Magnetic correlations in ferromagnetic single-walled nanotubes

• Magnetic correlations (MCs) of ferromagnetic single-walled nanotubes (FM-SWNT's) are investigated.
• At Curie point, the neighboring spins are antiparallel for spin quantum number S<2.
• The rising of anisotropy causes longitudinal MC at Curie point increasing for S<2.
• Spin fluctuation effect becomes stronger for thinner tubes and weaker anisotropy.
• The effect of longitudinal MC is always in contrary to that of transverse MC.

The magnetic correlations, including transverse magnetic correlation (TMC) and longitudinal magnetic correlation (LMC), of ferromagnetic single-walled nanotubes are comprehensively investigated by use of the double-time Green's function method. The influence of temperature, spin quantum number, diameter of the tube, anisotropy strength and external magnetic field to magnetic correlations are carefully calculated. An interesting result is that for the two smallest spin quantum numbers S=1, and 3/2, the LMC around the Curie point is negative, demonstrating that the neighboring spins in ferromagnetic single-walled nanotubes are antiparallel to each other along the tube axis direction in spite of the ferromagnetic exchanges between them, while it is not so along the transverse direction. This is due to the fact that the quantum spin fluctuation is believed anisotropic. The effect of the LMC is always in contrary to that of the TMC effect: if one is stronger, the other is weaker.