Dynamic magnetocaloric effect in bcc iron and hcp gadolinium

The magnetocaloric effect in bcc iron and hcp gadolinium is simulated on pico- and nanosecond time scales using Langevin spin dynamics on a discrete lattice, with parameters determined from ab initio calculations. It is found that transient external magnetic fields can drive thermodynamic cycles even in strongly nonequilibrium spin configurations, and that these are correlated with changes to the dynamic spin temperature. The theoretical predictions are found to agree closely with existing experimental measurements.

Figure 1

Temperature and magnetization of bcc Fe and hcp Gd predicted by spin-dynamics simulations. Simulation cells containing 54 000 spins are initially thermalized at 950 K for Fe and at 300 K for Gd. Thermodynamic cycles are triggered by applying an external magnetic field, ${\tilde{\mathbf{H}}}_{\text{ext}}=200$ T in the case of Fe and ${\tilde{\mathbf{H}}}_{\text{ext}}=20$ T in the case of Gd. Instantaneous spin temperature is evaluated using the formula $T={\sum }_i{|{\mathbf{S}}_i\left(t\right)\times {\mathbf{H}}_i\left(t\right)|}^2/2k_B{\sum }_i{\mathbf{S}}_i\left(t\right)·{\mathbf{H}}_i\left(t\right)$ derived in Ref. [27]. The plots illustrate how a magnetic material responds to a transient external magnetic field.

Figure 2

Brayton cycles corresponding to Fig. 1. Each cycle involves adiabatic magnetization, isofield cooling down, adiabatic demagnetization, and isofield heating up, respectively. Note that 1 $\mu$eV ${\mathrm{K}}^{-1}$ ${\mathrm{at}}^{-1}$ = 1.73 J ${\mathrm{kg}}^{-1}$ ${\mathrm{K}}^{-1}$ for Fe and 0.62 J ${\mathrm{kg}}^{-1}$ ${\mathrm{K}}^{-1}$ for Gd.