Phase-transition-induced giant Thomson effect for thermoelectric cooling

The Seebeck and Peltier effects have been widely studied and used in various thermoelectric technologies, including thermal energy harvesting and solid-state heat pumps. However, basic and applied studies on the Thomson effect, another fundamental thermoelectric effect in conductors, are limited despite the fact that the Thomson effect allows electronic cooling through the application of a temperature gradient bias rather than the construction of junction structures. In this article, we report the observation of a giant Thomson effect that appears owing to magnetic phase transitions. The Thomson coefficient of FeRh-based alloys reaches large values approaching $-$1,000 $\mu$VK$^{-1}$ around room temperature because of the steep temperature dependence of the Seebeck coefficient associated with the antiferromagnetic-ferromagnetic phase transition. The Thomson coefficient is several orders of magnitude larger than the Seebeck coefficient of the alloys. Using the active thermography technique, we demonstrate that the Thomson cooling can be much larger than Joule heating in the same material even in a nearly steady state. The operation temperature of the giant Thomson effect in the FeRh-based alloys can be tuned over a wide range by applying an external magnetic field or by slightly changing the composition. Our findings provide a new direction in the materials science of thermoelectrics and pave the way for thermal management applications using the Thomson effect.


I. INTRODUCTION
The Thomson effect refers to the release or absorption of heat as a result of applying a charge current to a conductor under a temperature gradient. The effect was predicted by William Thomson, who later became known as Lord Kelvin. 1,2 The Thomson effect is one of the nonlinear thermoelectric phenomena; in contrast to the linear-response thermoelectric phenomena, e.g., the Seebeck and Peltier effects, the heat production rate induced by the Thomson effect is proportional to both the applied charge current density j c and temperature gradient T: where  is the Thomson coefficient. Thus, when  is finite, the Thomson effect enables thermoelectric cooling/heating in homogenous materials ( Fig. 1), which is in stark contrast to conventional Peltier devices that require junction structures comprising different materials. Despite its technological potential and scientific importance, [3][4][5] the fundamental physics, materials science, and thermoelectric applications of the Thomson effect remain to be investigated. To address this gap, direct imaging measurements of the temperature modulation induced by the Thomson effect have recently been reported. 6 This versatile measurement technique makes it possible to investigate the detailed behaviors and functionalities of this phenomenon.
Materials with large Thomson coefficients are indispensable for realizing thermoelectric applications of the Thomson effect. In a conductor,  obeys the first Thomson (or Kelvin) relation ( 2 ) where Sis the Seebeck coefficient and T is the absolute temperature. Equation (2) indicates that materials with a sharp temperature dependence of S are potential candidates to show large cooling/heating induced by the Thomson effect.
However, the temperature derivative of S, that is, , is usually very small. Although recent experiments have shown that  in a Bi 88 Sb 12 alloy is strongly enhanced under a magnetic field, 6 the obtained  value is still below 100 VK -1 .
The small magnitude of  hinders research on the Thomson effect.
In this work, we demonstrate that the Thomson coefficient can be much larger than the Seebeck coefficient with the aid of magnetic phase transitions. We focus on FeRh-based alloys, which show a sharp temperature dependence of S associated with the antiferromagnetic-ferromagnetic phase transition. 7 1). This demonstration reveals the potential of nonlinear thermoelectric effects and provides unconventional concepts for designing thermal management devices that do not require junction structures.

A. Estimation of Thomson coefficient of Ni-doped FeRh alloy
FeRh-based alloys are well-known materials that exhibit a first-order magnetic phase transition from the antiferromagnetic (ferromagnetic) to ferromagnetic (antiferromagnetic) state with increasing (decreasing) T. Over the past decades, FeRh-based alloys have become popular among researchers owing to their unique physical properties governed by this phase transition. These alloys can be utilized in various applications, such as magnetic refrigeration, [17][18][19][20] heat-assisted magnetic recording, 21,22 and multiferroic devices. 23 Fig. 2(b)].

