Using a computationally driven screening to enhance magnetocaloric effect of metal monoborides

PAPER • OPEN ACCESS Using a computationally driven screening to enhance magnetocaloric effect of metal monoborides To cite this article: Carlos Romero-Muñiz et al 2023 J. Phys. Energy 5 024021 View the article online for updates and enhancements. You may also like Semiconducting MnB5 monolayer as a potential photovoltaic material Fanjunjie Han, Tong Yu, Xin Qu et al. - In vivo neutron activation analysis of bone manganese in workers Yingzi Liu, Danelle Rolle-McFarland, Farshad Mostafaei et al. - Covalent magnetism, exchange interactions and anisotropy of the high temperature layered antiferromagnet MnB2 S Khmelevskyi and P Mohn - This content was downloaded from IP address 150.214.182.235 on 08/05/2024 at 09:26 J. Phys. Energy 5(2023) 024021 https://doi.org/10.1088/2515-7655/acce6e Journal of Physics: Energy OPEN ACCESS RECEIVED 14 February 2023 REVISED 10 April 2023 ACCEPTED FOR PUBLICATION 19 April 2023 PUBLISHED 2 May 2023 Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. PAPER Using a computationally driven screening to enhance magnetocaloric effect of metal monoborides Carlos Romero-Mu˜ niz, Jia Yan Law, Luis M Moreno-Ramírez,´ Alvaro Díaz-García and Victorino Franco∗ Departamento de Física de la Materia Condensada, ICMS-CSIC, Universidad de Sevilla, PO Box 1065, 41080 Sevilla, Spain ∗Author to whom any correspondence should be addressed. E-mail: [email protected] Keywords: magnetocaloric effect, density functional theory, computational screening of materials Supplementary material for this article is available online Abstract In most cases, substitution studies that aim to optimize magnetic properties are performed at the magnetic atomic site. However, in the case of MnB, magnetic substitutions at the Mn site significantly decrease the once promising magnetocaloric and magnetic properties. This study employs computationally directed search to optimize the magnetocaloric properties of MnB where partial substitutions of boron atoms (Mn50B50−xSixand Mn50B50−xGexwhere x=3.125, 6.25, and 12.5) reveal new compounds with a greater magnetocaloric effect than pure MnB at the same Curie temperature. These new compounds were obtained by arc melting the pure elements and further characterized. The computationally driven screening process is based on density functional theory calculations that do not require large databases of known compounds. This work demonstrates that using simple computational screening procedures to search for new magnetocaloric materials with improved properties can be done quickly, cost-effectively, and while maintaining reliability. 1. Introduction Magnetic refrigeration has established itself as a viable alternative to conventional refrigeration technologies based on gas compression cycles [1–3]. As of now, the main advantages of this proposal are higher efficiency, reduced vibration and noise, and the use of solid-state materials that are more environmentally friendly without gas emissions. Magnetic refrigeration can be achieved due to the magnetocaloric effect (MCE) displayed by materials with large intrinsic magnetization or another magnetic ordering. By applying and removing a magnetic field, a temperature variation is induced in the working material, which is ultimately the driving force for the construction of a refrigeration device. With modern active magnetic refrigeration schemes, even with moderate magnetic fields of 1.5 T produced by permanent magnets, it is possible to fabricate viable devices with a competitive performance, which has been attained in many operating prototypes produced all over the world [2]. A such magnetic refrigeration and MCE can ameliorate the current energy concerns. Yet, the commercialization of their devices has been hindered by several impediments, the most significant of which is the lack of magnetocaloric materials with optimal cyclic properties at a competitive cost despite having hundreds of magnetic materials studied in depth for their suitability for magnetocaloric devices [1,4–6]. It is shown in a recent survey on the current trends in magnetocaloric materials that the MCE of Gd remains the benchmark for high MCE without hysteresis [7]. Due to its limited resource availability and high cost, it is essential to explore alternatives. The MCE of MnB, which is similar to that of Gd, makes it a promising candidate [8,9]. MnB belongs to the class of magnetic metal monoborides, of which only FeB and MnB display remarkable ferromagnetic ordering [10,11]. Both compounds behave as soft ferromagnetic materials with Curie temperatures of 600 and 575 K respectively. The permanent magnetic moment is carried by transition metal ions, which display relatively low values of 1.12 µBfor Fe and 1.92 µB[11]. These inexpensive magnetic materials, free of critical and rare-earth elements, have drawn renewed interest in the recent years. FeB is © 2023 The Author(s). Published by IOP Publishing Ltd J. Phys. Energy 5(2023) 024021 