# Ultra-low hysteresis in giant magnetocaloric Mn1-V Fe0.95(P,Si,B) compounds

Jiawei Lai, Xinmin You, Jiayan Law, Victorino Franco, Bowei Huang, Dimitrios Bessas, Michael Maschek, Dechang Zeng, Niels van Dijk, Ekkes Brück

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► To cite this version:

Jiawei Lai, Xinmin You, Jiayan Law, Victorino Franco, Bowei Huang, et al. Ultra-low hysteresis in giant magnetocaloric Mn1-V Fe0.95(P,Si,B) compounds. Journal of Alloys and Compounds, 2023, 930, pp.167336. 10.1016/j.jallcom.2022.167336. hal-05087946

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# Ultra-low hysteresis in giant magnetocaloric Mn₁₋ₓVₓFe₀.₉₅(P,Si,B) compounds

<figure><img src="image_3.png" /></figure>

Jiawei Lai a,b, Xinmin You b, Jiayan Law c, Victorino Franco c, Bowei Huang a,b, Dimitrios Bessas d, Michael Maschek b, Dechang Zeng a,*, Niels van Dijk b, Ekkes Brück b,†

## ARTICLE INFO

**Article history:**

Received 24 January 2022

Received in revised form 21 September 2022

Accepted 22 September 2022

Available online 30 September 2022

**Keywords:**

(Mn, V, Fe)1.95(P, Si, B)

Giant magnetocaloric effect

Magnetic properties

Entropy

Low hysteresis

## ABSTRACT

Large thermal hysteresis in the (Mn,Fe)₂(P,Si) system hinders an efficient heat exchange and thus limits the magnetocaloric applications. Substitution of manganese by vanadium in the Mn₁₋₁Vₓ₁Fe₀.₉₅P₀.₅₉₃Si₀.₃₃B₀.₀₇₇ and Mn₁₋₂Vₓ₂Fe₀.₉₅P₀.₅₆₃Si₀.₃₆B₀.₀₇₇ compounds enable a significant reduction in the thermal hysteresis without losing the giant magnetocaloric effect. For the composition closest to the critical one, where first-order crossovers to second-order phase transition in the series of x₂ = 0.02, Mn₀.₉₈V₀.₀₂Fe₀.₉₅P₀.₅₆₃Si₀.₃₆B₀.₀₇₇ exhibits a thermal hysteresis that is reduced from 1.5 to 0.5 K by 67%, yielding an adiabatic temperature change of 2.3 K and magnetic entropy change of 5.6 J/kgK for an applied field of 1 T, which demonstrates its potential for highly efficient magnetic heat pumps utilizing low-cost permanent magnets.

© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

## 1. Introduction

Room temperature magnetic heat pumps attract broad attention due to their advantages compared to the traditional heat pumps, such as a high efficiency and a low impact on the environment [1,2]. Materials with a giant magnetocaloric effect (GMCE), which are the working materials of this technique, will release heat when an external magnetic field is applied, while they absorb heat when the magnetic field is removed. The performance of GMCE materials mainly determines the working efficiency and the cooling power of this technology. The GMCE usually occurs in materials that show a first-order magnetic transition (FOMT), such as Gd₅Ge₂Si₂, [3] LaFe₁₃₋ₓSiₓ, [4-7] MnFeP₁₋ₓAsₓ, [8] MnFeP₁₋ₓ-ySiₓBᵧ, [9-11] MnCoGe (Cu, B)ₓ [12,13] and Heusler [14] compounds. Among them, the MnFeP₁₋ₓ-ySiₓBᵧ compounds are regarded as one of the most promising materials that can be industrialized because of their cheap and non-toxic elements, high cooling capacity and tunable T_c near room temperature [9].

MnFeP₁₋ₓSiₓ compounds with a strong FOMT show a significant change in lattice parameters across the magnetic phase transition

while keeping its hexagonal structure, which is a magneto-elastic transition [15]. However, a strong FOMT is often accompanied by large hysteresis, including both magnetic field hysteresis and thermal hysteresis (ΔT_hys), which will reduce field-induced temperature change. Hysteresis limits the practical application of these materials since it will largely reduce the working efficiency [16]. For some first-order materials that undergo a first-order magnetostructural transition, for instance Heusler alloys, the thermal hysteresis and magnetic field hysteresis may show a very different behavior. The magneto-structural transition is suppressed in field and thus a low hysteresis at low applied field and a lager hysteresis at high applied field could occur [17]. However, the presently studied (Mn,Fe)₂(P,Si) based alloys undergo a magneto-elastic transition without a structural transition. In magneto-elastic transitions the thermal hysteresis and the magnetic field hysteresis are generally closely coupled, as reported previously [18]. We therefore consider that the low thermal hysteresis ΔT_hys is representative for a low magnetic field hysteresis, and thereby provides important information for the thermodynamic properties for magnetic heat pumps and magnetic refrigerators.

