Thermoelectric properties and the first-order transition nature.
\({\text{M}\text{n}}_{2-x}{\text{C}\text{r}}_{x}\text{S}\text{b}\) single-crystalline samples with \(x\) = 0.04 were used in this work. The samples were cut into cuboids. The largest plane corresponds to the a–b plane of the crystal structure, and transport measurements were carried out in the a–b plane. First, we examined the thermoelectric properties to demonstrate the first-order transition of Mn1.96Cr0.04Sb. Figure 1d shows the temperature dependence of the Seebeck coefficient. In the FI phase, the Seebeck coefficient is positive and slightly decreases with decreasing temperature. It changes abruptly at the FI-to-AF transition temperature (approximately 190 K) and shows a negative value in the AF phase. Figures 1e and 1f show magnified images of the temperature dependence of the Seebeck coefficient and resistivity around the AF-FI transition temperature, respectively. The resistivity shows clear hysteresis at the AF-FI transition, indicating the first-order transition. The Seebeck coefficient is approximately 8 \({\mu }\)V/K above the transition temperature (FI phase), while it is approximately -7 \({\mu }\)V/K immediately below the transition temperature (AF phase), also showing hysteresis.
Device settings and measurement process.
Our experiment was performed as follows (Fig. 2a and see also Methods for details). First, we lower the sample temperature to 170 K so that the whole sample region is in the AF state as the most thermodynamically stable state. Then, we raise the temperature to the base temperature (Tbase). Here, Tbase is set to a temperature within the hysteresis loop (see below for the discussion when Tbase lies outside the hysteresis loop). After that, we supply a heat pulse to the centre part of the cuboid sample by applying a pulsed electric current to a chip heater attached to the centre of the sample (Fig. 2a). This heater current is used to make an AF/FI/AF junction structure; as shown in Fig. 2b, when the pulsed heater current is small, the temperature of the centre region does not reach the AF-to-FI transition temperature. Thus, the whole sample remains in the AF phase [Fig. 2b (i)]. In contrast, when the pulsed heater current is large enough to make the temperature exceed the AF-to-FI transition temperature, the magnetic state of the centre region changes from the AF to FI phase. After turning off the heater current (i.e., the sample returns to Tbase), the FI state remains because Tbase is in the hysteresis loop [Fig. 2b (ⅱ)]. In this way, an AF/FI/AF junction structure is created.
Observation of the single-material Peltier effect.
In Fig. 2c, we plot the pulsed heater current dependence of the Peltier coefficient for the device (Π) of S1 (see Methods for the calculation of Π). Tbase is 193 K (inside the hysteresis loop). Without a heat pulse (0 mA), Π takes a small negative value. As the pulsed heater current increases, Π dramatically increases and reaches its maximum at approximately 10 mA. This large enhancement of Π emerges from the creation of the AF/FI/AF structure due to the local heating, as described above (Fig. 2d). This is further confirmed by a numerical simulation (see below). With a further increase in the pulsed heater current from 10 mA, Π decreases and almost saturates at approximately 20 mA. The behaviour of Π above 10 mA is due to expansion of the FI region; with increasing heater current from 10 mA, the FI region expands towards both sample edges, exceeding the positions where the thermocouple is attached, and finally, the whole sample is in the FI phase at approximately 20 mA. This process induces the observed reduction and saturation of Π.
We note that the nonzero Π observed in the low- and high-power regions originates from the difference in Seebeck coefficients between the electrodes and the sample; in the case of a low heat pulse, the whole sample is in the AF phase (Fig. 2d). In this situation, absorption and release of heat occur at the interfaces between the Cu electrodes and the AF phase of the sample. Since the Seebeck coefficient of the Cu electrodes is almost 0 \({\mu }\)V/K24, whereas that of the AF phase is negative, the heat absorption and release at the electrode-AF phase interface is expected to cause a negative Peltier coefficient (ΠAF/el), which is consistent with the sign of the observed Peltier coefficient in the low-power region. This assumption is also justified by our simulation (see below). The positive Peltier coefficient observed in the high-power region also originates from the difference in the Seebeck coefficients between the electrodes and the FI state; since the Seebeck coefficient in the FI state is positive, the observation of a positive Peltier coefficient (ΠFI/el) is consistent with this assumption.
We identified that the peak of the Peltier coefficient at approximately 10 mA corresponds to the state in which the interfaces of the AF/FI/AF junction are located at the positions of the thermocouple. Hence, we define the difference between the peak value and the background value at 0 mA as the single-material Peltier coefficient arising from the AF/FI/AF structure (ΠFI/AF). The maximum value of ΠFI/AF in the device made of S1 is 0.3 mV, which is comparable to or even higher than the previously reported single-material Peltier coefficient originating from the anisotropic magneto-Peltier effect in Ni (0.11 mV)8. A similar dependence of the Peltier coefficient on the pulsed heater current is observed for another device made of S2 (see Supplementary Fig. 2). To confirm the formation of the AF/FI/AF junction structure, we also measured the resistivity of the centre part under the same setup as the Peltier coefficient measurement. The decrease in the resistivity after the pulse heating verified the formation of the FI domains in the centre part (see Supplementary Fig. 4 and Note 1).
