Previously I posted about some fascinating experimental results on anisotropic thermal expansion and elastic softening near superconducting and magnetic transitions in organic charge transfer salts.
Subsequently, I became aware that the new iron pnictide superconductors do exhibit somewhat similar phenomena. A combined theory-experimental PRL (10 co-authors!) describes shear acoustic mode spectroscopy in terms of nematic spin fluctuations.
They find in undoped BaFe2As2 that the shear modulus (C66) softens significantly as one approaches the magnetically ordered phase (which is a associated with a tetragonal-orthorhombic lattice distortion). For the optimally doped material there is a hardening of the lattice as one enters the superconducting phase.
The figure above explains the nematic order parameter and how it couples to shear lattice distortions. A key is the that the magnetic phase consists of Neel antiferromagnetic order on two separate sublattices . They are weakly coupled together and the nematic order parameter phi equals the dot product of m1 and m2, the antiferromagnetic order parameters on the two separate lattices. phi then couples directly to the shear strain.
The softening into the superconducting (SC) phase is explained by a coupling of the SC and AFM order parameters. This leads to a change in the static spin susceptibility upon entering the SC phase. This in turn effects the fluctuations in the nematic order parameter.
A couple of comments:
a. Experimental data is presented just for C66. It would be helpful to see it for longitudinal sound and for other transverse modes besides epsilon_s=epsilon_xy. These modes should not have significant coupling to superconductivity and magnetism if the nematic mode is where all the action is.
b. In other antiferromagnets lattice anomalies at magnetic transitions are explained in terms of the spin anisotropy (e.g. due to the Dzyaloshinsky-Moriya interaction) coupling to the different components of the stain tensor. This is reviewed here by Lines. Can that be ruled out in the pnictides?
Subsequently, I became aware that the new iron pnictide superconductors do exhibit somewhat similar phenomena. A combined theory-experimental PRL (10 co-authors!) describes shear acoustic mode spectroscopy in terms of nematic spin fluctuations.
They find in undoped BaFe2As2 that the shear modulus (C66) softens significantly as one approaches the magnetically ordered phase (which is a associated with a tetragonal-orthorhombic lattice distortion). For the optimally doped material there is a hardening of the lattice as one enters the superconducting phase.
The figure above explains the nematic order parameter and how it couples to shear lattice distortions. A key is the that the magnetic phase consists of Neel antiferromagnetic order on two separate sublattices . They are weakly coupled together and the nematic order parameter phi equals the dot product of m1 and m2, the antiferromagnetic order parameters on the two separate lattices. phi then couples directly to the shear strain.
The softening into the superconducting (SC) phase is explained by a coupling of the SC and AFM order parameters. This leads to a change in the static spin susceptibility upon entering the SC phase. This in turn effects the fluctuations in the nematic order parameter.
A couple of comments:
a. Experimental data is presented just for C66. It would be helpful to see it for longitudinal sound and for other transverse modes besides epsilon_s=epsilon_xy. These modes should not have significant coupling to superconductivity and magnetism if the nematic mode is where all the action is.
b. In other antiferromagnets lattice anomalies at magnetic transitions are explained in terms of the spin anisotropy (e.g. due to the Dzyaloshinsky-Moriya interaction) coupling to the different components of the stain tensor. This is reviewed here by Lines. Can that be ruled out in the pnictides?
We were glad to hear about our work in the blog! Regarding the two points raised, here are a few thoughts:
ReplyDelete1) In our measurements, due to sample size limitations, we could not resolve the full elastic tensor. However, there is a paper in arxiv (1008.1479) where Yoshizawa et al measure all the elastic components. They observe a softening in some other moduli as well, but smaller than the softening in C66. Further evidence for the connection between the lattice softening and nematic fluctuations is that, for highly doped samples, we actually observed a mild increase in the resonant frequencies as the temperature was decreased.
2) That's an interesting point. Note that, in our model, what drives the structural transition are the magnetic fluctuations, precisely through the magneto-elastic coupling. In most materials, one usually has the coupling between the squared magnetization and the longitudinal distortion. In the pnictides, by symmetry, there is a direct coupling between the shear distortion and the nematic order parameter (m1.m2). Then, the onset of nematic ordering coincides with the structural transition. Notice also that the hardening of the shear modulus below Tc is an unexpected feature, since there is no nearby structural instability. In our model, it is naturally explained by the presence of nematic fluctuations and the competition between magnetism and superconductivity.
Rafael Fernandes, Premala Chandra, David Mandrus, and Joerg Schmalian