Theoretically, for a thermal hysteresis ΔT_hys of 2 K, the efficiency can be 60% of the Carnot efficiency and it can reach 75% of the Carnot efficiency if a value of 0.5 K is achieved [16]. Therefore, in the premise of keeping the GMCE, the thermal hysteresis should be made as narrow as possible by tailoring the microstructure or by tuning the

<footnote>a School of Materials Science & Engineering, South China University of Technology, Guangzhou 510640, China</footnote>

<footnote>b Fundamental Aspects of Materials and Energy, Department of Radiation Science and Technology, TU Delft, Mekelweg 15, 2629JB Delft, the Netherlands</footnote>

<footnote>c Dpto. Física de la Materia Condensada ICMSE-CSIC, Universidad de Sevilla, Apdo1065, 41080 Sevilla, Spain</footnote>

<footnote>d European Synchrotron Radiation Facility, F-38043 Grenoble, France</footnote>

<footnote>* Corresponding authors.
E-mail addresses: medczeng@scut.edu.cn (D. Zeng), E.H.Bruck@tudelft.nl (E. Brück).</footnote>
chemical composition. Recently, through 0.075 at% of B substitution in the MnFe<sub>0.95</sub>P<sub>0.595</sub>Si<sub>0.33</sub>B<sub>0.075</sub> compounds, ΔT<sub>hys</sub> can be optimized to 1.6 K according to the temperature-dependent magnetization curves and to 2.0 K according to in-field DSC measurements, both at magnetic field of 1 T (see the supporting information of reference [11]). This compound is generally regarded as one of the benchmarks for the Fe<sub>2</sub>P-type compounds. It can be cycled for 10 thousand times and the sample geometry remains intact. A higher level of B substitution can further decrease ΔT<sub>hys</sub> but fails to provide a sufficiently large GMCE [17]. It is essential to find a new approach to further decrease ΔT<sub>hys</sub> and simultaneously provide a sufficiently high GMCE, as characterized by the isothermal magnetic entropy change (ΔS<sub>M</sub>) and the adiabatic temperature change (ΔT<sub>ad</sub>). To evaluate the size of ΔS<sub>M</sub>, Gd with a value of ΔS<sub>M</sub> is 3 J/kgK under 1 T is generally used as a standard to compare with [18]. Another design criterion is that ΔT<sub>ad</sub> should be larger than 2.0 K [19], since Engelbrecht and Bahl [20] demonstrated that cooling (and heating) is ineffective when ΔT<sub>ad</sub> drops below 2.0 K.

On the other hand, the magnetic field currently used in the
prototypes of heat pumps are generated by NdFeB permanent
magnets, which varies from 0.9 to 1.9 T [21–24]. The overall cost to
reach a field of 1.9 T can be 10 times higher than the cost to reach a
field of 0.9 T. It is therefore of interest to explore the lower magnetic
field potential of the magnetic heat pump system. dT_c/dB is defined
as the shift of T_c induced by an applied magnetic field. As the
magnitude of dT_c/dB is regarded as the driving force of the magneto-
elastic transition [25], if enhanced, the magnetic phase transition
can be induced in lower magnetic fields. It is positive for conven-
tional first-order magnetic transition materials, such as MnFeP<sub>1-x</sub>
<sub>y</sub>Si<sub>x</sub>By [11] and La-Fe-Si [26], while it is negative for the inverse first-
order magnetic transition materials, for instance the Ni-Mn-X--
Heusler compounds with X = Sn, Sb and In [27] or Fe-Rh [28]. For the
conventional first-order magnetic transition materials, this shift is
attributed to the magnetic field stabilization of the phase with the
higher magnetization, being the low-temperature ferromagnetic
phase [13,29]. In an external magnetic field, extra thermal energy is
then needed to induce the magnetic phase transition. Thus, T_c shifts
to higher temperature. One of our motivations of this work is to
increase the driving force (i.e. dT_c/dB) of FOMT and make it feasible
to be utilized in devices with low-cost permanent magnets.

In previous reports we have shown an enhanced GMCE in the low
magnetic field range by introducing V substitution to Mn-Fe-P-Si
compounds [30,31]. From the motivation of minimizing ΔT<sub>hys</sub> and
achieving a large GMCE under a magnetic field of 1.0 T, the combined
effect of B and V additions to the Mn-Fe-P-Si compounds is in-
vestigated in this study. The effect of V substitution on the thermal
hysteresis ΔT<sub>hys</sub>, the lattice parameters, the magnetic properties and
dT<sub>c</sub>/dB in polycrystalline Mn-V-Fe-P-Si-B compounds are system-
atically investigated. Through optimization of the composition and V
substitution, an ultra-low ΔT<sub>hys</sub> of 0.5 K and a large GMCE with |ΔS<sub>M</sub>|
= 6.2 J/kgK and ΔT<sub>ad</sub> = 2.5 K at an internal magnetic field of 1 T is
achieved simultaneously.

