Spectroscopic signature of the superparamagnetic transition and surface spin disorder in CoFe ₂O ₄ nanoparticles

Figure Persented: Phonons are exquisitely sensitive to finite length scale effects in a wide variety of materials. To investigate confinement in combination with strong magnetoelastic interactions, we measured the infrared vibrational properties of CoFe ₂O ₄ nanoparticles and compared our results to trends in the coercivity over the same size range and to the response of the bulk material. Remarkably, the spectroscopic response is sensitive to the size-induced crossover to the superparamagnetic state, which occurs between 7 and 10 nm. A spin-phonon coupling analysis supports the core-shell model. Moreover, it provides an estimate of the magnetically disordered shell thickness, which increases from 0.4 nm in the 14 nm particles to 0.8 nm in the 5 nm particles, demonstrating that the associated local lattice distortions take place on the length scale of the unit cell. These findings are important for understanding finite length scale effects in this and other magnetic oxides where magnetoelastic interactions are important.