Could anyone explain the difference between spin correlation length and charge correlation length? Will spin correlation length show similar features to charge correlation length? For example, in Fe-based pnictide CeFeAsO, the magnetic transition from PM to AFM occurs below the Tetragonal-Orthorhombic structure transition temperature TS. Based on the nematic model, the spin-correlation length will increase rapidly below TS. Will the charge correlation length also increase below TS?
According to the definition, spin correlation length is how far two spins can be apart to feel each other. Similar for charge correlation length, but for charges rather than spins. For AFM or FM states spins are aligned on each lattice site, so the spin correlation length is infinite. There is, however, no direct relation to the charge correlations. One can imagine latter as modulation of the charge density - charge-density wave (as opposed to spin-density wave). Then correlation length depends on how charges are modulated. Infinite correlation length is a long-range order. It corresponds to divergence of different susceptibilities - spin susceptibility for spin-density wave and charge susceptibility for charge-density wave instabilities. So, answering the second part of your question, I would not expect the increase of charge correlation length below TS in pnictides.
Thanks very much for your directions! I still have one question. For Fe-based pnictide CeFeAsO, the tetragonal phase (a=b=3.996) changes to orthorhombic phase (a=5.64, b=5.63) at TS. Will the charge correlation length increase or decrease with the decrease of temperature at TS?
The spin correlation length in a ordered magnetic phase at low temperature is usually infinite. The width of he magnetic Bragg peak in this case is resolution limited. In neutron diffraction we see that the magnetic peak is a delta function convolved with the instrument resolution function. Below T_N the magnetic correlation length becomes infinte usually. Now the charge correlation length is much more shuttle. First of all the charge ordering phenomenon is not as clear cut as the spin ordering. Neutron diffraction is only indirectly sensitive to charge ordering. Even normal X-ray diffraction is also similarly insensitive because the charge ordering involves very small differences in charges. The charge ordering phenomenon was first discovered in magnetite Fe3O4 in fifties of the last century but it still remains enigmatic. The charge ordering involves lattice distortion and symmetry lowering that are often very small. The charge ordering in strongly correlated electron system is seldom complete. Instead of charge difference \delta = 1 we get delta = 0.2 or so. The charge ordering phenomenon is best studied in transition metal oxides viz. magnetite Fe3O4 and doped manganites La1-xCaxMnO3. The half-doped manganite La0.5Ca0.5MnO3 is a standard example. The charge correlation length can be infinite. Then the superlattice peaks are resolution limited. It can be finite as well. Then the superlattice peaks are broader than the instrumental resolution. Each case has to be studied by the scattering method individually and there is no general statement possible. But normally one expects in ideal cases both spin and charge correlation lengths diverge as one cools down from above Tc and becomes infinite below Tc. They do not change anymore below Tc. But there are exceptions of course.
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