## 2. Experimental

Polycrystalline Mn<sub>1-x1</sub>V<sub>1</sub>Fe<sub>0.95</sub>P<sub>0.593</sub>Si<sub>0.33</sub>B<sub>0.077</sub> (x<sub>1</sub> = 0.00, 0.02, 0.03) compounds were prepared by a powder metallurgy method. The vanadium substitution started from 0.02 since it was reported to be optimal to tune the hysteresis and entropy change in low magnetic fields [30]. The starting materials in the form of Mn, Fe, red P, Si and V powders were mechanically ball milled for 10 h in an Ar atmosphere with a constant rotation speed of 380 rpm, then pressed into small pellets, and finally sealed in quartz ampoules under 200 mbar of Ar before employing the various heat treatment conditions. The pellets were annealed at 1323 K for 2 h to promote crystallization and cooled to room temperature in the furnace. Then they

were heated up to the same annealing temperature for 20 h to
homogenize the compound and finally quenched in water. This batch
samples were labeled as series A. In this series, the composition of
sample with x₁ = 0.00 is designed to be the same as to the previous
benchmark material MnFe₀.₉₅P₀.₅₉₅Si₀.₃₃B₀.₀₇₅ [11]. In order to en-
hance the |ΔSₘ|, an optimal composition series of Mn₁-
x₂Vₓ₂Fe₀.₉₅P₀.₅₆₃Si₀.₃₆B₀.₀₇₇ (x₂ = 0.00, 0.02, 0.03) compounds with a
higher Si content was prepared with the same procedure as series A
at a higher annealing temperature of 1373 K. This batch samples are
labeled as series B.

X-ray diffraction (XRD) patterns were collected on a PANalytical X-pert Pro diffractometer with Cu-Kα radiation (1.54056 Å) at room temperature. The temperature dependence and magnetic field dependence of the magnetization were measured with a commercial superconducting quantum interference device (SQUID) magnetometer (Quantum Design MPMS 5XL) in the reciprocating sample option (RSO) mode. The adiabatic temperature change (ΔT<sub>ad</sub>) was measured in a Peltier cell based differential scanning calorimeter (DSC) using a Halbach cylinder providing a magnetic field of up to 1.5 T. In this setup, the iso-field calorimetric scans were performed at a rate of 3 K min<sup>-1</sup>, while the temperature had been corrected for the effect of the thermal resistance of the Peltier cells.

3. Results and discussion

Fig. 1(a) shows the room temperature XRD patterns and the re-
fined results for the Mn<sub>1-x2</sub>V<sub>2</sub>Fe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> (x<sub>2</sub> = 0.02)
compound. The main phase is identified as the hexagonal Fe<sub>2</sub>P-type
phase (2:1) with a space group of P-62 <i>m</i> and the impurity phase is
the cubic MnFe<sub>2</sub>Si-type phase (3:1) with a space group of Fm<sub>3</sub>m,
which agrees with the previously reported data [1]. A high weight
fraction of 96.3 wt% is obtained for the main phase, suggesting that
the annealing condition and composition are suitable to achieve a
high purity of Fe<sub>2</sub>P-type phase. Based on the refinement results, the
weight fraction of the impurity phase is 1.8 ± 0.1, 2.4 ± 0.1 and
2.0 ± 0.1 wt% for x<sub>1</sub> = 0.00, 0.02 and 0.03 and is 4.5 ± 0.1, 3.8 ± 0.1
and 4.3 ± 0.1 wt% for x<sub>2</sub> = 0.00, 0.02 and 0.03, respectively. Thus, the
variation in the amount of impurity phase by V substitution is
negligible within the same series.

In Fig. 1(b), the results of the Fullprof refinement [32] for the
lattice parameters of the *series A* compounds are shown. An increase
in V substitution leads to a decrease in *a* axis and an increase in *c*
axis. The lattice constant *a* decreases from 6.0459 to 6.0339 Å and *c*
increases from 3.3966 to 3.4076 Å when *x*₁ increases from 0 to 0.03.
In Fig. 1(c) and 1(d), the lattice parameters, *c/a* ratio and *T*<sub>C</sub> are
shown for the *series B* compounds. The lattice constant *a* decreases
from 6.0508 to 6.0422 Å and *c* increases from 3.3998 to 3.4063 Å
when *x*₂ is increased from 0 to 0.03, see the Fig. 1(c). The increase in
the *c/a* ratio leads to a decrease in *T*<sub>C</sub>, as shown in Fig. 1(d). The
correlation between the *c/a* ratio and *T*<sub>C</sub> originates from the distinct
mixed magnetism of the Fe<sub>2</sub>P type compounds [33]. The Fe atoms
prefer to occupy the plane and Mn atoms prefer to occupy the 3*g*
plane with P and Si randomly distributed in the hexagonal lattice.
When transforming from the paramagnetic to the ferromagnetic
state, the lattice constant *a* increases and causes a stronger locali-
zation for the 3*d* electrons of Fe (3*f*) instead of chemical bonding
with non-metallic P and Si. Jointly with the lattice constant *c*,
decreases the interlayer distance between the Mn and Fe atoms
and thereby enhances the magnetic exchange interaction between
two magnetic atoms [34]. Therefore, adding V to Mn<sub>1-
x₂Vₓ₂Fe₀.₉₅P₀.₅₉₃Si₀.₃₃B₀.₀₇₇ compounds will increase the *c/a* ratio and
leads to a reduction in the magnetic exchange interaction. Similar
trend is observed for the Mn<sub>1-x1</sub>V<sub>1</sub>Fe<sub>0.95</sub>P<sub>0.593</sub>Si<sub>0.33</sub>B<sub>0.077</sub> com-
pounds. As a result, *T*<sub>C</sub> is reduced. These trends are consistent with
the previous investigation for the effect of V substitution in the Mn-
Fe-P-Si compounds [30].
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** (a) XRD pattern and the refined results for Mn<sub>1-x2</sub>V<sub>x2</sub>Fe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> (x<sub>2</sub> = 0.02) compounds; (b) Lattice parameters *a* and *c* as function of value of *x*<sub>1</sub> for Mn<sub>1-x1</sub>V<sub>x1</sub>Fe<sub>0.95</sub>P<sub>0.593</sub>Si<sub>0.33</sub>B<sub>0.077</sub> (series A) and (c) Lattice parameters *a* and *c* and (d) *c/a* ratio and *T*<sub>C</sub> as function of value of *x*<sub>2</sub> for Mn<sub>1-x2</sub>V<sub>x2</sub>Fe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> (series B).</figcaption></figure>

