Magnetoentropic signatures of skyrmionic phase behavior in FeGe

We demonstrate that magnetocaloric measurements can rapidly reveal details of the phase diagrams of high-temperature skyrmion hosts, concurrently yielding quantitative latent heats of the field-driven magnetic phase transitions. Our approach addresses an outstanding issue in the phase diagram of the skyrmion host FeGe by showing that dc magnetic anomalies can be explained in terms of entropic signatures consistent with a phase diagram containing a single pocket of skyrmionic order and a Brazovskii transition.

Figure 1

(a) Crystal structure of cubic B20 FeGe (space-group $P{2}_{1}3)$, shown along the (111) axis. (b) Magnetization as a function of field collected at 10 K is very sharp, saturates at low fields, and shows no hysteresis. (c) Magnetization as a function of temperature collected under applied field $H=20\mathrm{mT}$ shows an anomaly near $T_C$. (d) $M\left(T\right)$ collected under different applied fields. This is a subset of the dataset (18 total fields) used to calculate the course-grained map of $\mathrm{\Delta }{S}_M(H,T)$ shown in (e).

Figure 2

The process for obtaining high-resolution magnetoentropic information using Eq. (1). (a) dc $M\left(T\right)$ data taken at many closely spaced fields (24 fields between 5 and 120 mT) (b) Temperature derivatives of magnetization $dM/dT=dS/dH$ are calculated directly using Tikhonov regularization. For visual clarity, the curves are each offset by $0.1\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}{\mathrm{T}}^{-1}$. The antiderivatives of the calculated derivatives are shown as colored lines in (a) and match the raw data (gray crosses) very well. (c) Integrals of the $dM/dT$ curves with respect to the field give the isothermal magnetic entropy change at each temperature and applied field. The curves are each offset by $1\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$.

Figure 3

Detailed magnetoentropic maps of FeGe near the ordering temperature. (a) A map of $dM/dT=dS/dH$ reveals clear ridges (red) and valleys (blue) indicating lines of first-order phase transitions. Note that the ridges and valleys are actually continuous; the segmented appearance is an artifact of the two-dimensional interpolation. (b) A map of $\mathrm{\Delta }{S}_M(T,H)$. (c) $dM/dH$ calculated from the dc magnetization dataset. (a) is used to find the phase boundaries of the phase diagram drawn on (b) where the solid lines represent first-order phase transitions.The dashed line between C and P indicates a continuous transition. The dashed line between FD and FP represents a crossover. P: paramagnetic; FD: fluctuation disordered; FP: field polarized; C: conical; SkX: skyrmion lattice, TCP: tricritical point.

Figure 4

(a)–(c) shows $dS/dH$ vs $H$ at four representative temperatures. Field-driven phase transitions are easily found: First-order transitions show up as peaks (ii–vi) in this thermodynamic capacity, whereas continuous phase transitions show up as changes in the slope (i). Integration of the peaks gives entropies of transitions and latent heats as shown in Table 1. (d) gives a reproduction of the heat map of $dS/dH$ vs $T$ and $H$ as shown in Fig. 3 with the slices shown in (a)–(c) overlaid as dashed colored vertical lines. Refer to the caption of Fig. 3 for the definitions of the phase abbreviations.