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Page 4 of 14 Kautsar et al. Energy Mater. 2025, 5, 500129 https://dx.doi.org/10.20517/energymater.2025.26

offset to the slabs along the longitudinal direction of the sample’s long side, perpendicular to the magnet’s
c-axis. The first harmonic of the detected thermal images was extracted and subjected to Fourier analysis to
determine the lock-in amplitude (A) and phase (ϕ). Using this process, the pure contribution of
thermoelectric response, i.e., AEE and the Peltier effect, can be detected free from Joule heating. The A
image represents the magnitude of current-induced temperature modulation, while the ϕ image indicates
the sign of the temperature modulation and the time delay caused by thermal diffusion. To enhance the
infrared emissivity, the top surface of the samples was coated with insulating black ink of which the infrared
emissivity is > 0.94. The LIT measurements were conducted in the M state without applying H, where the
r
magnets were magnetized along the c-axis. The detected infrared radiation intensity is converted to
[44]
temperature values through the calibration process described in ref. . Since the AEE-induced temperature
modulation exhibits the H-odd dependence, the H-odd-dependent component of the lock-in amplitude
A and the phase ϕ were evaluated using A = |A(+M ) -A(-M ) |/2 and ϕ =
odd
r
odd
odd
r
odd
-arg[A(+M )e - A(-M )e ], where A(+M ) [ϕ(+M )] and A(-M ) [ϕ(-M ] show the A (ϕ) value
r
r
r
r
r
r
measured at the sample M of +M and -M , respectively. The M reversal process was performed by applying
r
r
a 3T H in the opposing direction to the sample slabs. D was measured using the laser flash method. κ was
t
then estimated by multiplying the D value with the specific heat capacity (c ) obtained from differential
t
p
scanning calorimetry (DSC, Rigaku Thermo Plus EV02) and the density determined using the Archimedes
method. The Hall measurement was performed to estimate the transverse electrical resistivity (ρ ) using a
yx
physical property measurement system (PPMS, Quantum Design, Inc.).
RESULTS AND DISCUSSION
Figure 1A presents the magnetization curves of the HP and HD samples, with the y-axis representing M and
the x-axis corresponding to H. The y-intercept of the graph corresponds to M , which represents the sample
r
M at zero H. The saturation magnetization (M ) of the samples was measured under the maximum H. The
s
HP sample displays a low remanence to saturation magnetization ratio (M /M ) of 0.63 and a slightly
s
r
rounded demagnetization curve in the second quadrant which is a typical feature for the isotropic
permanent magnets. In contrast, the HD sample shows an increase in the M /M ratio to 0.94, indicating a
r
s
large degree of texture in the studied magnet . Furthermore, the demagnetization curves become more
[49]
square-shaped, reflecting a substantial enhancement in the crystallographic texture of the Nd Fe B grains
2
14
after hot-deformation. Consequently, the µ M of the magnet improves significantly, increasing from 0.72 T
0
r
in the HP state to 1.30 T in the HD state.
Figure 1B presents the magnetization curves for the Dy-Nd-Cu, Nd-Cu, and Pr-Cu GBDP magnets, with
the HD magnet included for comparison. These magnets retain the anisotropic loop shape, though their M
is reduced due to the dilution of Nd Fe B phase after the diffusion process. µ M values for the Dy-Nd-Cu,
r
2
0
14
Nd-Cu, and Pr-Cu GBDP magnets are 1.01, 0.99, and 1.06 T, respectively. In contrast, their μ H increases
c
0
significantly, rising from 1.00 T in the initial HD magnet to 2.28 T, 1.62 T, and 1.85 T after the Dy-Nd-Cu,
Nd-Cu, and Pr-Cu diffusion process, respectively. The corresponding values of µ M , µ M , M /M , μ H and
0
0
s
s
r
0
c,
r
maximum energy product (BH) for each magnet are given in Supplementary Table 1 of the
max
supplementary information.
Supplementary Figure 1 presents the XRD patterns of the studied magnets. In the HP magnets, the (410),
(214), and (330) reflections dominate, indicating a random grain orientation. After HD, however, the (006),
(105), and (004) reflections become prominent, signifying strong c-axis crystallographic alignment [50,51] . This
high degree of alignment is preserved after GBDP, as evident in the XRD of Dy-Nd-Cu, Nd-Cu, and Pr-Cu
magnets and in agreement with M /M ratio data [Supplementary Table 1].
s
r