The Peltier effect, discovered in 1834, converts a charge current into a heat current in a conductor, and its performance is described by the Peltier coefficient, which is defined as the ratio of the generated heat current to the applied charge current1,2. To exploit the Peltier effect for thermoelectric cooling or heating, junctions of two conductors with different Peltier coefficients have been believed to be indispensable. Here we challenge this conventional wisdom by demonstrating Peltier cooling and heating in a single material without junctions. This is realized through an anisotropic magneto-Peltier effect in which the Peltier coefficient depends on the angle between the directions of a charge current and magnetization in a ferromagnet. By using active thermography techniques3,4,5,6,7,8,9,10, we observe the temperature change induced by this effect in a plain nickel slab. We find that the thermoelectric properties of the ferromagnet can be redesigned simply by changing the configurations of the charge current and magnetization, for instance, by shaping the ferromagnet so that the current must flow around a curve. Our experimental results demonstrate the suitability of nickel for the anisotropic magneto-Peltier effect and the importance of spin–orbit interaction in its mechanism. The anisotropic magneto-Peltier effect observed here is the missing thermoelectric phenomenon in ferromagnetic materials—the Onsager reciprocal of the anisotropic magneto-Seebeck effect previously observed in ferromagnets—and its simplicity might prove useful in developing thermal management technologies for electronic and spintronic devices.
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We thank K. Masuda, Y. Miura, T. Seki, S. Takahashi, K. Sato and G. E. W. Bauer for discussions, and the Materials Processing Group, Materials Manufacturing and Engineering Station, National Institute for Materials Science, for technical support in sample preparation. This work was supported by CREST “Creation of Innovative Core Technologies for Nano-enabled Thermal Management” (JPMJCR17I1), PRESTO “Phase Interfaces for Highly Efficient Energy Utilization” (JPMJPR12C1) and ERATO “Spin Quantum Rectification Project” (JPMJER1402) from JST, Japan; Grant-in-Aid for Scientific Research (A) (JP15H02012) and Grant-in-Aid for Scientific Research on Innovative Area “Nano Spin Conversion Science” (JP26103005) from JSPS KAKENHI, Japan; and the NEC Corporation. S.D. is supported by JSPS through a research fellowship for young scientists (JP16J02422).Reviewer information
Nature thanks S. Boona and A. Fert for their contribution to the peer review of this work.
Extended data figures and tables
a, b, Frequency dependence of Aeven and ϕeven on the areas CL/R of the U-shaped Ni slab at Jc = 1.00 A and |H| = 12.0 kOe. c, d, Aeven and ϕeven images for the U-shaped Ni slab at Jc = 1.00 A and |H| = 12.0 kOe for various values of f. The data points in a and b are respectively obtained by averaging the Aeven and ϕeven values over the areas defined by the squares with size 11 × 11 pixels in the leftmost images of c and d. The error bars represent the standard deviation of the data in the corresponding squares. In Figs. 2–4, to determine the positions of heat sources induced by the AMPE, the lock-in frequency was fixed at the maximum value, f = 25.0 Hz, because the temperature broadening due to thermal diffusion is reduced by increasing f. However, in general, the temperature distribution obtained from the LIT images at high f values is different from the steady-state distribution. To discuss the magnitude of the AMPE, it is important to observe the temperature modulation at nearly steady-state conditions. As shown in c and d, the AMPE signal around the corners CL/R of the U-shaped structure broadens with decreasing f owing to thermal diffusion. Although the magnitude of the AMPE signal at CL/R is Aeven = 2.2 mK at f = 25.0 Hz, it increases to Aeven = 3.9 mK at f = 2.0 Hz, which is closer to the value at the steady state. In Extended Data Fig. 3, these experimental results are compared with the results of numerical calculations to estimate the anisotropy of the Peltier coefficient for Ni quantitatively.
