Relevant crystal field interaction in the magnetically ordered state

Abstract

Abstract Experimental data are discussed showing that in contrast to the paramagnetic phase, in the magnetically ordered state the action of the crystal electric field on the spin dynamics is quantized. In the Curie-Weiss regime of the paramagnetic susceptibility the spin dynamics is determined by local exchange interactions between individual pairs of spins and by single particle anisotropies (crystal field interaction). As we know from Renormalization Group (RG) theory, these local interactions are of no importance on the spin dynamics in the long range ordered state. On the other hand, a sufficiently strong crystal electric field is known to decrease the saturation magnetic moment for T → 0. In the critical paramagnetic range and for all lower temperatures the spin dynamics is controlled by a field of delocalized bosons instead by exchange interactions between spins. As we could show, the bosons are essentially magnetic dipole radiation emitted by the precessing spins. It is observed that the spontaneous generation of magnetic dipole radiation involves all N = 2S + 1 spin states, and is different in magnets with an integer and a half-integer spin. The dynamics of the boson field therefore is quantized and can be characterized by a limited number of universality classes. The effect of a relevant crystal field interaction is to reduce the number of thermodynamically relevant spin states per magnetic atom by ΔN = 1 or multiples thereof. This happens as discrete crossover events and reduces the saturation magnetic moment for T → 0 in discrete steps. The dynamics remains quantized. Each reduction by ΔN = 1 changes the universality class. Since a crossover is a threshold induced event, we have to distinguish between a relevant and a non-relevant crystal field interaction. Only a sufficiently strong crystal field interaction can become relevant. The crossover from S to Seff = S − 1/2 can occur in the critical paramagnetic range, and manifests as a functional change in the temperature dependence of either the longitudinal or the transverse susceptibility. A very particular observation is that in the insulating magnets a relevant crystal field interaction lets the magnetic heat capacity collapse to its absolute minimum. The magnetic entropy saturates at the lowest possible value of R·ln(2), irrespective of the value of Seff (R = gas constant). This does not mean that a crossover to atomistic Ising behavior has occurred. For the metallic magnets the action of a relevant crystal electric field is also to reduce the number of relevant spin states for T → 0 but the magnetic entropy saturates only gradually below the expected value of R·ln(2S + 1). Indications are discussed that each reduction of the spin by ΔS = 1/2 generates an additional energy band in the magnon excitation spectrum. In the metals the gap energy of the lowest magnon band is lower than in the insulators. Due to the lower excitation gap, spin dynamics and magnetic heat capacity are less suppressed in the metals compared to the insulators.