The temperature dependence of the magnetization in the com-
pounds of series A and B are shown in Fig. 2(a) and 2(b), respectively.
For decreasing temperature, they have a temperature-induced
magnetic phase transition from paramagnetic to ferromagnetic
state. The transition temperature T<sub>C</sub> is determined from the max-
imum value of -dM/dT in the M-T curve measured during heating at
1 T. For series A, T<sub>C</sub> tends to decrease with increasing V substitution.
When x<sub>1</sub> increases from 0 to 0.02, T<sub>C</sub> decreases from 290.0 to 255.2 K.
For series B, T<sub>C</sub> decreases from 300 to 286.2 K when x<sub>2</sub> increases from
0 to 0.02. Thus, T<sub>C</sub> in series B is tuned to the near room-temperature
region, which makes it suitable as a series of working materials for
near room temperature applications. The value of -dM/dT indicates
how strong the FOMT is. The values of -dM/dT are 7.6, 5.0 and
3.0 Am<sup>2</sup>/kgK for x<sub>1</sub> = 0.00, 0.02 and 0.03 and are 11.1, 5.6 and

5.2 Am²/kgK for x₂ = 0.00, 0.02 and 0.03, respectively. Thus, -dM/dT decreases by increasing V content, i.e. the FOMT is weakened.

The value of Δ*T*<sub>hys</sub> is determined by calculating the difference in
the maximum value of -d*M/dT* during cooling and heating in an
applied magnetic field of *μ*<sub>0*H*</sub> = 1 T at a ramp rate of 2 Kmin<sup>-1</sup>. For
series A, Δ*T*<sub>hys</sub> decreases by 36% from 1.1 to 0.7 K when *x*<sub>1</sub> increases
from 0.00 to 0.03. For series B, Δ*T*<sub>hys</sub> decreases by 93% from 1.5 to
0.1 K when *x*<sub>2</sub> increases from 0.00 to 0.03, see Table 1. The M-H
curves for series B are measured under ascending and descending
fields around the Curie temperature using a loop process [35]. The
magnetic hysteresis is also found to decrease when *x*<sub>2</sub> increases from
0 to 0.02, as shown in the Fig. S1. Thus, magnetic and thermal hys-
teresis show the same trend. When a Δ*T*<sub>hys</sub> of 0.5 K is achieved, up to
75% of the Carnot efficiency is feasible for the sample with *x*<sub>2</sub> = 0.02

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Temperature dependence of magnetization for (a) Mn<sub>1-x1</sub>V<sub>x1</sub>Fe<sub>0.95</sub>P<sub>0.593</sub>Si<sub>0.33</sub>B<sub>0.077</sub> and (b) Mn<sub>1-x2</sub>V<sub>x2</sub>Fe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> compounds under an applied magnetic field of 1 T.</figcaption></figure>
<caption>**Table 1**</caption>

Curie temperature ($T_c$), thermal hysteresis ($\Delta T_{hys}$), latent heat (L), magnetic entropy change ($|\Delta S_M|$) and adiabatic temperature change $\Delta T_{ad}$ at a field change of 1 T for series A and B. The value of $\Delta T_{hys}$ is determined in an applied magnetic field of $\mu_0H = 1$ T at a ramp rate of 2 Kmin$^{-1}$.