B. Direct measurement of Thomson-effect-induced temperature modulation
To directly observe the temperature modulation induced by the giant Thomson effect in the Fe 49.0 Rh 50.8 Ni 0.2 alloy, we used the thermoelectric imaging method based on lock-in thermography (LIT). 6,[14][15][16] The experimental setup for the LIT measurement is shown in Fig. 3(a). A bar-shaped Fe 49.0 Rh 50.8 Ni 0.2 slab was bridged between two heat baths and a chip heater was attached to the center of the slab. A steady temperature gradient was generated along the y direction by applying a charge current to the heater. In this configuration, the direction of T is reversed between y > 0 (around region R1) and y < 0 (around region R2) [ Fig. 3(a)], where y = 0 is set at the heater position. This T distribution is useful for direct imaging measurements of the Thomson effect because the dependence of the heat release/absorption on the T direction can be confirmed in a single measurement. 6 To perform the LIT measurements, a square-wave-modulated AC charge current with the amplitude J c , frequency f, and zero DC offset was applied to the slab along the y direction in the presence of a steady temperature gradient. The distribution of the periodic temperature change in response to the charge current at the top surface of the slab was recorded using an infrared camera. The obtained thermal images are transformed into lock-in amplitude A and phase  images through Fourier analysis, where A represents the magnitude of the current-induced temperature change and  the sign as well as the time delay of the temperature modulation. Under these conditions, the direction of the charge current is the same over the slab, whereas the direction of T at R1 is opposite to that at R2 [ Fig. 3(a)]. Therefore, the sign of the temperature modulation due to the Thomson effect is expected to be reversed between R1 and R2 [ Fig. 3(b) and Eq. (1)]. During the LIT measurements, the sample was first heated by applying a large heater power of P > 60 mW and then the P value was set in the order of 60, 45, 30, 15, and 0 mW. Thus, the thermal history of the sample resembles the cooling cycle in Fig. 2(d). The LIT measurements were performed at room temperature and atmospheric pressure.
In Fig. 3(c), we show the observed A and  images for the Fe 49.0 Rh 50.8 Ni 0.2 slab at J c = 300.0 mA, f = 1.0 Hz, and P = 60 mW. The A signals exhibit two peaks around R1 and R2 and that the  difference between R1 and R2 is approximately 180°, indicating that the sign of the current-induced temperature modulation at R1 is opposite to that at R2. This behavior is consistent with Eq. (1), and confirms the presence of heating/cooling due to the Thomson effect.
It should be noted that in this experimental configuration, the measured LIT images may include contributions not only from the Thomson effect but also from the Peltier effect generated at the ends of the sample connected to the electrodes. 6 In fact, we observed finite Peltier signals at P = 0 mW, that is, in the absence of a steady temperature gradient [ Fig. 3(d)]. However, the magnitude of the Peltier-effect-induced temperature modulation in the present experiment is negligibly small as compared to the temperature modulation at P = 60 mW. We can thus regard the observed temperature modulation in Fig. 3(c) as the pure Thomson-effect-induced signals without any background subtraction. The spatial distribution of the temperature modulation in Fig. 3(c) appears as a consequence of the sign reversal of the Thomson signal across the center of the slab and the thermal connection of both ends of the slab to the heat baths.
To investigate the detailed behaviors of the Thomson effect in the Fe 49.0 Rh 50.8 Ni 0.2 alloy, we performed LIT measurements at different P values. Figure 4(a) shows the steady-state temperature profiles along the y direction on the top surface of the sample measured at P = 60, 45, 30, and 15 mW. We confirmed that the temperature gradient bias monotonically increases with increasing P and that the temperature distribution is not affected by the Joule heating due to the charge current applied to the sample. As shown in the A profiles along the y direction , the magnitude of the temperature modulation due to the Thomson effect increases with increasing P. We also found that the A signals at R1 and R2 are proportional to J c [ Fig. 4(b)]. These behaviors are in good agreement with the characteristics of the  Figure 6(b) shows the corresponding  values calculated using Eq. (2). We found that the position of the  peak monotonically decreases with increasing the magnetic field, although the magnitude of  remains unchanged. The magnetic field dependence of the  peak position is consistent with the field dependence of the firstorder phase transition in similar alloys. 10, 11 We also confirmed that the  peak position shifts to higher (lower) temperatures with decreasing (increasing) Ni content in Ni-doped FeRh alloys. As shown in Figs. 6(c) and 6(d), the to drive the Thomson device, i.e., a charge current and an external temperature gradient, needs to be taken into consideration in the coefficient of performance appropriately. 31 Thus, not only materials science studies but also fundamental physics studies are necessary to develop thermal management applications based on the Thomson effect.

A. Sample preparation
To prepare the undoped and Ni-doped FeRh alloy samples, pure Fe, Rh, and Ni shots with 99.99 % purity were first weighed in appropriate amounts and placed into an arc-melting chamber. Sufficiently large alloy ingots were then prepared by completely melting and mixing the metals in an Ar atmosphere. To ensure homogeneous mixing, each alloy was melted 10 times followed by annealing in a high-temperature vacuum furnace at 1000 °C for 72 h, and then slowly cooled to room temperature for 10 h. The alloy pieces used for various characterizations were cut from the same ingots using a diamond wire saw. Here, the post-annealing process is necessary to observe the giant Thomson effect in these alloys since the steep change in S cannot be obtained in as-prepared alloys without the post-annealing due to the absence of clear first-order ferromagnetic-antiferromagnetic phase transition. The compositions of the alloys were evaluated using an inductively coupled plasma optical emission spectrometer and determined to be

B. Measurement of magnetization
The T dependence of the magnetization of the Fe 49.0 Rh 50.8 Ni 0.2 alloy in Fig. 2(a) was measured using a vibrating sample magnetometer. A slab with dimensions of 2.5 × 2.5 × 2.0 mm 3 was used for the magnetization measurement. The data were recorded during the warming and cooling cycles under a constant magnetic field of 1 T along the 2.5-mm direction. We confirmed that the magnetization of the Fe 49.0 Rh 50.8 Ni 0.2 alloy in the ferromagnetic state was saturated at 1 T.

C. Measurement of Seebeck coefficient and electrical resistivity
The T dependence of S was measured by the steady-state method. Here, we used a bar-shaped applying a charge current to the heater, the temperature gradient of which the direction is reversed around the center (almost uniform temperature gradient) was generated. In the experiments shown in Fig. 3, the heater output was used only for generating the temperature gradient. In contrast, in the experiments shown in Fig. 5, the heater output was transferred not only to the sample but also to the Al block. Thus, the heater power applied during the LIT measurements in Fig. 5 (P = 1.5 W) was much larger than that in Fig. 3 (P  60 mW). If the Thomson-effect-induced temperature modulation is normalized by the temperature gradient, not the heat power, the magnitudes of the signals in both the experiments are comparable. We note that the temperature and magnetic field dependences of the heater resistance are negligibly small. 6 To enhance the infrared emissivity and ensure uniform emission properties, the top surface of the sample was coated with insulating black ink with an emissivity of > 0.95.  (2). The solid curves connecting the data points in (c) and (d) were obtained using the Akima spline interpolation.