# Neutron Scattering and Cuprates

Because many of us were born after the cuprates were discovered, and because of the sheer number of papers that have been written on them, it can seem like a daunting task for the young researcher to get a good grip on high-temperature superconductivity. Fortunately, there are some great review papers out there that help synthesize a lot of data and provide references to much of the original work. These review articles tend to concentrate either on one experimental technique or one part of the cuprate phase diagram (e.g. the pseudogap).

In a similar spirit, this blog post will concentrate on some of the significant findings in the cuprates discovered using neutron scattering. It should be kept in mind that most neutron scattering experiments have been done on YBCO and LSCO because large single crystals can be made of these compounds. The list below is a little biased, but I hope some will find it useful.

1. Spin Gap: A low energy gap in the magnetic inelastic neutron scattering  cross section has been observed  below Tc in both optimally doped LSCO and YBCO. For YBCO, the magnitude of the spin gap is larger (consistent with its higher Tc) and the spin gap exists for underdoped and overdoped samples as well. In YBCO the relation $2\Delta_s=3.8k_BT_c$ is approximately observed, where $\Delta_s$ is the magnitude of the spin gap.
2. Dispersive Incommensurate Fluctuations and the Hourglass Spectrum: There exist incommensurate magnetic fluctuations near the antiferromagnetic Bragg point in both underdoped and optimally doped LSCO and YBCO. These peaks show up in the magnetic inelastic neutron scattering cross section and seem to gain in intensity below the superconducting transition. On a $\delta$ vs. energy plot (where $\delta$ is the incommensurability away from the anti-ferromagnetic Bragg point) the spectrum seem to have an hourglass-like shape. It should be noted that (to my knowledge) the hourglass spectrum has not been observed in electron-doped cuprates with studies having been conducted on (NCCO and PLCCO).
3. Resonance Mode: The magnetic resonance mode is a peak at ~40-50meV, which is located at the “pinching point” in the hourglass spectrum. This peak has been observed in many underdoped and optimally doped cuprates, including BSCCO and TBCCO. It is probably the weakest in  LSCO, where it is broad and does not carry much spectral weight. It also only shows up dramatically around Tc. Interestingly, a similar mode has been seen in electron-doped cuprates and some of the Fe-based superconductors.

While there have been some other discoveries in the cuprates with neutron scattering, most of the studies tend to concentrate on one or all of these three general experimental observations.

Here are some links to some papers which discuss these observations in a little more detail: