# Preparation of Fe-rich giant magnetocaloric (Mn,Fe)2(P,Si) ribbons and calorimetric analysis of the first-order magnetic transition

W. Hanggai, H. Yibole, F. Guillou, C. Kwakernaak, N.H. van Dijk, E. Brück

► To cite this version:

W. Hanggai, H. Yibole, F. Guillou, C. Kwakernaak, N.H. van Dijk, et al., Preparation of Fe-rich giant magnetocaloric (Mn,Fe)2(P,Si) ribbons and calorimetric analysis of the first-order magnetic transition. *Acta Materialia*, 2025, 302, pp.121677. 10.1016/j.actamat.2025.121677. hal-05508733

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Submitted on 13 Feb 2026

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Preparation of Fe-rich giant magnetocaloric $(Mn,Fe)_2(P,Si)$ ribbons and calorimetric analysis of the first-order magnetic transition

W. Hanggai¹*, H. Yibole², F. Guillou²,³, C. Kwakernaak⁴, N.H. van Dijk¹, E. Brück¹

¹ Fundamental Aspects of Materials and Energy (FAME), Faculty of Applied Sciences, Delft University of Technology, Mekelweg 15, 2629JB Delft, The Netherlands.

² College of Physics and Electronic Information, Inner Mongolia Key Laboratory for Physics and Chemistry of Functional Materials, Inner Mongolia Normal University, 81 Zhaowuda Rd., Hohhot 010022, China.

³Normandie University, ENSICAEN, UNICAEN, CNRS, CRISMAT, Caen 14000, France

⁴Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, the Netherlands

* Corresponding author: H.Gai@tudelft.nl

**Abstract:**

The $(Mn,Fe)_2(P,Si)$ compounds are one of the rare materials systems that exhibit an isostructural first-order ferromagnetic transition (FOMT) near ambient temperature. Since the discovery of its giant magnetocaloric effect (GMCE), this system is garnering ongoing interest, both for its promising performances for applications and for the scientific interest in uncovering the fundamental mechanisms driving the FOMT. This study examines the evolution of the structure, the microstructure, the thermal and magnetic properties in $Mn_{0.60+x}Fe_{1.3-x}P_{0.66-y}Si_{0.34+y}$ ($0 \le x \le 0.08$, $x = 2y$) compounds prepared by the melt-spun technique. The simultaneous increase in Mn and Si concentrations leads to a 40% enhancement in the isothermal entropy change ($|\Delta S_{max}|$) compared to parent compound. Furthermore, we propose a method to separate the latent heat ($L$) from the reversible specific heat. This allows us to establish a convincing correlation between two intrinsic quantities, the latent heat ($L$) and the elastic strain energy ($U_e$). Our results demonstrate that both latent heat ($L$) and thermal hysteresis ($\Delta T_{hys}$) are proportionally linked and vanish simultaneously at a critical end point.

**Keywords:** Magnetocaloric effect; magneto-elastic coupling; Phase transition; Heat capacity; Elastic strain energy; Latent heat.
# 1. Introduction

The magnetocaloric effect (MCE) is an intrinsic magneto-thermal phenomenon that links a sudden change in the magnetic field to a temperature change in a material, thereby enabling magnetic refrigeration technologies [1–10]. The MCE is characterized by the isothermal entropy change (ΔS) or the adiabatic temperature change (ΔT_ad), depending on whether the magnetic field change is applied isothermally or adiabatically. When the MCE for different materials is compared, it is important to note that a large |ΔS| does not always correspond to a large ΔT_ad, so both quantities must be optimized simultaneously [5,11]. Integrating this effect opens up novel possibilities for magnetic cooling [2,4,12,13], heat pumping [14–18], and energy conversion, such as thermomagnetic harvesting applications [19,20]. These applications present a higher energy efficiency and do not use greenhouse gases, and could therefore contribute to mitigate the climate change.

A giant magnetocaloric effect (GMCE) is typically associated with a first-order magnetic transition (FOMT). Depending on their intrinsic mechanisms, the FOMT can be classified into two types: the magneto-elastic transition that does not change the crystal symmetry, as observed in materials like La(Fe,Si)₃ [21–23], FeRh [24,25], Eu₂In [26] and (Mn,Fe)₂(P,Si) [4,6], and the magneto-structural transition, where the change in magnetic state is associated with a change in crystal symmetry, as found in compounds such as Gd₅ (Si,Ge)₄ [27], MnMX TiNiSi-Ni₂In [28,29] and NiMn-based Heusler alloys [30,31], etc. Among these different material systems, the Fe₂P-based compounds, particularly (Mn,Fe)₂(P,Si), stand out as one of the most promising for real application due to their low raw material costs, absence of rare earth elements, the absence of toxic elements and a tuneable Curie temperature near room temperature. These features make this system especially suitable for eco-sustainable applications.

Besides their advantages, the present systems with a GMCE at a FOMT often also have negative aspects such as thermal hysteresis (ΔT_hys), which impers the reversibility of the effect [7,32] and mechanical embrittlement. Previous studies on MnFe(P,Si) materials have shown that reducing the hysteresis can be achieved by adjusting the Mn/Fe and P/Si ratios. However, this adjustment typically leads to a decrease in magnetization. To enhance both the magnetization and ΔM, it is necessary to work near the MnFeP₂/₃Si₁/₃ composition, which represents a dual optimum for achieving a high saturation magnetization [33,34]. At the FOMT, not only a sharp magnetization jump is observed, but also discontinuities in other physical parameters are found [35]. For the (Mn,Fe)₂(P,Si) system at the ferromagnetic
transition temperature (T~C~), the unit-cell contracts in the hexagonal basal plane across the FOMT, while it expands along the hexagonal axis. This overall lattice deformation results in a discontinuity in c/a ratio reaching up to 10%, while the unit-cell volume change ΔV/V = 0.1-0.3% is nearly negligible. Such discontinuities can induce strong shear strains and stresses at the grain boundaries in random orientated polycrystals, particularly for larger grains. Thermal or magnetic field cycling potentially results in the formation of fractures or even the destruction of the bulk materials. These issues can be addressed by technical solutions, such as embedding the MCE material in a resin or using porous shaping techniques. However, these approaches will dilute the MCE effect, which is unwanted as it results in an inefficient use of the magnetic field source. In recent years, numerous studies have explored the introduction of a fifth element. This includes doping with 3d through 5d transition metals [32,36–40], which can potentially fine-tune the Curie temperature (T~C~) and reduce ΔT~hys~. Substitutions of P by As, Ge, Al and B have also been investigated as potential dopants [41–45]. However, from the perspectives of layering the transition temperatures along the regenerator or for scaling-up the synthesis, multiplying the number of elements with small quantities of substitutions raises some challenges.

Here, we tackle the above issue by compositional control and manipulating the microstructure to achieve smaller grain sizes. On the Fe-rich side of the (Mn,Fe)₂(P,Si) phase diagram, higher Si concentrations result in smaller discontinuities in Δa and Δc across the FOMT [6,46]. At the same time, metallurgical challenges have been widely reported in the Mn-Fe-P-Si system. Previous studies have predominantly employed ball-milling methods [32,34,36,45]. Samples prepared by this conventional approach often display significant porosity [64,66], which adversely affects thermal conductivity. Furthermore, this family of materials is highly sensitive to the purity of the starting elements, often leading to the formation of secondary phases such as (Mn,Fe)₃Si [66]. In contrast, melt spinning, which combines liquid-phase segregation with rapid solidification, enables the synthesis of fine-grained, single-phase materials [46]. The refinement of grains can mitigate shear strains and stresses at grain boundaries, thereby enhancing mechanical stability, which is particularly critical given the intrinsic brittleness of these compounds. Despite these advances, a systematic comparison of the microstructural features between conventionally processed and melt-spun samples remains unexplored. Therefore, in this work, we employ the melt-spinning technique to investigate both the microstructure and magnetic properties of Mnₐ₆₀+xFe₁.₃-xP₀.₆₆-ySi₀.₃₄+y compounds.
The Mn<sub>0.60+x</sub>Fe<sub>1.3-x</sub>P<sub>0.66-y</sub>Si<sub>0.34+y</sub> compounds presently studied show a strengthening of the FOMT characteristics (hysteresis, discontinuity, specific heat peak), which led us to investigate the evolution of the latent heat (L) along this series. While the latent heat is an intrinsic quantity highly relevant for the development of GMCMs, its separation from the reversible specific heat background is challenging. Temperature modulated DSC methods allow to separate a reversing, time independent, heat flow reflecting the specific heat background from an irreversible kinetic heat flow that may encompass the latent heat. But this technique generally yields a modest accuracy on the specific heat [47–51]. Thermopile calorimeters operated in AC or scanning mode have proved capable of separating specific heat from latent heat in giant magnetocaloric materials such as in CoMnSi compounds [52]. But this method requires homemade instruments and is limited to relatively small samples. We propose a method based on commercial calorimeter to separate latent heat from the total thermal response of the material in (Mn,Fe)<sub>2</sub>(P,Si) materials. This investigation led us to establish a correlation between L and another intrinsic quantity, U<sub>e</sub> the (magneto-) elastic energy.

Our detailed magnetic and thermal measurements carried out up to high magnetic
fields demonstrate that the present materials show a change in the nature of the phase
transition when the applied magnetic field causes the transition to reach a critical end point.
The reduction of both ΔT<sub>hys</sub> and L is gradual with applied magnetic field, and both vanish at
the critical end point.

**2. Materials and Experimental Methods**

Mn<sub>0.60+x</sub>Fe<sub>1.3-x</sub>P<sub>0.66-y</sub>Si<sub>0.34+y</sub> alloys (with x = 2y ranging from x = 0.00 until x = 0.08) were synthesized by ball milling from powders of high-purity starting materials of Mn (99.7%), Fe (99.8%), Fe<sub>2</sub>P (99.5 %), and Si (99.6%), using a ball-to-sample mass ratio of 5:1 and ball milling for 10 hours at 380 rpm. Subsequently, the resulting powders were compacted into cylinders of approximately 2.5 g each using an uniaxial press with a force of 8 tons. Then the pellets were melted and quenched by melt spinning with a copper-wheel speed of v ≈ 30 m/s. Melt spun ribbons with widths of 2-3 mm and a thickness of 20-40 µm were produced. Following this, the samples were sealed in quartz tubes filled with argon gas at a pressure of 200 mbar. Sintering of the samples took place in a vertical furnace, which had been preheated to 1100°C. This sintering process lasted for 2 hours before the samples were quenched in room temperature water. The choice of the sintering temperature of 1100°C was based on previous studies, which identified it as the optimal temperature for sintering [53,54].
Additionally, for comparative purposes, a ball-milled sample was annealed at the same temperature for 24 h to complement the analysis of differences observed before and after melt spinning.

Powder X-Ray Diffraction (XRD) was carried out on a PANalytical X-Pert PRO diffractometer, using Cu-Kα radiation with a wave length of 1.5405 Å (probing an angular range of 10°- 90°, with an angular step of 0.02°, 1s exposure per step). Temperature-dependent XRD measurements were performed with an Anton Paar TTK450 temperature chamber. The Rietveld method [55], as implemented in the FullProf software, was used for the crystal structure refinement [56].

Scanning electron microscopy (SEM, JEOL JSM-IT800SHL) and energy-disperse X-ray spectroscopy (EDS, Oxford Instruments Ultim Max 100 mm² with Aztec data-acquisition software) was used to characterize the microstructure and the composition. SEM measurements were performed on the free side of the ribbon samples and on eroded surfaces of compacted pellets, using a Nital etchant. For the grain size evaluation, about 15 SEM images per samples were analysed using the MIPAR software [57] for a quantitative estimate of the average grain size.

The temperature- and field-dependent magnetization was measured with a superconducting quantum interference device (Quantum Design MPMS XL) magnetometer, using the reciprocating sample option (RSO). Isofield magnetization curves were recorded as a function of the temperature in sweep mode at a rate of 1.0 K/min.

Heat capacity measurements were performed on a semi-adiabatic heat capacity option of a VersaLab system (Quantum Design) using the built-in "2τ" relaxation method supplemented by an external analysis referred to as Single Pulse Method (SPM) [58,59]. By leveraging the finite thermal hysteresis of the FOMT, we propose using the standard 2τ measurements and analyses performed consecutively at the same bath temperature to insulate the reversible specific heat. This approach assumes that repeatedly performing heat pulses of amplitude significantly smaller than the hysteresis will consume the latent heat in order to get access to the underlying reversible specific heat. It bares certain conceptual features with modulated DSC or amplitude modulated DSC techniques [60], as it allows separating a time- or history- independent specific heat. Contrary to DSC methods usually employing a continuous underlying thermal ramp, our method is based on discrete successive heat pulses. In practice, three consecutive heat pulses of 2 K amplitude (i.e. <ΔT<sub>hyster</sub> ≈ 3 K) were performed. The time evolution of the sample temperature and the influence of the latent heat are illustrated in Fig. S1 (Supplementary Information). During the 1st pulse, the *T(t)* branch
upon heating exhibit a “kink” marking out the heat absorbed as latent heat at $T_c^{heating}$. During the subsequent relaxation process, the sample temperature remains higher than $T_c^{cooling}$, so that the reverse transformation does not occur. The time profile of the next heat pulses performed at the same bath temperature is notably different from the first pulse, and reflects only a reversible specific heat. The latent heat peak is measured by SPM during an independent measurement based on a 7 K heat pulse. Fig. 1 illustrates the method by comparing the third $2\tau$ standard measurements with the SPM. The SPM yields a strong and symmetrical latent heat peak typical of a FOMT with a thermal hysteresis between heating and cooling branches of approximately 3.0 K. As illustrated in Fig. S2 in the supplementary information, using the standard $2\tau$ method, the first heat pulse will contain a partial latent

<figure><img src="image_2.png" /></figure>

heat contribution (only a partial latent heat contribution due to the thermal stabilisation prior to the pulse and because of the built-in specific heat analysis using both heating and cooling branches [58]). The subsequent pulses carried out at the same bath temperature will not contain latent heat and will thereby reflect the reversible specific heat background ($C_{rev}$). The latent heat contribution ($dL/dT$) can then be obtained by subtracting this $C_{rev}$ to the total $C_{rev}+dL/dT$ measured by SPM.

<caption>**Fig. 1.** Heat capacity of Mn<sub>0.66</sub>Fe<sub>1.24</sub>P<sub>0.63</sub>Si<sub>0.37</sub> at μ<sub>0</sub>H = 0, 3<sup>rd</sup> repetition (closed circles) of the standard "2τ" method) and SPM (closed squares). The shaded area marks the latent heat.</caption>

# 3. Results and discussion

## 3.1 Crystal structural information and average crystallite size
The X-ray diffraction patterns at 400 K shown in Fig. 2a confirm that the synthesized Mn<sub>0.60+x</sub>Fe<sub>1.3-x</sub>P<sub>0.66-y</sub>Si<sub>0.34+y</sub> (0≤x≤0.08, x = 2y) samples are single phase with the expected hexagonal P-62<em>m</em> symmetry. As shown in Fig. 2b and 2c, the lattice parameter *a* and the unit-cell volume *V* clearly increase with the increase in Mn and Si contents, whereas the lattice parameter *c* presents a less significant evolution; as a result, the *c/a* ratio decrease. The structural refinement parameters obtained from the XRD data are summarized in Table 1. The unit-cell volume expansion is in line with the expectation from Vegard's law and the respective metallic radii of the elements. The temperature evolution of the (300), (211) and (002) powder XRD reflections upon heating is illustrated in Fig. 2d for the Mn<sub>0.66</sub>Fe<sub>1.24</sub>P<sub>0.63</sub>Si<sub>0.37</sub> compound. The effect of temperature on the unit cell dimensions is presented in Fig. S3 (Supplementary Information). The FM and PM phases show a phase transition centred at *T*<sub>tr</sub> = 320 K with step-like anomalies of: Δ*a*/*a* = -0.98%, Δ*c*/*c* = 1.88%, Δ(*c/a*)/(*c/a*) = 2.81 %, Δ*V*/*V* = 2(Δ*a*/*a*) + Δ*c*/*c* ≈ -0.1%, as shown in Fig. S3 (Supplementary Information). The amplitude of the discontinuities in lattice parameters significantly increase with *x*, indicating a strengthening of the FOMT. Theoretical calculations have noted that the *c/a* ratio bears a significant correlation with the magnetic exchange interactions governing the magnetoelastic coupling in Fe<sub>2</sub>P-type materials [61,62]. The reduction in *c/a* with the increase in *x* is anticipated to result in increasing Curie temperatures.

When comparing the grain size of the hexagonal phase between samples with x = 0.60 and 0.68, no clear trend is observed for a simultaneous increase of Mn and Si contents. As shown in Fig. 3, both samples show a low porosity and a similar log-normal distribution of grain size with an average size of about 8 µm. For bulk (Mn,Fe)<sub>2</sub>(P,Si) prepared by ball-milling followed by solid state reaction, grain sizes are strongly influenced by the sintering temperature and the annealing time [63]. Considering a typical high-temperature sintering for 24-48 h, the grain size was found to range from about 27 µm in Mn-rich compositions [64] to 24-26 µm in compositions with a Mn/Fe = 1 ratio [65,66]. In contrast, a comparison of the microstructures of the melt-spun and ball-milled samples shows pronounced differences (see Fig. S4, Supplementary Information). The ball-milled sample exhibits a significant amount of porosity, with a SiO<sub>2</sub> impurity phase concentrated at the pores. However, EDS analysis indicates that the overall compositions of the main phase are nearly the same for the two different methods, as shown in Table S1 (Supplementary Information). The melt-spinning process therefore offers the advantage of eliminating oxide impurities. Furthermore, the melt-spun ribbons display a significantly smaller average grain size and a finer overall microstructure. This is critical for the stabilization of the mechanical properties, as the
reduction in grain size is anticipated to reduce the maximum shear strain at grain boundaries, thereby enhancing the mechanical stability of these materials. In the ribbon samples, thermal cycling induces microcrack initiation at grain boundaries, followed by subsequent propagation into the interior of the grains, as shown in Fig. S5 (Supplementary Information). Using these ribbon samples, we constructed a bulk sample and sintered it at 1100°C for 24 h. Encouragingly, as shown in Fig. S6 (Supplementary Information), the average grain size remained nearly constant at 8-10 µm, highlighting the potential of shaping bulk samples from ribbon materials.

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** (a) Powder XRD patterns collected at 400 K for samples of Mn<sub>0.60+x</sub>Fe<sub>1.3-x</sub>P<sub>0.66-y</sub>Si<sub>0.34+y</sub> (x = 2y), with simultaneous changes in the Mn/Fe and P/Si ratios. (b) Lattice parameter *a* and *c*, (c) Unit-cell volume *V* and *c/a* ratio derived from XRD as a function of the Mn concentration for Mn<sub>0.60+x</sub>Fe<sub>1.3-x</sub>P<sub>0.66-y</sub>Si<sub>0.34+y</sub> (x = 2y). (d) Intensity versus scattering angle 2Θ (°) as a function of temperature *T* (K) for the Mn<sub>0.66</sub>Fe<sub>1.24</sub>P<sub>0.63</sub>Si<sub>0.37</sub> compound.</figcaption></figure>

<caption>**Table 1.** Lattice parameters *a* and *c*, *c/a* ratio and unit-cell volume *V* obtained from XRD at 400 K, saturation magnetization *M*<sub>s</sub> and Curie temperature *T*<sub>c</sub> for the Mn<sub>0.60+x</sub>Fe<sub>1.3-x</sub>P<sub>0.66-y</sub>Si<sub>0.34+y</sub> (x = 2y) compounds. *M*<sub>s</sub> is obtained from magnetization measurements at 5 K and the transition temperature *T*<sub>c</sub> is defined as the minimum in *dM/dT* in an applied field of 0.01T.</caption>
<figure><img src="image_4.png" /><figcaption>**Fig. 3.** SEM images of (a) Mn<sub>0.60</sub>Fe<sub>1.30</sub>P<sub>0.66</sub>Si<sub>0.34</sub> and (b) Mn<sub>0.68</sub>Fe<sub>1.22</sub>P<sub>0.62</sub>Si<sub>0.38</sub> samples sintered at 1100 °C for 2 h. A colour code highlighting the equivalent diameter of each grain is superposed on the images.</figcaption></figure>

**3.2 Magnetic and magnetocaloric properties**

The temperature-dependent magnetization *M*(*T*), is shown in Fig. 4a for field-cooling (FC) and field-heating (FH) conditions. The same overall magnetic response with a relatively sharp ferromagnetic FOMT and a finite thermal hysteresis (Δ*T*<sub>hys</sub>) is found in all samples. The magnetization curves at 5 K, shown in Fig. 4b, start to saturate in an applied field of 1 T. The saturation magnetizations at 5 K and 5 T fall in the range 160-190 Am<sup>2</sup>kg<sup>-1</sup>. While in overall agreement with the literature for similar Fe<sub>2</sub>P-based compounds [39,67,68], these large saturation magnetization values primarily originate from the high phase purity of the ribbon samples. As expected, the saturation magnetizations tend to increase with the increase in Mn content. However, the evolution does not follow a perfectly linear evolution, which can be attributed to minor compositional variations. According to EDS results (see table S2), the effective compositions can present deviations with respect to the nominal ones; but the overall trend, an increase in effective Mn and Si contents with *x*, is observed. The transition temperature *T*<sub>C</sub> is estimated from the minimum in the temperature derivative of the magnetization (d*M*/dT), as shown in the inset of Fig. 4c. *T*<sub>C</sub> increases linearly with the simultaneous increase in Mn and Si concentrations, in line with the c/a trend. The parent compound Mn<sub>0.6</sub>Fe<sub>1.3</sub>P<sub>0.66</sub>Si<sub>0.34</sub> shows a thermal hysteresis Δ*T*<sub>hys</sub> of about 3 K. The value of Δ*T*<sub>hys</sub> progressively increases with *x*, yet it remains relatively limited, within 5 K for all compounds (recalling that thermal lags in sweeping conditions overestimate Δ*T*<sub>hys</sub>). The origin of the thermal hysteresis can be separated into intrinsic (associated with the mechanism of the transition at atomic scale [7]) and extrinsic contributions related to
microstructure; the presence of nano-precipitates [69], micro-cracks [70] or micro-pores [71],
strains and stresses at interfaces [7], etc. For instance, recent studies by Suye et al. [65] and
Zhang et al. [72] have reported that ΔT_hys tends to decrease with a reduction in particle size.
Here, the increase in ΔT_hys with x involves an intrinsic contribution from the strengthening of
the transition with x as indicated by the increased Δ(c/a) in Fig. S3 (Supplementary
Information) and by the increased latent heat in the next subsection. Furthermore, a
comparison of the magnetic properties of the melt-spun and ball-milled samples reveals clear
differences in magnetization, the sharpness of the phase transition, and thermal hysteresis
(see Fig. S7). The melt spun samples exhibit a higher saturation magnetization, a sharper
transition and a lower thermal hysteresis than ball milled samples. These differences can be
attributed to the elimination of the SiO₂ phase and microstructural voids, the refinement of
the grain size, and the potentially more efficient annealing for ribbon with a limited thickness.
These findings suggest that the grain refinement in melt-spun ribbons was beneficial to
extrinsically reduce the ΔT_hys, which in turn is advantageous for MCE applications.

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** (a) Magnetization as a function of temperature in an applied field of 1 T and (b) magnetization as a function of magnetic field at 5 K of Mn<sub>0.60+x</sub>Fe<sub>1.3-x</sub>P<sub>0.66-y</sub>Si<sub>0.34+y</sub> (x = 2y). (c) Values of T<sub>tr</sub><sup>Heating</sup> and T<sub>tr</sub><sup>cooling</sup> as a</figcaption></figure>
function of the Mn content (inset shows $dM/dT$ curves and thermal hysteresis $\Delta T_{hys}$ as a function of the Mn content at an applied field of 0.01T). (d) Isothermal entropy change $-\Delta S$ from the temperature-dependent magnetization $M(T)$ upon heating for a magnetic field change of 2 T for Mn$_{0.60+x}$Fe$_{1.3-x}$P$_{0.66-y}$Si$_{0.34+y}$ ($x = 2y$).

The magnetocaloric performance expressed as the isothermal entropy change $\Delta S$ is shown in Fig. 4d. The isothermal entropy change is calculated by applying the Maxwell relation $\Delta S(T)_{\Delta H} = \int_{H_i}^{H_f} \mu_0 \left(\frac{\partial M(T,H)}{\partial T}\right)_H dH$ [27,73] to the isofield $M(T)$ data. All samples show high $|\Delta S|$ values typical for the GMCE observed at the FOMT in Mn$_{0.60+x}$Fe$_{1.3-x}$P$_{0.66-y}$Si$_{0.34+y}$ compounds. The parent compound Mn$_{0.6}$Fe$_{1.3}$P$_{0.66}$Si$_{0.34}$ exhibits $|\Delta S_{max}| = 12 \text{ J kg}^{-1} \text{ K}^{-1}$ for an applied field change of 2 T. The simultaneous increase of Mn and Si concentration increased $|\Delta S_{max}|$ by 40%. Furthermore, the heating-cooling averaging $\Delta S$ method offers an estimate of the reversible $\Delta S_{rev}$, as shown in the inset of Fig. 4d, confirming the possibility to use these large $\Delta S$ in applications. The present results demonstrate the achievement of a well-balanced combination of a small hysteresis and a large $|\Delta S_{max}|$ in the Fe-rich Mn-Fe-P-Si without doping with other elements.

<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Field exponent of the isothermal entropy change $n = \frac{d \ln(|\Delta S|)}{d \ln(H)}$ for the Mn$_{0.60+x}$Fe$_{1.3-x}$P$_{0.66-y}$Si$_{0.34+y}$ ($x = 2y$) compounds.</figcaption></figure>

To qualitatively evaluate the order of the magnetic phase transition in Mn$_{0.60+x}$Fe$_{1.3-x}$P$_{0.66-y}$Si$_{0.34+y}$ compounds the field exponent of the entropy change is examined. As proposed by Franco and coworkers [74,75] and Van Dijk [76] the field-dependence of the isothermal entropy change follows a power law of the form $|\Delta S| \propto H^n$. The field exponent $n$ can be employed to determine the FOMT or SOMT nature of the magnetic phase transition. For a FOMT the field exponent has a minimum value of $n = 0$ and a divergent maximum value ($n \to \infty$) near the transition [76]. This behavior is due to the step change in entropy ($S$) associated with the FOMT. In experimental studies, a maximum value of the field exponent $n$
above 2 is taken as indication of a FOMT. Fig. 5 shows the field exponent *n* of the isothermal
entropy change (Δ*S*) for the Mn<sub>0.60+x</sub>Fe<sub>1.3-x</sub>P<sub>0.66-y</sub>Si<sub>0.34+y</sub> compounds. The field exponent *n* is
consistently above 2 near *T*<sub>C</sub> for all compounds. This is in line with the observation of finite
Δ*T*<sub>hys</sub> and latent heat peaks. Note that the minimum value of *n* remains above zero near the
transition due to the persistence of short-range ferromagnetic fluctuations above *T*<sub>C</sub>.

**3.3 Indirect measurements of the giant magnetocaloric effect from specific heat**

To evaluate the MCE performance, both the isothermal entropy change (ΔS) and the adiabatic
temperature change (ΔT_ad) need to be considered. In field specific-heat measurements allow
to indirectly evaluate these two quantities. A S-T diagram relative to the starting temperature
T₀ can be built, with S(T,B)-S(T₀,B) = ∫<sub>T₀</sub><sup>T_f</sup> <sup>C<sub>total</sub></sup>&frasl;<sub>T</sub> dT for which C<sub>total</sub> contains both the
reversible C_rev and the latent heat contribution. As illustrated in Fig.6, subtraction between
entropy lines at constant entropy or temperature yields ΔT_ad and ΔS, respectively. The
measurements were carried out for all compositions. Fig. 6 illustrates the case of
Mn<sub>0.66</sub>Fe<sub>0.24</sub>P<sub>0.63</sub>Si<sub>0.37</sub>, which is detailed hereafter. An intense specific heat peak with a
maximum value of 3.12 Jg<sup>-1</sup>K<sup>-1</sup> is found at 320 K. The maximum value of C<sub>total</sub> decreases
continuously with increasing applied magnetic field. The shift of T_tr with the applied
magnetic field corresponds to dT_tr/μ₀dH ≈ 3.9 K T<sup>-1</sup>, as listed in Table 2. Calorimetric
measurements lead to a |ΔS_max| = 16.66 J kg<sup>-1</sup> K<sup>-1</sup> at a field change of 2 T well in line with that
measured from magnetization data |ΔS_max| = 17.61 J kg<sup>-1</sup> K<sup>-1</sup> at a field change of 2 T. This
agreement confirms that the ΔS data from magnetization measurements were not affected by
spike artifacts. Furthermore, a large ΔT_ad of 5.4 K was observed at 2 T. Even tough
determinations of ΔT_ad for (Mn,Fe)<sub>2</sub>(P,Si) compounds are scarcer than ΔS [66], the present
performances turn out on par or larger than the best performances observed so far. The
simultaneously achieved high values of both |ΔS_max| and ΔT_ad underscore the potential of
(Mn,Fe)<sub>2</sub>(P,Si) ribbons for heat pump applications, particularly given the ability to fine tune
the transition temperature above room temperature.
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Thermal and magnetocaloric properties of Mn<sub>0.66</sub>Fe<sub>1.24</sub>P<sub>0.63</sub>Si<sub>0.37</sub>. (a) In-field heat capacity measurements upon heating. (b) Total entropy versus temperature (S-T diagram) in a magnetic field of 0, 1, 2 and 3 T. (c) Isothermal entropy change. (d) Adiabatic temperature change from calorimetry measurements.</figcaption></figure>

**3.4 Correlation of pure latent heat with elastic strain energy**

The heat capacity is a basic physical quantity reflecting all degrees of freedom and usually is decomposed into magnetic, structural and electronic terms $C_p^{tot} = C_p^{el} + C_p^{ph} + C_p^m$. Each of these terms could be individually estimated outside the FOMT [65], but such a decomposition could not legitimately be carried out at the magneto-elastic transition. Here, one does not seek to separate magnetic, lattice and electronic terms, but rather to quantify the peak-shaped latent heat ($T \approx L_{max}G(T)$), where $G(T)$ is a normalised Gaussian distribution centred at $T_C$. Experimentally, this requires a subtraction of the reversible heat capacity ($C_{rev}$) background from the total specific heat. While this is commonly done by considering a linear extrapolation in the transition region, here we used the method presented in the method section to determine $C_{rev}$.
Fig. 7 illustrates the evolution for different magnetic fields of the latent heat
contribution to the Mn<sub>0.66</sub>Fe<sub>1.24</sub>P<sub>0.63</sub>Si<sub>0.37</sub> compound. The latent heat progressively decreases
with the increase in magnetic field. A linear extrapolation indicates that it would vanish at a
critical field of about 6.4 T. The full width at half maximum (FWHM) of the latent heat peak
was derived from a Gaussian fit. FWHM progressively increases with the applied magnetic
field, indicating a broadening of the transition at higher fields. Complementary magnetization
measurements were carried out as a function of temperature and field near the FOMT and a
magnetic phase diagram was constructed. The thermal hysteresis ΔT<sub>hys</sub> estimated from M(T)
curves decreases as the first-order nature of the transition is gradually suppressed by the
applied magnetic field, with a linear extrapolation indicating that ΔT<sub>hys</sub> vanishes at 6.4 T, as
show in panel 7c of Fig. 7. In the M(H) curves, the field induced transition reveals that the
magnetic hysteresis is gradually reduced as temperature increases, with the derivative
dM/dμ<sub>0</sub>H suggesting that hysteresis vanishes beyond 6.6 T, as show in Fig. S8c-d
(Supplementary Information). Both magnetization and the calorimetric data identify a critical
field in the range of 6.4-6.6 T. Beyond this critical field, L and ΔT<sub>hys</sub> are no longer observable
within the experimental resolution. Fig. 7d depicts both L and ΔT<sub>hys</sub> at different fields. The
apparent correlation suggests that these two parameters are linked.

**Table 2.** FOMT parameters as a function of the Mn concentration, showing changes in the lattice parameters *Δa* and *Δc* at *T*<sub>C</sub> obtained from XRD measurements. The elastic strain energy was calculated from the step changes in lattice parameters observed in XRD *vs* *T* at *μ*<sub>0</sub>*H* = 0. The isothermal entropy change (at 1 and 2 T), adiabatic temperature change, the field dependence of the transition temperature (*dT*<sub>tr</sub>/μ<sub>0</sub>*dH*), latent heat (*L*) upon heating by integration of *dL/dT* data at *μ*<sub>0</sub>*H* = 0 and thermal hysteresis were derived from calorimetry measurements.
<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Thermal and magnetocaloric properties of the Mn<sub>0.66</sub>Fe<sub>1.24</sub>P<sub>0.63</sub>Si<sub>0.37</sub> compound (a) dL/dT peak from substruction of the latent heat (L) (insert shows an value of L at different magnetic field). (b) Full width at half maximum (FWHM) of the dL/dT peak for recorded in different applied field. (c) Thermal hysteresis (ΔT<sub>hys</sub>) versus magnetic fields, derived from magnetization measurements, with ±1K/min of heating and cooling curves recorded at different applied field. (d) Proportional relation between latent heat (L) and thermal hysteresis (ΔT<sub>hys</sub>) in the presence of an applied field, as derived from calorimetric and magnetization measurements.</figcaption></figure>

The latent heat determination was carried out at different applied fields for all compounds, as shown in Fig. 8. The five compositions follow the same trend, indicating that the latent heat *L* decreases as the applied field increases. Regarding the zero-field latent heat, the simultaneous increase in Mn and Si (with *x* = 2*y*) results in an increase in *L* from 2.02 J g⁻¹ to 5.79 J g⁻¹. This result is consistent with the observed increase in Δ*T*<sub>hys</sub> and the trends for the discontinuity of the lattice parameters for increasing Mn and Si concentrations. In former studies [6, 32, 67, 90, 91], attempts were made to establish a relation between various factors involved in the FOMT of Fe<sub>2</sub>P-based compounds. Miao *et al.* [32] proposed the existence of a relation between Δ*T*<sub>hys</sub> and *U*<sub>e</sub> for a large range of Fe<sub>2</sub>P-based compounds. However, Δ*T*<sub>hys</sub> can hardly be regarded as an intrinsic quantity for the FOMT. A recent report demonstrated a
correlation between entropy change at the transition ($\Delta S_{tr}$) and the lattice deformation (c/a ratio) [79]. As these two are intrinsic physical quantities, they provide a more reliable basis for scaling. This prompted us to investigate a possible relation between the latent heat and the elastic strain energy (magneto-elastic coupling). The transition-induced elastic strain energy can be expressed as: $U_e = (C_{11} + C_{12})e_1^2 + 2C_{13}e_1e_3 + C_{33}e_3^2/2$ where $e_{ij}$ represent the tensile strains and $C_{ij}$ correspond to the elastic constants [32,77]. For an hexagonal lattice: $e_1 = e_2 = \Delta a/a$ within the a-b plane and $e_3 = \Delta c/c$ along the c axis. For the evaluation of the elastic strain energy we applied the elastic constants from DFT calculations reported by Roy *et al.* [80] and the experimental elastic strain values for $\Delta a/a$ and $\Delta c/c$ at $T_C$, as shown in Fig. S3 (Supplementary Information).

A striking proportional relation is observed between $L$ and $U_e$, with data points aligning along the diagonal, as shown in Fig. 8b. The scaling between intrinsic quantities of $L$ and $U_e$ suggests that these quantities are directly related. This correlation indicates that nearly all the latent heat originates from the elastic deformation. For comparison, we reconstructed the elastic strain energy (30.89 kJ kg⁻¹) from previous studies using DFT calculations [81] and found that it is of a similar order of magnitude to the calculated latent heat (19.97 kJ kg⁻¹) for MnFeSi<sub>0.33</sub>P<sub>0.66</sub> compounds, which is line with our present results. To strengthen the statistical robustness of our analysis, we incorporated experimental results from previous studies on the Fe<sub>2</sub>P-compounds [32,35,82–84]. The latent heat values from previous studies are generally higher than the diagonal in Fig. 8. This difference may be caused by the subtraction of the reversible specific heat in the present study. Using a linear background will underestimate the reversible specific heat near the transition and therefore overestimate the latent heat. Nevertheless, the slope remains consistent, supporting our proposition that a correlation exists between $L$ and $U_e$. Further experiments are needed to refine these results, in particular to extend the investigations to other (Mn,Fe)<sub>2</sub>(P,X) series with $X = As, Ge$ and $B$ while using the present methodology. The present scaling strategy may also be considered for other magnetoelastic FOMT materials, such as La(Fe,Si)<sub>13</sub> [21–23], FeRh [24,25], and Eu<sub>2</sub>In [26], where elastic-strain energy similarly impact the first-order magnetic phase transition.
<figure><img src="image_9.png" /><figcaption>**Fig. 8.** (a) Latent heat (L) versus applied magnetic field of the Mn<sub>0.60+x</sub>Fe<sub>1.3-x</sub>P<sub>0.66-y</sub>Si<sub>0.34+y</sub> (x = 2y) compounds. (b) Proportional relation between latent heat (L) and elastic strain energy (U<sub>e</sub>) of the FOMT in the Mn<sub>0.60+x</sub>Fe<sub>1.3-x</sub>P<sub>0.66-y</sub>Si<sub>0.34+y</sub> (x = 2y) compounds.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 9.** Latent heat (L) of the FOMT as a function of elastic strain energy (U<sub>e</sub>) for the Fe<sub>2</sub>P-based system, with the current data compared to reference data from earlier generations of (Mn,Fe)<sub>2</sub>(P,Si) compounds, lines are used as guides for the eyes.</figcaption></figure>
## 4. Conclusions

Fe-rich $(Mn,Fe)_2(P,Si)$ ribbons achieve minimal thermal hysteresis, a significant isothermal entropy change and a significant adiabatic temperature change, without the introduction of additional doping elements, making them promising giant magnetocaloric materials. Melt spinning can be used to tailor the microstructure of $(Mn,Fe)_2(P,Si)$ alloys. We also demonstrate the possibility to shape high-performance bulk samples from ribbon precursors. A comparison between melt-spun ribbons and samples prepared by ball-milling indicates significant differences in magnetization and on the sharpness of the phase transition. Additionally, grain refinement in melt-spun ribbons contributes to an extrinsic reduction of $\Delta T_{hys}$. By performing two types of calorimetry measurements to separate the latent heat from reversible heat capacity and quantifying the elastic transformation strain energy by XRD, we establish a direct correlation between the latent heat ($L$) and the elastic transformation strain energy ($U_e$) in the $(Mn,Fe)_2(P,Si)$ family. The application of an external magnetic field is found to gradually weaken the first-order character of the transition, with both $L$ and $\Delta T_{hys}$ decreasing and disappearing simultaneously at a critical end point. Generally, achieving a GMCE requires a sizable latent heat, which is inherently accompanied by significant lattice deformations that can introduce undesirable effects, such as thermal hysteresis and mechanical embrittlement. By tailoring the microstructure, melt-spinning offers an approach to break the circle.

## Acknowledgements

The authors thank Anton Lefering, Bert Zwart, Sebastian Couweleers, and Robert Dankelman for their technical assistance. This work is financially supported by the Dutch Research Council NWO TTW with Project no. 17877 and RSP Technology. H. Yibole and F. Guillou acknowledge the support from the National Natural Science Foundation of China (grant n° 12464015 and 52461036).
References

[1] O. Tegus, E. Brück, K.H.J. Buschow, F.R. De Boer, Transition-metal-based magnetic refrigerants for room temperature applications, Nature 415 (2002) 150–152. https://doi.org/10.1038/415150a.

[2] E. Brück, O. Tegus, D.T.C. Thanh, K.H.J. Buschow, Magnetocaloric refrigeration near room temperature (invited), J. Magn. Magn. Mater. 310 (2007) 2793–2799. https://doi.org/10.1016/j.jmmm.2006.10.1146.

[3] J.D. Moore, K. Morrison, K.G. Sandeman, M. Katter, L.F. Cohen, Reducing extrinsic hysteresis in first-order La(Fe,Co,Si)₁₃ magnetocaloric systems, Appl. Phys. Lett. 95 (2009) 252504. https://doi.org/10.1063/1.3276565.

[4] N.H. Dung, Z.Q. Ou, L. Caron, L. Zhang, D.T.C. Thanh, G.A. De Wijs, R.A. De Groot, K.H.J. Buschow, E. Brück, Mixed magnetism for refrigeration and energy conversion, Adv. Energy Mater. 1 (2011) 1215–1219. https://doi.org/10.1002/aenm.201100252.

[5] F. Guillou, G. Porcari, H. Yibole, N. van Dijk, E. Brück, Taming the first-order transition in giant magnetocaloric materials, Adv. Mater. 26 (2014) 2671–2675, https://doi.org/10.1002/adma.201304788.

[6] N.H. Dung, L. Zhang, Z.Q. Ou, E. Brück, Magnetoelastic coupling and magnetocaloric effect in hexagonal Mn-Fe-P-Si compounds, Scr. Mater. 67 (2012) 975–978. https://doi.org/10.1016/j.scriptamat.2012.08.036.

[7] O. Gutfleisch, T. Gottschall, M. Fries, D. Benke, I. Radulov, K.P. Skokov, H. Wende, M. Gruner, M. Acet, P. Entel, M. Farle, Mastering hysteresis in magnetocaloric materials, Phil. Trans. R. Soc. A. 374 (2016) 20150308. https://doi.org/10.1098/rsta.2015.0308.

[8] T. Gottschall, K.P. Skokov, M. Fries, A. Taubel, I. Radulov, F. Scheibel, D. Benke, S. Riegg, O. Gutfleisch, Making a Cool Choice: The materials library of magnetic refrigeration, Adv. Energy Mater. 9 (2019) 1901322. https://doi.org/10.1002/aenm.201901322.

[9] V. Franco, J.S. Blázquez, J.J. Ipus, J.Y. Law, L.M. Moreno-Ramírez, A. Conde, Magnetocaloric effect: From materials research to refrigeration devices, Prog. Mater. Sci. 93 (2018) 112–232. https://doi.org/10.1016/j.pmatsci.2017.10.005.

[10] V. Zverev, A.M. Tishin, Magnetocaloric Effect: From Theory to Practice, in: Reference Module in Materials Science and Materials Engineering, Elsevier, 2016: p. B9780128035818028137. https://doi.org/10.1016/B978-0-12-803581-8.02813-7.

[11] K.P. Skokov, A.Yu. Karpenkov, D.Yu. Karpenkov, O. Gutfleisch, The maximal cooling power of magnetic and thermoelectric refrigerators with La(FeCoSi)₁₃ alloys, Journal of Applied Physics 113 (2013) 17A945. https://doi.org/10.1063/1.4801424.

[12] M.F.J. Boeije, P. Roy, F. Guillou, H. Yibole, X.F. Miao, L. Caron, D. Banerjee, N.H. Van Dijk, R.A. De Groot, E. Brück, Efficient room-temperature cooling with magnets, Chem. Mater. 28 (2016) 4901–4905. https://doi.org/10.1021/acs.chemmater.6b00518.

[13] J. Lyubina, Magnetocaloric materials for energy efficient cooling, J. Phys. D: Appl. Phys. 50 (2017) 053002. https://doi.org/10.1088/1361-6463/50/5/053002.

[14] A. Kitanovski, Energy Applications of Magnetocaloric Materials, Adv. Energy Materials 10 (2020) 1903741. https://doi.org/10.1002/aenm.201903741.

[15] C. Zimm, A. Boeder, B. Mueller, K. Rule, S.L. Russek, The evolution of magnetocaloric heat-pump devices, MRS Bull. 43 (2018) 274–279. https://doi.org/10.1557/mrs.2018.71.

[16] E. Brück, H. Yibole, V.T. Nguyen, X.F. Miao, M. Boeije, N. Van Dijk, Transition Metal Based Magneto Caloric Materials for Energy Efficient Heat Pumps, SSP 257 (2016) 129–134. https://doi.org/10.4028/www.scientific.net/SSP.257.129.

[17] E. Brück, H. Yibole, L. Zhang, A universal metric for ferroic energy materials, Phil.Trans.R.Soc.A374: 20150303. http://dx.doi.org/10.1098/rsta.2015.0303.

[18] D.J. Silva, J.S. Amaral, V.S. Amaral, Cooling by sweeping: A new operation method to achieve ferroic refrigeration without fluids or thermally switchable components, INT. J. REFRIG. 101 (2019) 98–105. https://doi.org/10.1016/j.ijrefrig.2019.02.029.
[19] R.A. Kishore, S. Priya, A review on design and performance of thermomagnetic devices, Renew. Sustain. Energy Rev. 81 (2018) 33-44. https://doi.org/10.1016/j.rser.2017.07.035.

[20] A. Waske, D. Dzekan, K. Sellschopp, D. Berger, A. Stork, K. Nielsch, S. Fähler, Energy harvesting near room temperature using a thermomagnetic generator with a pretzel-like magnetic flux topology, Nat Energy 4 (2018) 68-74. https://doi.org/10.1038/s41560-018-0306-x.

[21] F. Hu, B. Shen, J. Sun, Z. Cheng, G. Rao, X. Zhang, Influence of negative lattice expansion and metamagnetic transition on magnetic entropy change in the compound LaFe<sub>11.4</sub>Si<sub>1.6</sub>, Appl. Phys. Lett. 78 (2001) 3675-3677. https://doi.org/10.1063/1.1375836.

[22] F.X. Hu, L. Chen, J. Wang, L.F. Bao, J.R. Sun, B.G. Shen, Particle size dependent hysteresis loss in La<sub>0.7</sub>Ce<sub>0.3</sub>Fe<sub>11.6</sub>Si<sub>1.4</sub>C<sub>0.2</sub> first-order systems, Appl. Phys. Lett. 100 (2012) 072403. https://doi.org/10.1063/1.3684244.

[23] E. Lovell, A.M. Pereira, A.D. Caplin, J. Lyubina, L. F. Cohen, Dynamics of the first-order metamagnetic transition in magnetocaloric La(Fe,Si)<sub>13</sub>: reducing hysteresis, Adv. Energy Mater. 5 (2015) 1401639. https://doi.org/10.1002/aenm.201401639.

[24] G. Li, R. Medapalli, J.H. Mentink, R.V. Mikhaylovskiy, T.G.H. Blank, S.K.K. Patel, A.K. Zvezdin, Th. Rasing, E.E. Fullerton, A.V. Kimel, Ultrafast kinetics of the antiferromagnetic-ferromagnetic phase transition in FeRh, Nat Commun 13 (2022) 2998. https://doi.org/10.1038/s41467-022-30591-2.

[25] A. Aubert, K. Skokov, G. Gomez, A. Chirkova, I. Radulov, F. Wilhelm, A. Rogalev, H. Wende, O. Gutfleisch, K. Ollefs, Simultaneous Multi-Property Probing During Magneto-Structural Phase Transitions: An Element-Specific and Macroscopic Hysteresis Characterization at ID12 of the ESRF, IEEE Trans. Instrum. Meas. 71 (2022) 1-9. https://doi.org/10.1109/TIM.2022.3157001.

[26] F. Guillou, A.K. Pathak, D. Paudyal, Y. Mudryk, F. Wilhelm, A. Rogalev, V.K. Pecharsky, Non-hysteretic first-order phase transition with large latent heat and giant low-field magnetocaloric effect, Nat Commun. 9 (2018) 2925. https://doi.org/10.1038/s41467-018-05268-4.

[27] V.K. Pecharsky, K.A. Gschneidner, Jr., Giant Magnetocaloric Effect in Gd<sub>5</sub>(Si<sub>2</sub>Ge<sub>2</sub>), Phys. Rev. Lett. 78 (1997) 4494-4497. https://doi.org/10.1103/PhysRevLett.78.4494.

[28] T. Krenke, E. Duman, M. Acet, E.F. Wassermann, X. Moya, L. Mañosa, A. Planes, Inverse magnetocaloric effect in ferromagnetic Ni-Mn-Sn alloys, Nat Mater. 4 (2005) 450-454. https://doi.org/10.1038/nmat1395.

[29] W. Hanggai, O. Tegus, H. Yibole, F. Guillou, Structural and magnetic phase diagrams of MnFe<sub>0.6</sub>Ni<sub>0.4</sub>(Si,Ge) alloys and their giant magnetocaloric effect probed by heat capacity measurements, J. Magn. Magn. Mater. 494 (2020) 165785. https://doi.org/10.1016/j.jmmm.2019.165785.

[30] E. Liu, W. Wang, L. Feng, W. Zhu, G. Li, J. Chen, H. Zhang, G. Wu, C. Jiang, H. Xu, F. De Boer, Stable magnetostructural coupling with tunable magnetoresistive effects in hexagonal ferromagnets, Nat Commun. 3 (2012) 873. https://doi.org/10.1038/ncomms1868.

[31] K. Mandal, D. Pal, N. Scheerbaum, J. Lyubina, O. Gutfleisch, Magnetocaloric effect in Ni-Mn-Ga alloys, IEEE Trans. Magn. 44 (2008) 2993-2996. https://doi.org/10.1109/TMAG.2008.2002481.

[32] X. Miao, Y. Gong, F. Zhang, Y. You, L. Caron, F. Qian, W. Guo, Y. Zhang, Y. Gong, F. Xu, N. Van Dijk, E. Brück, Enhanced reversibility of the magnetoelastic transition in (Mn,Fe)<sub>2</sub>(P,Si) alloys via minimizing the transition-induced elastic strain energy, J. Mater. Sci. Technol. 103 (2022) 165-176. https://doi.org/10.1016/j.jmst.2021.05.087.

[33] Z.Q. Ou, L. Zhang, N.H. Dung, L. Van Eijck, A.M. Mulders, M. Avdeev, N.H. Van Dijk, E. Brück, Neutron diffraction study on the magnetic structure of Fe<sub>2</sub>P-based Mn<sub>0.66</sub>Fe<sub>1.29</sub>P<sub>1-x</sub>Si<sub>x</sub> melt-spun ribbons, Journal of Magnetism and Magnetic Materials 340 (2013) 80-85. https://doi.org/10.1016/j.jmmm.2013.03.028.

[34] N.H. Dung, L. Zhang, Z.Q. Ou, L. Zhao, L. Van Eijck, A.M. Mulders, M. Avdeev, E. Suard, N.H. Van Dijk, E. Brück, High/low-moment phase transition in hexagonal Mn-Fe-P-Si compounds, Phys. Rev. B 86 (2012) 045134. https://doi.org/10.1103/PhysRevB.86.045134.

[35] F. Guillou, H. Yibole, N.H. Van Dijk, L. Zhang, V. Hardy, E. Brück, About the mechanical stability of MnFe(P,Si,B) giant-magnetocaloric materials, J. Alloys Compd. 617 (2014) 569-574. https://doi.org/10.1016/j.jallcom.2014.08.061.
[36] Z.Q. Ou, N.H. Dung, L. Zhang, L. Caron, E. Torun, N.H. Van Dijk, O. Tegus, E. Brück, Transition metal substitution in Fe<sub>2</sub>P-based MnFe<sub>0.95</sub>P<sub>0.50</sub>Si<sub>0.50</sub> magnetocaloric compounds, J. Alloys Compd. 730 (2018) 392–398. https://doi.org/10.1016/j.jallcom.2017.09.315.

[37] J. Lai, B. Huang, X. Miao, N. Van Thang, X. You, M. Maschek, L. Van Eijck, D. Zeng, N. Van Dijk, E. Brück, Combined effect of annealing temperature and vanadium substitution for mangetocaloric Mn<sub>1.2-x</sub>V<sub>x</sub>Fe<sub>0.75</sub>P<sub>0.5</sub>Si<sub>0.5</sub> alloys, J. Alloys Compd. 803 (2019) 671–677. https://doi.org/10.1016/j.jallcom.2019.06.239.

[38] S. Hu, X. Miao, J. Liu, Z. Ou, M. Cong, O. Haschuluu, Y. Gong, F. Qian, Y. You, Y. Zhang, F. Xu, E. Brück, Small hysteresis and giant magnetocaloric effect in Nb-substituted (Mn,Fe)<sub>2</sub>(P,Si) alloys, Intermetallics 114 (2019) 106602. https://doi.org/10.1016/j.intermet.2019.106602.

[39] F. Zhang, I. Batashev, N. Van Dijk, E. Brück, Effect of off-stoichiometry and Ta doping on Fe-rich (Mn,Fe)<sub>2</sub>(P,Si) based giant magnetocaloric materials, Scr. Mater. 226 (2023) 115253. https://doi.org/10.1016/j.scriptamat.2022.115253.

[40] F. Zhang, P. Feng, A. Kiecana, Z. Wu, Z. Bai, W. Li, H. Chen, W. Yin, X. Yan, F. Ma, N.H. Van Dijk, E. Brück, Yang Ren, Achieving tunable high-performance giant magnetocaloric effect in hexagonal Mn-Fe-P-Si materials through different D-block doping, Adv. Funct. Mater. 2024, 2409270. https://doi.org/10.1002/adfm.202409270.

[41] D.M. Liu, H. Zhang, S.B. Wang, W.Q. Xiao, Z.L. Zhang, N. Tian, C.X. Liu, M. Yue, Q.Z. Huang, J.X. Zhang, J.W. Lynn, The effect of Al doping on the crystal structure and magnetocaloric behavior of Mn<sub>1.2</sub>Fe<sub>0.8</sub>P<sub>1-x</sub>Ge<sub>x</sub> compounds, J. Alloys Compd. 633 (2015) 120–126. https://doi.org/10.1016/j.jallcom.2015.01.141.

[42] D.T. Cam Thanh, E. Brück, O. Tegus, J.C.P. Klaasse, K.H.J. Buschow, Influence of Si and Ge on the magnetic phase transition and magnetocaloric properties of MnFe(P,Si,Ge), J. Magn. Magn. Mater. 310 (2007) e1012–e1014. https://doi.org/10.1016/j.jmmm.2006.11.194.

[43] P. Wlodarczyk, L. Hawelek, M. Kowalczyk, M. Kaminska, P. Zackiewicz, M. Polak, M. Hreczka, A. Kolano-Burian, Impact of silicon doping on the magnetocaloric effect of MnFeP<sub>0.35</sub>As<sub>0.65</sub> powder, Solid State Sci. 56 (2016) 23–28. https://doi.org/10.1016/j.solidstatesciences.2016.04.003.

[44] S. Kim, H. Shin, I. Chu, K. Lee, K.H. Lee, W. Lee, Tunable Curie temperature in Mn<sub>1.15</sub>Fe<sub>0.85</sub>P<sub>0.55</sub>Si<sub>0.45</sub> via lattice engineering by Al addition, J. Alloys Compd. 890 (2022) 161798. https://doi.org/10.1016/j.jallcom.2021.161798.

[45] H. Yibole, F. Guillou, L. Zhang, N.H. Van Dijk, E. Brück, Direct measurement of the magnetocaloric effect in MnFe(P,X) (X=As,Ge,Si) materials, J. Phys. D: Appl. Phys. 47 (2014) 075002. https://doi.org/10.1088/0022-3727/47/7/075002.

[46] Z.Q. Ou, L. Zhang, N.H. Dung, L. Caron, E. Brück, Structure, magnetism and magnetocalorics of Fe-rich (Mn,Fe)<sub>1.95</sub>P<sub>1-x</sub>Si<sub>x</sub> melt-spun ribbons, J. Alloys Compd. 710 (2017) 446–451. https://doi.org/10.1016/j.jallcom.2017.03.266.

[47] B. Wunderlich, A. Boller, I. Okazaki, K. Ishikiriyama, Heat-capacity determination by temperature-modulated DSC and its separation from transition effects, Thermochimica Acta 304–305 (1997) 125–136. https://doi.org/10.1016/S0040-6031(97)00184-6.

[48] J.E.K. Schawe, T. Hütter, C. Heitz, I. Alig, D. Lellinger, Stochastic temperature modulation: A new technique in temperature-modulated DSC, Thermochimica Acta 446 (2006) 147–155. https://doi.org/10.1016/j.tca.2006.01.031.

[49] P. Claudy, J.M. Vignon, Temperature Modulated DSC Theoretical Explanation interpretation, J. Therm. Anal. Calorim. 60 (2000) 333–343. https://doi.org/10.1023/A:1010148200201.

[50] S.L. Simon, Temperature-modulated differential scanning calorimetry: theory and application, Thermochimica Acta 374 (2001) 55–71. https://doi.org/10.1016/S0040-6031(01)00493-2.

[51] R.L. Danley, New modulated DSC measurement technique, Thermochimica Acta 402 (2003) 91–98. https://doi.org/10.1016/S0040-6031(02)00541-5.

[52] Y. Miyoshi, K. Morrison, J.D. Moore, A.D. Caplin, L.F. Cohen, Heat capacity and latent heat measurements of CoMnSi using a microcalorimeter, Review of Scientific Instruments 79 (2008) 074901. https://doi.org/10.1063/1.2960556.
[53] N.V. Thang, H. Yibole, N.H. Van Dijk, E. Brück, Effect of heat treatment conditions on MnFe(P,Si,B) compounds for room-temperature magnetic refrigeration, J. Alloys Compd. 699 (2017) 633-637.
https://doi.org/10.1016/j.jallcom.2016.12.402.

[54] F. Guillou, Sun-Liting, O. Haschuluu, Z.Q. Ou, E. Brück, O. Tegus, H. Yibole, Room temperature magnetic anisotropy in Fe₂P-type transition metal based alloys, J. Alloys Compd. 800 (2019) 403-411.
https://doi.org/10.1016/j.jallcom.2019.05.327.

[55] H.M. Rietveld, The Rietveld method, Phys. Scr. 89 (2014) 098002. https://doi.org/10.1088/0031-8949/89/9/098002.

[56] J. Rodríguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction, Physica B: Condensed Matter 192 (1993) 55-69. https://doi.org/10.1016/0921-4526(93)90108-I.

[57] J.M. Sosa, D.E. Huber, B. Welk, H.L. Fraser, Development and application of MIPAR™: a novel software package for two- and three-dimensional microstructural characterization, Integr. Mater. Manuf. Innov. 3 (2014) 123-140. https://doi.org/10.1186/2193-9772-3-10.

[58] V. Hardy, Y. Bréard, C. Martin, Derivation of the heat capacity anomaly at a first-order transition by using a semi-adiabatic relaxation technique, J. Phys.: Condens. Matter 21 (2009) 075403.
https://doi.org/10.1088/0953-8984/21/7/075403.

[59] F. Guillou, R. Hamane, H. Yibole, J.Y. Xu, B. Narsu, V. Hardy, Heat capacity of a MnFe(P,Si,B) compound with first-order magnetic transition, J. Magn. Magn. Mater. 541 (2022) 168513.
https://doi.org/10.1016/j.jmmm.2021.168513.

[60] F.J. Romero, M.C. Gallardo, J.-M. Martín-Olalla, J. Del Cerro, Experimental method to determine specific heat capacity and transition enthalpy at a first-order phase transition: Fundamentals and application to a Ni-Mn-In Heusler alloy, Thermochimica Acta 706 (2021) 179053.
https://doi.org/10.1016/j.tca.2021.179053.

[61] E.K. Delczeg-Czirjak, Z. Gercsi, L. Bergqvist, O. Eriksson, L. Szunyogh, P. Nordblad, B. Johansson, L. Vitos, Magnetic exchange interactions in B-, Si-, and As-doped Fe₂P from first-principles theory, Phys. Rev. B 85 (2012) 224435. https://doi.org/10.1103/PhysRevB.85.224435.

[62] Z. Gercsi, E.K. Delczeg-Czirjak, L. Vitos, A.S. Wills, A. Daoud-Aladine, K.G. Sandeman, Magnetoelastic effects in doped Fe₂P, Phys. Rev. B 88 (2013) 024417. https://doi.org/10.1103/PhysRevB.88.024417.

[63] T. Qianbai, H. Yibole, F. Guillou, Structure, Microstructure and Magnetocaloric/Thermomagnetic Properties at the Early Sintering of MnFe(P,Si,B) Compounds, Metals 14 (2024) 385.
https://doi.org/10.3390/met14040385.

[64] M. Fries, L. Pfeuffer, E. Bruder, T. Gottschall, S. Ener, L.V.B. Diop, T. Gröb, K.P. Skokov, O. Gutfleisch, Microstructural and magnetic properties of Mn-Fe-P-Si (Fe₂P-type) magnetocaloric compounds, Acta Materialia 132 (2017) 222-229. https://doi.org/10.1016/j.actamat.2017.04.040.

[65] B. Suye, H. Yibole, W. Meijuan, B. Wurentuya, F. Guillou, Influence of the particle size on a MnFe(P,Si,B) compound with giant magnetocaloric effect, AIP Advances 13 (2023) 025203.
https://doi.org/10.1063/9.0000371.

[66] B. Suye, H. Yibole, Z.Q. Song, B. Tana, W. Wei, O. Haschuluu, O. Tegus, F. Guillou, Influence of cold compaction pressure on intergranular secondary phase distribution and magnetocaloric/thermomagnetic performances of MnFe(P,Si,B) compounds, J. Alloys Compd. 976 (2024) 172918.
https://doi.org/10.1016/j.jallcom.2023.172918.

[67] A. Kiecana, I. Batashev, A.I. Dugulan, C. Kwakernaak, L. Pieter, F. Zhang, N.H. Van Dijk, E. Brück, Effect of Co and Ni doping on the structure, magnetic and magnetocaloric properties of Fe-rich (Mn,Fe)₂(P,Si) compounds, J. Magn. Magn. Mater. 561 (2022) 169710.
https://doi.org/10.1016/j.jmmm.2022.169710.

[68] A. Kiecana, C. Kwakernaak, N.H. Van Dijk, E. Brück, Effect of the heat treatment on the microstructure, magnetism and magnetocaloric effect in Fe-rich (Mn,Fe) (P,Si) melt-spun ribbons, J. Alloys Compd. 932 (2023) 167635. https://doi.org/10.1016/j.jallcom.2022.167635.

[69] R. Niemann, S. Hahn, A. Diestel, A. Backen, L. Schultz, K. Nielsch, M.F.-X. Wagner, S. Fähler, Reducing the nucleation barrier in magnetocaloric Heusler alloys by nanoindentation, APL Materials 4 (2016) 064101. https://doi.org/10.1063/1.4943289.
[70] A. Waske, L. Giebeler, B. Weise, A. Funk, M. Hinterstein, M. Herklotz, K. Skokov, S. Fähler, O. Gutfleisch, J. Eckert, Asymmetric first-order transition and interlocked particle state in magnetocaloric La(Fe,Si)₁₃, Phys. Status Solidi RRL 9, No. 2, (2015) 136–140. https://doi.org/10.1002/pssr.201409484.

[71] J. Lyubina, R. Schäfer, N. Martin, L. Schultz, O. Gutfleisch, Novel Design of La(Fe,Si)₁₃ Alloys Towards High Magnetic Refrigeration Performance, Advanced Materials 22 (2010) 3735–3739. https://doi.org/10.1002/adma.201000177.

[72] F. Zhang, C. Taake, B. Huang, X. You, H. Ojiyed, Q. Shen, I. Dugulan, L. Caron, N.H. van Dijk, E. Brück, Magnetocaloric effect in the (Mn,Fe)₂(P,Si) system: From bulk to nano, Acta Mater. 224 (2022) 117532. https://doi.org/10.1016/j.actamat.2021.117532.

[73] K.A. GschneidnerJr, V.K. Pecharsky, A.O. Tsokol, Recent developments in magnetocaloric materials, Rep. Prog. Phys. 68 (2005) 1479–1539. https://doi.org/10.1088/0034-4885/68/6/R04.

[74] V. Franco, J.S. Blázquez, A. Conde, Field dependence of the magnetocaloric effect in materials with a second order phase transition: A master curve for the magnetic entropy change, Appl. Phys. Lett. 89 (2006) 222512. https://doi.org/10.1063/1.2399361.

[75] J.Y. Law, V. Franco, L.M. Moreno-Ramírez, A. Conde, D.Y. Karpenkov, I. Radulov, K.P. Skokov, O. Gutfleisch, A quantitative criterion for determining the order of magnetic phase transitions using the magnetocaloric effect, Nat Commun 9 (2018) 2680. https://doi.org/10.1038/s41467-018-05111-w.

[76] N.H. Van Dijk, Landau model evaluation of the magnetic entropy change in magnetocaloric materials, J. Magn. Magn. Mater. 529 (2021) 167871. https://doi.org/10.1016/j.jmmm.2021.167871.

[77] M. Maschek, X. You, M.F.J. Boeije, D. Chernyshov, N.H. Van Dijk, E. Brück, Charge redistribution and the magnetoelastic transition across the first-order magnetic transition in (Mn,Fe)₂(P,Si,B), Phys. Rev. B 98 (2018) 224413. https://doi.org/10.1103/PhysRevB.98.224413.

[78] X. You, M. Maschek, N.H.H. Van Dijk, E. Brück, Magnetic Phase Diagram of the MnₓFe₂₋ₓP₁₋ᵧSiᵧ System, Entropy 24 (2021) 2. https://doi.org/10.3390/e24010002.

[79] F. Guillou, H. Yibole, B. Narsu, V. Hardy, Correlation between deformation and total entropy change at the first-order magnetic transition of Fe₂P-based magnetocaloric materials, Results Phys. 44 (2023) 106203. https://doi.org/10.1016/j.rinp.2022.106203.

[80] P. Roy, E. Torun, R.A. De Groot, Effect of doping and elastic properties in (Mn,Fe)₂(Si,P), Phys. Rev. B 93 (2016) 094110. https://doi.org/10.1103/PhysRevB.93.094110.

[81] P. Roy, E. Brück, R.A. De Groot, Latent heat of the first-order magnetic transition of MnFeSi₀.₃₃P₀.₆₆, Phys. Rev. B 93 (2016) 165101. https://doi.org/10.1103/PhysRevB.93.165101.

[82] F. Guillou, H. Yibole, N.H. Van Dijk, E. Brück, Effect of boron substitution on the ferromagnetic transition of MnFe₀.₉₅P₂/₃Si₁/₃, J. Alloys Compd. 632 (2015) 717–722. https://doi.org/10.1016/j.jallcom.2015.01.308.

[83] M. Yue, D. Liu, Q. Huang, T. Wang, F. Hu, J. Li, G. Rao, B. Shen, J.W. Lynn, J. Zhang, Structure evolution and entropy change of temperature and magnetic field induced magneto-structural transition in Mn₁.₁Fe₀.₉P₀.₇₆Ge₀.₂₄, J. Appl. Phys. 113 (2013) 043925. https://doi.org/10.1063/1.4788803.

[84] F. Zhang, I. Batashev, Q. Shen, Z. Wu, R.I. Smith, G.A. De Wijs, N. Van Dijk, E. Brück, Impact of F and S doping on (Mn,Fe)₂(P,Si) giant magnetocaloric materials, Acta Mater. 234 (2022) 118057. https://doi.org/10.1016/j.actamat.2022.118057.