Simulation of the single-material Peltier effect.
To further verify that the observed signal arises from the Peltier effect in the AF/FI/AF structure, we performed a simulation based on two-dimensional finite element methods (see Methods for details). The model system for this simulation is shown in Fig. 3a. We set the base temperature to 192 K and assumed that the AF-to-FI transition temperature during the heating process is 196 K. At 0 mA, the whole sample is in the AF phase (Fig. 3b and Fig. 3c). The temperature distribution originating from the Peltier effect is shown in Fig. 3d and Fig. 3e. In this case, heat absorption and release occur only at the interfaces between the electrodes and the sample, generating a negative temperature gradient, i.e., a negative Peltier coefficient. When a heater current of 6.3 mA is applied, the temperature in the centre of the sample increases (Fig. 3f). Then, from the temperature increase presented in Fig. 3f, we calculated the distribution of the magnetic phases using the AF-to-FI transition temperature and obtained the AF/FI/AF junction as shown in Fig. 3g (see Methods for details). In this case, a large amount of heat is absorbed and released at the AF-FI domain boundary, and the Peltier coefficient becomes positive (Fig. 3h and Fig. 3i). At 14.1 mA, the sample temperature is far above the AF-to-FI transition temperature in the whole sample (Fig. 3j); thus, a single domain FI phase is formed (Fig. 3k). As shown in Fig. 3l and Fig. 3m, heat absorption and release occur only at the interfaces between the electrodes and the sample, bringing about a positive temperature gradient (i.e., a positive Peltier coefficient). These features are quite consistent with the experimental results and the abovementioned explanation. To further confirm the agreement between the experiment and the simulation, in Fig. 3n, we show the heater current dependence of the temperature difference at two points denoted by the triangles in Figs. 3a, 3e, 3i, and 3m. These points correspond to the positions of the thermocouple in the experiment. The profile shows good agreement with the experimental result presented in Fig. 2c. The simulated Peltier coefficient is estimated to be ΠFI/AF = 0.32 mV, which is the same order of magnitude as the experimental value of 0.3 mV in S1. This consistency indicates that magnetic-phase junctions were indeed realized in our experiment.
Base temperature dependence of the single-material Peltier effect.
The dependence of Π on the base temperature (Tbase) also strongly supports that the observed Peltier effect emerges from the magnetic-phase junction. Figure 4a shows the pulsed heater current dependence of the Peltier coefficient of S1 at various Tbase. In S1, the FI-to-AF transition temperature (during the cooling process) is 190 K, and the AF-to-FI transition temperature (during the heating process) is 195 K. At Tbase = 180 K, which is sufficiently below the hysteresis loop, Π is independent of the heater current (Fig. 4a). This is because the whole sample remains in the AF phase; the heat pulse with 20 mA is probably not sufficient to make the sample temperature exceed the AF-to-FI transition temperature, or even if the FI state is created, the FI state relaxes to the AF state immediately because Tbase is outside the hysteresis loop and the FI state is energetically unstable. In addition, at Tbase = 200 K, because the whole sample is already in the FI phase, Π does not vary with the pulsed heater current. In contrast, when Tbase =190 K and 193 K, which are inside the hysteresis loop, the Peltier coefficients clearly vary as a function of the pulsed heater current; Π of Tbase = 193 K shows a peak around the pulsed heater current of 10 mA, which is consistent with the expected behaviour in the single-material Peltier effect due to the magnetic-phase junction, as mentioned above. The Peltier coefficient Π at Tbase = 190 K also shows a peak at approximately 10 mA. However, unlike for Tbase = 193 K, the reduction of the Peltier coefficient when the pulsed heater current further increases from 10 mA is small. This is because the heater current is not sufficient to let the side areas of the sample change to the FI phase due to the lower Tbase.
In Fig. 4b, the ΠFI/AF for S1 and S2 is plotted as a function of the base temperature. The base temperature dependences of ΠFI/AF for S1 and S2 show similar trends, exhibiting a clear peak around the transition temperature. Note that the transition temperatures are slightly different between the samples due to the slight variation in Cr composition; the hysteresis loops in the resistivity of S1 and S2 are observed at approximately 190 K \(\le\) T \(\le\) 195 K and 185 K \(\le\) T \(\le\) 195 K, respectively. The maximum value of ΠFI/AF is 0.3 mV for S1 and 0.58 mV for S2. The difference in the peak values of the two samples may result from the difference in the clarity of their first-order transition.
Relaxation of the single-material Peltier effect.
Finally, we investigate the stability of the magnetic-phase junction. The magnitude of the single-material Peltier coefficient will be reduced with time because the metastable magnetic state will gradually relax to the equilibrium state. The relaxation of the single-material Peltier coefficient is described as a stretched exponential function as follows (see Methods):
where τ is a characteristic relaxation time and β is a phenomenological parameter representing the distribution of τ. The measured relaxation curve of the single-material Peltier coefficient is shown in Fig. 4c. We created an AF/FI/AF junction by applying a pulsed heater current of 10 mA and monitored ΠFI/AF as a function of time. The dotted line is a fitting curve with τ = 108 hours \(\approx\)104 years and yields β = 0.18. This guarantees the high stability of the single-material Peltier effect.