<table><thead><tr><th></th><th>Annealed T (K)</th><th>Sample</th><th>T<sub>C</sub> (K)</th><th>ΔT<sub>hys</sub> (K)</th><th>L (kJ/kg)</th><th>|ΔS<sub>M</sub>| (J/(kg·K))</th><th>ΔT<sub>ad</sub> (K)</th></tr></thead><tbody><tr><td>series A</td><td>1323</td><td>x<sub>1</sub> = 0.00</td><td>290.0</td><td>1.1</td><td>5.2</td><td>6.5</td><td>2.7</td></tr><tr><td>series A</td><td>1323</td><td>x<sub>1</sub> = 0.02</td><td>255.2</td><td>0.9</td><td>2.4</td><td>4.6</td><td>1.6</td></tr><tr><td>series A</td><td>1323</td><td>x<sub>1</sub> = 0.03</td><td>242.5</td><td>0.7</td><td>1.7</td><td>2.7</td><td>/</td></tr><tr><td>series B</td><td>1373</td><td>x<sub>2</sub> = 0.00</td><td>300.2</td><td>1.5</td><td>6.2</td><td>11.3</td><td>3.5</td></tr><tr><td>series B</td><td>1373</td><td>x<sub>2</sub> = 0.02</td><td>286.2</td><td>0.5</td><td>3.3</td><td>5.6</td><td>2.3</td></tr><tr><td>series B</td><td>1373</td><td>x<sub>2</sub> = 0.03</td><td>264.2</td><td>0.1</td><td>2.8</td><td>4.8</td><td>1.6</td></tr><tr><td>Ref. [11]</td><td>1373</td><td>x<sub>1</sub> = 0.00</td><td>281</td><td>1.6</td><td>3.8</td><td>9.8</td><td>2.5</td></tr></tbody></table>

[14]. The value of $\Delta T_{hys}$ is determined by both intrinsic properties, i.e. the strength of the FOMT and extrinsic properties like the fraction of the impurity phase [13]. Here the intrinsic weakening of FOMT is the dominant factor that reduces $\Delta T_{hys}$ to an ultra-low value as the compounds have very similar amount of impurity phase within the series.

The latent heat is an important quantity to characterize how strong the FOMT is. The DSC curves for series A and B are measured under zero field, as shown in the Fig. 3, and the derived latent heat is also listed in Table 1.

In Fig. 3, the DSC curves for series A and B were measured under zero field. By increasing the V content, the heat capacity is largely decreased, indicating that a strong FOMT is transferred to a weak FOMT. For the sample with $x_1 = 0.00$ and $x_2 = 0.00$, sharp heat capacity peaks are shown, indicating a strong FOMT. When increasing V content, the heat capacity is decreased, suggesting the FOMT is weaker. As shown in the Table 1, increasing $x_1$ from 0.00 to 0.03 results in a strong reduction of the latent heat by 67% from 5.2 to 1.7 J/g for series A. Similarly, increasing $x_2$ from 0.00 to 0.03 results in a strong reduction of the latent heat by 55% from 6.2 to 2.8 J/g (listed in Table 1). The sample with $x_2 = 0.02$ in series B has a slightly lower latent heat of 3.3 J/g than the previous benchmark MnFe<sub>0.95</sub>P<sub>0.595</sub>Si<sub>0.33</sub>B<sub>0.077</sub> compound of 3.8 J/g [11]. Therefore, the lower latent heat and the high fraction of the Fe<sub>2</sub>P-type phase (96.3 wt%) can explain the low value of $\Delta T_{hys}$ of 0.5 K found in the sample with $x_2 = 0.02$.

The iso-thermal entropy change $|\Delta S_M|$ is widely used as a criterion to evaluate the amount of heat transferred in one thermodynamic cycle. The values of $|\Delta S_M|$ are derived from iso-field magnetization curves using the Maxwell relation [36,37]. The iso-field magnetization curves of series A and B for a magnetic field change are measured in the vicinity of $T_C$ with a temperature interval

of 1 K. In order to minimize the effect of demagnetization factor, the applied magnetic field starts from 0.6 T and increases to 2 T in a step of 0.1 T. The calculated temperature dependence of $|\Delta S_M|$ for series A and B are shown in Fig. 4(a) and 4(c), respectively. The values of $|\Delta S_M|$ are 5.9, 4.5, 2.7 J/(kgK) at 1 T and 10.5, 8.0, 5.5 J/(kgK) at 2.0 T for samples with $x_1 = 0.00$, 0.02, and 0.03, respectively. Note that the GMCE of the compound with $x_1 = 0.00$ is lower than the previous benchmark compound for Mn-Fe-P-Si-B [11] ($|\Delta S_M| = 9.2 J/(kgK)$ at 1 T), which is due to the decrease of annealing temperature from 1373 to 1323 K. In series B, values of $|\Delta S_M|$ are 11.3, 5.6, 4.8 J/(kgK) at 1 T and 14.9, 8.4, 8.0 J/(kgK) at 2.0 T for samples with $x_2 = 0.00$, 0.02, and 0.03, respectively. After increasing the Si content from 0.33 to 0.36, $|\Delta S_M|$ of the sample with $x_2 = 0.00$ in series B outperforms the previously benchmark compound for Mn-Fe-P-Si-B [11]. This provides some room for V substitution to decrease $\Delta T_{hys}$, while retaining a large $|\Delta S_M|$. When $x_2$ increases to 0.02, $|\Delta S_M|$ is reduced to 5.6 J/(kgK) at 0–1 T, which is still about two times larger than that of polycrystalline Gd ($|\Delta S_M| = 3.0 J/(kgK)$ [18]).

In the magnetocaloric properties, $\Delta T_{ad}$ illustrates the direct temperature span that can be achieved in the magnetic heat pump. In-field DSC measurements were conducted at a rate of 3 Kmin$^{-1}$ in the temperature range of 240–340 K. From these measurements, $|\Delta S_M|$ and $C_p$ were collected under a constant magnetic field ($\mu_0H = 0, 0.5, 1.0$ and $1.5$ T). The values of $\Delta T_{ad}$ were calculated by the following equation: [38].

$$ \Delta T_{ad} = - \left[ \frac{T}{C(T)_{Hf}} S_M(T)_{Hf} - \frac{T}{C(T)_{Hl}} S_M(T)_{Hl} \right] \quad (1) $$

Fig. 4(b) illustrates the temperature dependence of the in-field DSC values of $\Delta T_{ad}$ for series A ($x_1 = 0.00$ and 0.02) while Fig. 4(d) illustrates the temperature dependence of $\Delta T_{ad}$ for series B ($x_2 = 0.00, 0.02$ and 0.03). In the series A, when $x_1$ increases from 0.00 to 0.02 at %, the value of $\Delta T_{ad}$ decreases from 2.7 to 1.6 K under an applied magnetic field of 1 T. This value of $\Delta T_{ad}$ for the benchmark Mn-Fe-P-Si-B [11] was 2.5 K. In the series B, when $x_2$ increases from 0.00 to 0.02, its value of $\Delta T_{ad}$ is decreased from 3.5 to 2.3 K at 1 T. At 1.5 T, the value of $\Delta T_{ad}$ for the sample with $x_2 = 0.02$ is 3.2 K. Thus, $\Delta T_{ad}$ for the sample of $x_2 = 0.02$ is sufficiently high to be utilized in a device, since cooling (and heating) may be effective when one achieves $\Delta T_{ad}$ above 2.0 K [19].

The question is why the low hysteresis and high entropy change occurs in the sample with $x_2 = 0.02$. A quantitative criterion to determine the order of magnetic phase transitions through magnetocaloric curves has been proposed recently, i.e. the field exponent $n = d\ln(|\Delta S_M|)/d\ln(H)$ for the relative field dependence of magnetic entropy change shows a maximum of $n > 2$ near the transition

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Heating DSC curves of series A and B are measured under zero field.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** (a) and (c) Temperature dependence of |Δ*S*<sub>M</sub>| under a field change of 0–1.0 T (open symbols) and 0–2.0 T (filled symbols) for series A and B, respectively; (b) and (d) Temperature dependence of Δ*T*<sub>ad</sub> under a field change of 0–1.0 T (open symbols) and 0–1.5 T (filled symbols) during heating for series A and B, respectively; (e) Temperature dependence of the field exponent *n* = *d*ln(|Δ*S*<sub>M</sub>|)/*d*ln(*H*) under a field change of 1.0 T for *x*<sub>2</sub> = 0 and 0.02; (f) Temperature dependence of Δ*T*<sub>ad</sub> under a field change of 0–1.0 T during heating and cooling for series B.</figcaption></figure>

temperatures for a FOMT, while the absence of such overshoot in-
dicates a SOMT [39,40]. For the critical composition, the minimum
value of *n* corresponds to 0.4 [40–42]. The temperature dependence
of the field exponent *n* under a field change of 1.0 T for *x*₂ = 0 and
0.02 is shown in Fig. 4(e). For x₂ = 0 sample, a clear distinct overshoot
of *n* > 2 is observed near its transition temperature, which indicates
it is a FOMT. Due to the presence of impurity (3:1) phase (observed
from XRD results) in the samples, which itself exhibits a T_c= 575 °C,
[43] *n* decreases to values below 2 after the overshoot (the typical *n*
value for paramagnetic state is 2) due to the ferromagnetic state of
the existing (3:1) phase. It corresponds to the composition nearest to
critical point of the FOMT and SOMT for x₂ = 0.02, since it is in good
agreement with the shape of *n* for critical point proposed in

reference [39]. However, the presence of impurities can affect the
absolute value of *n*, decreasing below the expected value of 2 for
impurity phases with larger Curie temperatures. The observed slight
increase of *n* to values close to 2 followed by a decrease might be an
indication of a combined effect of a weakly first order phase tran-
sition and the presence of such impurities, which agrees with mi-
crostructural observations and the presence of a small thermal
hysteresis. Accordingly, a good combination of low hysteresis and
high entropy change can be obtained in this compound. For x₂ = 0.03,
the minimum of *n* near the transition is rather shallow and two
peaks are shown when passing the transition temperature. This type
of shape for the field exponent *n* indicates that it has phase se-
paration of Fe₂P-type structure, which agrees with the two peaks of
zero-field DSC in the Fig. 3. As shown in the Fig. S2, the phase separation of the Fe₂P-type phase is observed for $x_2$ = 0.03. There are two peaks in the DSC curves, which show an interval of transition temperature about 1 K. The zero-hysteresis is shown in the M-T curve of $x_2$ = 0.03 but is not shown for its in-field DSC data. The reason for the different value of hysteresis for M-T and DSC measurement is not clear yet. Recently, the origins for zero-hysteresis in the materials with IEM are investigated from the aspect of nanoscale phase separation [6,44,45] and the secondary phases [46]. Thus, we propose an explanation based on the in-field DSC data. Note that the $T_{peak}$ of heating DSC curve for phase 1 and cooling DSC curve for phase 2 are overlapped. When the paramagnetic phase is transferred to ferromagnetic phase, the phase 1 with higher $T_c$ will become ferromagnetic first and then the stray field [46] from this ferromagnetic phase can assist the phase transition of paramagnetic phase 2. As a result, the phase separation helps to achieve zero-hysteresis in M-T curves. Nevertheless, the phase separation may not be a good strategy for get a GMCE since it will also scarify the $|\Delta S_M|$ and $\Delta T_{ad}$, see Fig. 4 (c) and (d) and shows hysteresis in the DSC measurement.

In addition, $\Delta T_{hys-DSC}$ is determined by the difference of the heating and cooling process for the in-field DSC under a field change of 1 T measured at a rate of 3 Kmin⁻¹, as shown in Fig. 4(f). It differs from the $\Delta T_{hys}$ calculated by the M-T curves at a rate of 2 Kmin⁻¹. Due to the thermal-lag effect, a higher measuring rate leads to a higher $\Delta T_{hys}$, as demonstrated for the Eu₂In compound [47]. In series B, $\Delta T_{hys-DSC}$ decreases from 2.4 to 0.7 K when $x_2$ increases from 0.00 to 0.02,

see Fig. 4(f). The value of $\Delta T_{ad}$ for Mn<sub>0.98</sub>V<sub>0.02</sub>Fe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> ($\Delta T_{ad}$ = 2.3 K) in series B is competitive to that of MnFe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> compound ($\Delta T_{ad}$ = 2.5 K) [11], but its value for $\Delta T_{hys-DSC}$ is reduced by 85%. Thus, it is promising to achieve a large value of $\Delta T_{ad}$ and an ultra-low $\Delta T_{hys-DSC}$, which can significantly improve the heat exchange efficiency of the magnetic cooling (and heating) system.

The summary of maximum values for $|\Delta S_M|$, $\Delta T_{ad}$ and $\Delta T_{hys}$ at a magnetic field of 1.0 T for Gd, MnFe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub>, MnFe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> (this work) and Mn<sub>0.98</sub>V<sub>0.02</sub>Fe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> (this work) is shown in Fig. 5, demonstrating the merit of the compounds in this work. The value of $\Delta T_{ad}$ for $x_2$ = 0.02 is 2.3 K, comparable to 2.8 K of polycrystalline Gd, but its $|\Delta S_M|$ is almost twice larger than Gd [18]. Accordingly, the coefficient of refrigerant performance (RCP) = $\frac{\Delta S^* \cdot \Delta T_{ad}}{J_0^B M(T_c, B) \text{d}B}$ of the sample with $x_2$ = 0.02 is calculated to be 0.47, larger than Gd (RCP = 0.17) and Fe<sub>0.49</sub>Rh<sub>0.51</sub> (RCP = 0.22) [48]. Thus, the MnFe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> ($x_2$ = 0.00) and Mn<sub>0.98</sub>V<sub>0.02</sub>Fe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> ($x_2$ = 0.02) are clearly good candidates for magnetic heat pumps operating near room temperature.

To investigate the reason why V decreases the hysteresis without losing the GMCE, the effect of V on $dT_c/dB$ is investigated. The magnetic field dependence of $T_c$ and $dT_c/dB$ for series B are shown in Fig. 6(a). The value of $dT_c/dB$ increases from 4.0 to 4.8 K/T when the V content is changed from $x_2$ = 0.00 to $x_2$ = 0.02. This is comparable to the $dT_c/dB$ value for (Mn,Fe)<sub>2</sub>(P,As) compounds, where $dT_c/dB$ was found to be 5.2 K/T [49]. The Clausius–Clapeyron relation for a FOMT corresponds to $dT_c/dB = -T_c\Delta M/L$, where B is the applied magnetic field and $\Delta M$ is the jump in magnetization. Thus, the increase in $dT_c/dB$ is mainly caused by the decrease in latent heat (see Table 1), since the values of $T_c$ and $\Delta M$ are reduced (see Fig. 2). The increase in $dT_c/dB$ suggests that the driving force for the FOMT is enhanced. As a result, a strong field response is found for low fields, as shown in the magnetization curve of $x_2$ = 0.02 in the Fig. 6(b).

From the saturation magnetization displayed in Fig. 6(b), the value of the magnetic moment per formula unit ($\mu_{f.u.}$) for series B was calculated, as mentioned in reference [50]. For series B, the value of $\mu_{f.u.}$ increases from 3.75 to 3.96 $\mu_B$/f.u. when $x_2$ increases from 0.00 to 0.02. A larger value of $\mu_{f.u.}$ suggests a larger contribution to $|\Delta S_M|$. This agrees with the strengthening effect of V substitution on the magnetic moment formation in the Mn-Fe-P-Si-V compounds [31]. The higher values for $dT_c/dB$ and $\mu_{f.u.}$ illustrate why an ultra-low thermal hysteresis and a GMCE can be achieved simultaneously in the compounds with 0.02 at% V substitution for Mn in series B. Thus, introducing V as a new substitutional element is found to be capable of increasing both $dT_c/dB$ and $\mu_{f.u.}$, and thereby decreasing the hysteresis without losing the GMCE.

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Figure of merit of $|\Delta S_M|$, $\Delta T_{ad}$ and $\Delta T_{hys}$ for Gd [18], MnFe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> [11], MnFe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> and Mn<sub>0.98</sub>V<sub>0.02</sub>Fe<sub>0.95</sub>P<sub>0.563</sub>Si<sub>0.36</sub>B<sub>0.077</sub> in series B.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Field dependence of $T_c$ and $dT_c/dB$ (insets); (b) The magnetization as a function of the V content for series B measured at a temperature of 5 K.</figcaption></figure>
## 4. Conclusions

The ultra-low hysteresis and GMCE of optimal Mn₁-x₂Vₓ₂Fe₀.95P₀.563Si₀.36B₀.077 compounds pave a pathway to highly efficient magnetic heat pump applications. When x₂ increases from 0.00 to 0.02, the latent heat can be reduced by 55% from 6.2 to 3.3 J/g and thus ΔT<sub>hys</sub> decreases by 67% from 1.5 to 0.5 K, the |ΔS<sub>M</sub>| is decreased from 11.3 to 5.6 J/kgK and the ΔT<sub>ad</sub> is decreased from 3.5 to 2.3 K at 1 T. The optimal composition of x₂ = 0.02 is proven to be close to the critical point between the FOMT and the SOMT. The combination of increase in dT<sub>c</sub>/dB and increase in magnetic moment μ<sub>f.u.</sub> of Mn₀.98V₀.02Fe₀.95P₀.563Si₀.36B₀.077 compound can provide a sufficiently large GMCE and an ultra-low value (0.5 K) of ΔT<sub>hys</sub>. Thus, the coefficient of refrigerant performance (CRP) of this compound is two times larger than Gd. The current Mn₁-x₂VₓFe(P,Si,B) compounds provide an excellent candidate for designing materials towards magnetic heat pump applications using low-cost permanent magnets near-room temperature. The mechanical properties and thermal conductivity of the Mn₁-x₂Vₓ₂Fe₀.95P₀.563Si₀.36B₀.077 compounds will need to be investigated further to demonstrate the full potential for future utilization in practical devices.

### CRediT authorship contribution statement

**Ekkes Brück:** Conceptualization, Methodology, Reviewing. **Jiawei Lei:** Data curation, Writing – original draft. **Xinmin You:** Data curation, Writing. **Jiayan Law:** Data curation, Writing. **Victorino Franco:** Data curation, Writing. **Bowei Huang:** Data curation, Writing. **Michael Maschek:** Data curation, Writing. **Dechang Zeng:** Supervision, Methodology, Reviewing. **Niels van Dijk:** Visualization, Investigation, Writing – review & editing.

### Data availability

Data will be made available on request.

### Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Jiawei Lai, Victorino Franco reports financial support was provided by Guangzhou ethics project. Michael Maschek reports financial support was provided by EIT Climate KIC. Ekkes Bruck has patent #P1600096NL00 pending to Technische Universiteit Delft. Jiawei Lai has patent #P1600096NL00 pending to Technische Universiteit Delft.

### Acknowledgements

The authors acknowledge Anton Lefering, Kees Goubitz, L. Zhang, and Bert Zwart for their technical assistance. The authors also thank Yibole for fruitful discussions. This work is financially supported by the Dutch Science Foundation NWO under applied sciences project 14013. This work is also supported by Guangdong Provincial Science and Technology Program (Grant No. 2015A050502015), the Guangzhou Municipal Science and Technology Program (No. 201505041702137), Natural Science Foundation of the Guangdong Province (2016A030313494), and Zhongshan Municipal Science and Technology Program (Platform construction and innovation team). The author thanks for the financial support of the Guangzhou Ethics Project. V.F. and J.Y.L. acknowledge the financial support of AEI/FEDER-UE (grant PID2019-105720RB-100). M.M. acknowledges financial support from EIT Climate KIC project "Local, magnetocaloric power conversion opportunities for Cities" (ID 210045).

## Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jallcom.2022.167336.

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