Expt 10) Antiferromagnetism — the original “hidden order”

Ferromagnetism is a state of matter whose existence has been known for millennia (Fe₃O₄ supposedly was the first known permanent magnet, but is actually a ferrimagnet). Coincidentally, it was also the material that took center stage in Expt 8 in this series of posts. Antiferromagnetism is, in some sense, “hidden order”. Although predicted in 1932 by Louis Neel, it was not apparent how to convincingly demonstrate that spins could align antiparallel to one another when the magnetic moments perfectly cancel. There is no net magnetization to speak of or measure!

Suggestions of a such a state were hinted at through the observation of a phase transition in magnetic susceptibility measurements, but the origin of such a phase transition was unclear. In 1949, Clifford Shull and J. Stuart Smart definitively demonstrated that antiferromagnetism was present in MnO. In their experiment, which used the new technique of neutron diffraction, magnetic peaks suddenly showed up below , which indicated a doubling of the unit cell. Thus, the question of “hidden order” was finally settled — the evidence for antiferromagnetism was almost indisputable! The original paper, surprisingly and explicitly, states that it was Smart’s idea to use neutron diffraction to detect antiferromagnetism. Below is the original plot from MnO, taken from here, showing at least three peaks corresponding to the antiferromagnetism:

Expt 9) Soft phonons at continuous structural phase transitions

That continuous structural phase transitions are associated with soft phonon modes was first put forth theoretically by Cochran in 1959-60. He posited that as an optical phonon branch reaches zero frequency the material must become structurally unstable. Qualitatively, when the phonon frequency goes to zero, that mode becomes macroscopically occupied, which ushers in a structural change. The symmetry of the phonon determines the new low temperature structure.

While this theory was tested soon thereafter by many, a soft phonon associated with a structural instability had already been observed by Raman and Nedungadi nineteen years prior. In 1940, they saw that the transition between -quartz and -quartz at 573C was associated with a soft phonon using (you guessed it!) Raman spectroscopy. However, it is important to note that the transition in quartz is a discontinuous phase transition. So while the phonon does soften considerably, it does not actually reach zero frequency before the structural transition takes place.

Below is the original image, showing the rather spectacular result, where the arrow indicates the phonon that softens significantly upon approaching the transition temperature (it starts out at at ~220 cm^-1). Both the Stokes and anti-Stokes softening can be observed due to the high temperature of the studies.

Phonon softening in quartz. As the temperature is raised, a phonon that starts out at the position of the arrow shifts toward lower frequency (i.e. towards the region of large intensity Rayleigh scattering). (The phonon mode, for some reason, is barely visible in the -192C spectrum.) At high temperatures, the phonon linewidth broadens considerably and is very difficult to see at 530C. It is actually easier to see the softening on the anti-Stokes side (towards the left of the Rayleigh scattering).