Extended Data Fig. 2 Charge current and magnetic field dependences of anomalous Ettingshausen effect.
a, b, Jc dependence of Aodd and ϕodd on the areas BL/R of the U-shaped Ni slab at |H| = 12.0 kOe (red circles and blue squares). The solid lines in a represent the linear fits to the data. c, d, Aodd and ϕodd images for the U-shaped Ni slab at |H| = 12.0 kOe for various values of Jc. e, f, |H| dependence of Aodd and ϕodd on BL/R at Jc = 1.00 A (red circles and blue squares) and the magnetization M curve of the Ni slab (black line). g, h, Aodd and ϕodd images at Jc = 1.00 A for various values of |H|. The data points in a and b (e and f) are respectively obtained by averaging the Aodd and ϕodd values on the areas defined by the rectangles with size 101 × 11 pixels in the leftmost images of c and d (g and h). The error bars represent the standard deviation of the data in the corresponding rectangles. In the experimental configuration shown in Fig. 2b in addition to the AMPE, the heat current is generated along the z direction due to the AEE in BL/R of the U-shaped Ni slab, where M (along the x direction) is perpendicular to Jc (along the y direction). The Aodd and ϕodd images shown here clearly reflect the symmetry of the AEE. The temperature modulation with the H-odd dependence appears only on BL/R and its sign is reversed between BL and BR, where the Jc direction in BL is opposite to that in BR. The magnitude of the temperature modulation with the H-odd dependence is proportional to the charge current and varies in response to the magnetization process of the Ni slab. Here, we observed not only the AEE but also the small H-linear contribution coming from the ordinary Ettingshausen effect, as shown in e (grey dotted line).
a, b, Calculated f dependence of A and ϕ on the areas CL/R of the U-shaped ferromagnetic metal model at θ = 0° (red and blue lines). The grey plots are the experimental results shown in Extended Data Fig. 1a, b. c, d, Calculated A and ϕ images for the U-shaped ferromagnetic metal model at θ = 0° for various values of f. The data points in a and b are respectively obtained by averaging the A and ϕ values over the areas defined by the squares in the leftmost images of c and d. e, f, Calculated A and ϕ images at f = 25.0 Hz for various values of θ. The calculated temperature distributions reproduce well the observed H-angle dependence of the LIT images shown in Fig. 4.
a, Temperature-difference ΔT dependence of the voltage ΔV between the ends of the straight Ni slab at |H| = 6.0 kOe (1.0 kOe), measured when H was applied in the direction perpendicular to (parallel to) the temperature gradient ∇T. In the ΔV data, the offset due to H-independent thermopower is subtracted. b, c, H dependence of ΔV in the straight Ni slab for various values of ΔT, measured for H⊥∇T (b) and H||∇T (c). The difference in the shape of the H–ΔV curves between the data in b and c is attributed to the shape magnetic anisotropy in the Ni slab. We confirmed that the magnitude of the AMSE signal in the H||∇T configuration is twice as large as that in the H⊥∇T configuration, in a similar manner to the AMR16.
a, Experimental configuration for measuring the AMPE induced by the local magnetic field H. The field was applied near the centre of the straight Ni slab. Π denotes the Peltier coefficient of non-magnetized Ni, that is, the θ-averaged Peltier coefficient. b, c, Aodd and ϕodd images for the straight Ni slab at Jc = 1.00 A and |H| = 6.0 kOe. d, e, Aeven and ϕeven images at Jc = 1.00 A and |H| = 6.0 kOe.
Extended Data Fig. 6 Anisotropic magneto-Peltier and Seebeck effects in various ferromagnetic metals.
a, b, Aeven and ϕeven images for the U-shaped Ni95Pt5, Ni95Pd5, Ni, Ni45Fe55 and Fe slabs at Jc = 1.00 A, |H| = 12.0 kOe, and f = 25.0 Hz. The Ni95Pt5 and Ni95Pd5 slabs were found to exhibit clear AMPE signals with greater magnitude than that in Ni. Although the Ni45Fe55 slab also exhibits the AMPE, its magnitude is smaller than that in Ni95Pt5, Ni95Pd5 and Ni. The Fe slab does not show clear AMPE signals; the patchy patterns in the Aeven and ϕeven images for Fe may arise because the magnetization of the U-shaped Fe slab is not saturated at |H| = 12.0 kOe, the maximum magnetic field available with our electromagnet (note that, in the AMPE measurements, H was applied along the hard axis due to the shape magnetic anisotropy). c, H dependence of ΔV/ΔT in the straight Ni95Pt5, Ni95Pd5, Ni, Ni45Fe55 and Fe slabs, measured when H||∇T. As is the case for the AMPE, the Ni95Pt5 and Ni95Pd5 slabs exhibit clear AMSE signals with greater magnitude than that in Ni. In these AMSE measurements, the magnetization of the ferromagnetic metal slabs easily aligns along the H direction because H was applied along the longest direction of the slabs.