature Physics 5, 867 - 872 (2009);
[2]J.Phys.:Condens.Matter, 21:075702(2009)