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Page 2 of 14 Kautsar et al. Energy Mater. 2025, 5, 500129 https://dx.doi.org/10.20517/energymater.2025.26

INTRODUCTION
Thermoelectric technology enables the conversion of heat into electricity, and vice versa, offering a
promising alternative to meet the growing demand for sustainable energy. Conventional thermoelectric
generators (TEGs) operate based on the Seebeck effect, a longitudinal thermoelectric phenomenon where
the induced electric field aligns parallel to the temperature gradient. As a result, optimizing thermoelectric
output in Seebeck-based TEGs necessitates multiple legs of p- and n-type semiconductors connected in
[1,2]
series, typically arranged in a Π-shaped configuration . However, constructing this Π-shaped
configuration involves numerous electrode junctions, leading to potential drawbacks such as a low fill
[6]
[3,4]
factor , high power loss , and reduced device durability .
[5]
An alternative approach is to develop TEGs based on the transverse thermoelectric effect, where the
induced electric field is perpendicular to the temperature gradient. This reduces the number of required
junctions, simplifying the TEG design and addressing the limitations of conventional longitudinal TEGs. An
important transverse thermoelectric effect for power generation is the Nernst effect. The Nernst effect
generates a charge current perpendicular to both the temperature gradient and either an applied magnetic
field (H) or the material’s magnetization (M), referring to as the ordinary Nernst effect (ONE) when driven
by H, or as the anomalous Nernst effect (ANE) when driven by the M of the material. A major limitation of
both ONE and ANE in many materials is the need to apply a continuous H [7-21] , which complicates their
application in TEGs. To achieve zero-field operation in transverse Nernst-based TEGs, it is essential to
achieve high thermoelectric conversion performance of ANE in magnetic materials with high coercivity
(H ) and remanent magnetization (M ), such as permanent magnets, and integrate them into TEG devices.
c
r
Another viable approach is to utilize ONE and ANE with other transverse thermoelectric effects, such as the
off-diagonal Seebeck/Peltier effect [22,23] .

Among the currently available permanent magnets, Nd-Fe-B and Sm-Co-based magnets exhibit high H c
and M at room temperature [24-26] . Miura et al. observed a significant positive anomalous Nernst coefficient
[27]
r
-1
-6
-7
-1
(S ) in the SmCo -based sintered magnets (+3.5 × 10 VK ) and negative S (-8.7 × 10 VK ) in the
ANE
5
ANE
Nd Fe B-based sintered magnets. By combining these two permanent magnets, Ando et al. developed a
[1]
14
2
transverse TEG device with a high fill factor that achieved an ANE-driven power generation (power
-2
density) of 177 μW (65 μWcm ) at a temperature difference of 75 K, using a 273 K heat sink, the
record-high value among transverse TEGs utilizing ANE. However, this value is still a few orders of
magnitude lower than that of conventional Seebeck-based TEGs. Therefore, enhancing the S value of the
ANE
permanent magnets is crucial and requires fundamental research that focuses not only on exploring new
materials but also on advancing our understanding of microstructural factors.
Many efforts to enhance S ANE in magnetic materials are aimed at optimizing the Berry curvature
contribution in electronic band structures [20,28,29] . In contrast, recently, Gautam et al. demonstrated a new
[30]
direction for improving S ANE from the viewpoint of microstructure engineering. The formation of
nonmagnetic copper nanoclusters in an amorphous ferromagnetic Fe-based matrix was shown to enhance
both electrical conductivity (σ ) and thermal conductivity (κ) of the alloys, with an optimal nanocluster size
xx
increasing the S value by 70%. This raises the question of how microstructure engineering, traditionally
ANE
employed to optimize coercivity and remanence in the permanent magnets [31-35] , influences their σ , κ, and
xx
S .
ANE