Identifying the critical point of the weakly first-order itinerant magnet DyCo${}_2$ with complementary magnetization and calorimetric measurements

We examine the character of the itinerant magnetic transition of DyCo${}_2$ by different calorimetric methods, thereby separating the heat capacity and latent heat contributions to the entropy—allowing direct comparison to other itinerant electron metamagnetic systems. The heat capacity exhibits a large λ-like peak at the ferrimagnetic ordering phase transition, a signature that is remarkably similar to La(Fe,Si)${}_{13}$, where it is attributed to giant spin fluctuations. Using calorimetric measurements, we also determine the point at which the phase transition ceases to be first order: the critical magnetic field, ${\mu }_0$$H_{\mathrm{crit}}$ $=$ 0.4 ± 0.1 T and temperature $T_{\mathrm{crit}}$ $=$ 138.5 ± 0.5 K, and we compare these values to those obtained from analysis of magnetization by application of the Shimizu inequality for itinerant electron metamagnetism. Good agreement is found between these independent measurements, thus establishing the phase diagram and critical point with some confidence. In addition, we find that the often-used Banerjee criterion may not be suitable for determination of first order behavior in itinerant magnet systems.

Figure 1

Heat capacity as a function of field at selected temperatures about $T_c$ for both field increase and decrease; $C_{\mathrm{peak}}$ ∼ 1650 Jkg${}^{-1}$K${}^{-1}$ at $T$ $=$ 137.2 K, $\mu$${}_{0}H$ $=$ 0 T, almost 7 times larger than $C_p$($T$ > $T_c$). Inset left: Signature of distributed latent heat measured at 137.2 K. Inset right: $S$–$T$ plot determined by integrating the zero-field total heat capacity from 10 K.

Figure 2

Entropy change Δ$S_{HC}$ calculated by integrating $C_p$ from $T_{\mathrm{ref}}$ $=$ 220 K. The offset in Δ$S_{HC}$ compared to Δ$S_{\mathrm{Max}}$ below $T_c$ (∼135 K), is an indication of the temperature dependent latent heat Δ$S_L$. Inset shows this offset $K$(0,$H$) (in same units, Jkg${}^{-1}$K${}^{-1}$) plotted as a function of the critical field and indicates Δ$S_L$(0 T) $=$ 2.6 ± 0.5 Jkg${}^{-1}$K${}^{-1}$.

Figure 3

Landau fit at 137.5 K for DyCo${}_2$ where parameters $A$ and $B$, as defined in the text, are fixed at values determined as $M^2$ approaches zero. Similarly poor fits were observed for other temperatures ($T$ > $T_c$) when parameter $D$ was set to zero.

Figure 4

Stability of itinerant metamagnetic behavior as a function of temperature. The hashed area indicates possible values for stable first order IEM as defined by the Shimizu inequality given in the text. The data shown here indicates $T_{\mathrm{crit}}$ ∼ 138.5 K. Inset shows the value of $B$ as a function of temperature where $B$ < 0 for $T$ < 146 K, indicating by the Banerjee criterion that $T_{\mathrm{crit}}$ < 146 K.

Figure 5

(a) Example bulk and fragment M-H loop at 138 K. Inset shows hysteresis (Δ$H$ $=$ $H_c$${}^{\uparrow }$ − $H_c$${}^{\downarrow }$) as a function of temperature where the 0.05 T is a minimum baseline due to experimental artifacts. (b) Critical field $H_c$ determined from bulk magnetometry and position of the heat capacity peak $C_{\mathrm{peak}}$ from bulk and microcalorimetry data. The position of the ac heat capacity peak is the same (within symbol size) for field increase and decrease (as shown in Fig. 1). The dashed lines indicate the $T_{\mathrm{crit}}$ and $H_{\mathrm{crit}}$ as determined by magnetometry and calorimetry, respectively. The field and temperature at which hysteresis approaches zero [see inset of (a)] and $C_{\mathrm{peak}}$ approaches the bulk phase line corresponds to $H_{\mathrm{crit}}$ $=$ 0.45 T and $T_{\mathrm{crit}}$ $=$ 138.5 K.