C Romero-Mu˜ niz et al often synthesized as nanoparticles [12–14] while bulk MnB has been proposed for different applications [15, 16]. We have to keep in mind that the ceramic nature of metal monoborides offers materials with magnetic behavior and high electrical conductivities but with mechanical properties very different from those of more commonly used intermetallic compounds. In this sense the extremely high hardness and wear resistance of borides might help to overcome some current limitations of metallic materials. Despite having remarkably similar magnetic ordering and overall properties, each alloy exhibits a distinct level of magnetoelastic coupling, which is recently thought to be the cause of the difference in their magnetocaloric responses [9]: −10.7 vs −3.2 J kg−1K−1at 5 T for MnB and FeB respectively. Therefore, the MCE magnitude of MnB is as large as that of pure gadolinium and three times larger than that of FeB for 5 T. Another interesting characteristic of metal monoborides is the possibility of producing pseudobinary compounds with the general chemical formula M(1)1−xM(2)xB, often with a total solubility for the two metals (0 <x<1). If one of the metals possesses a magnetic moment (i.e. Mn or Fe in our case), this circumstance leads to a huge number of possibilities for tuning the magnetic properties of the resulting compound. For example, total solubility for the following systems has been confirmed: Mn1−xCrxB [17,18], Mn1−xFexB [17–19], Mn1−xCoxB [20,21], Fe1−xCoxB [19,20] as well as Cr1−xFexB with x<0.75 [19]. Even combinations of three transition metals in the same boride have been investigated [19]. This versatility opens the door to producing stable materials with very specific magnetic properties in terms of saturation magnetization or Curie temperature in a very broad range. In this way, Kanaizuka [17] demonstrated that single phases of Mn1−xCrxB and Mn1−xFexB with different values of xcovered the whole range of Curie temperatures between 100 K and 800 K. With the appropriate combinations of Co, Fe and Mn, the MCE of these monoborides can be tuned appropriately [8]. However, in that study, all the provided compositional combinations resulted in a noticeable decline in MCE. In this work, we aim to exploit the extremely rich chemistry of metal monoborides to design new magnetocaloric materials with similar or even superior properties to those of MnB or with additional features useful for a specific target application. Given the enormous number of elements to investigate and the possible combinations they could form, it would be impractical to synthesize all the compounds. Instead, we propose a theoretical approach based on density functional theory (DFT) calculations to provide an approximation of the overall picture and direct further experimental work. The high accuracy with which DFT can replicate the crystal structure of crystalline compounds including the lattice constants, crystal structure, bulk moduli, etc, makes this type of search strategy completely reliable. Many relevant magnetic properties can also be calculated with DFT, such as the atomic magnetic moments, the saturation magnetization, exchange couplings or the spin-resolved density of states. Currently, it is common practice to use DFT-based methods, sometimes in conjunction with machine learning algorithms, in the search for new magnetic materials using large data sets of materials [22–24]. Moreover, several theoretical approaches have been applied as high-throughput computational screening schemes in more focused contexts, such as the discovery of new two-dimensional magnetic materials [25] the search of better permanent magnets [26–28], high-spin metal organic frameworks [29] or bipolar magnetic semiconductors [30]. In addition, they can focus on optimizing or tuning the properties of a given material family such as ThMn12-type structure compounds [31] or Heusler alloys [32]. It is worth noting that there is a significant difference between our approach and those based on machine learning algorithms, which often provide outputs without supporting chemical arguments or allowing control of the intermediate steps. Moreover, our approach allows us to focus on a certain family of compounds and test a remarkable number of possibilities without having to use vast amounts of data. In the case of magnetocaloric materials, the DFT methods present a serious drawback: they do not provide, by themselves, any description of magnetic properties as a function of temperature. Nevertheless, they are still able to offer insightful knowledge regarding the MCE performance of materials. For instance, Bocarsly et al [33] devised a simple screening model based on a single parameter related to magnetic deformation. A value above a specific threshold can indicate whether a particular material will display a remarkable MCE or not. Despite its qualitative nature, this screening method has been successfully applied to identify promising compositions in solid solutions present in ternary manganese germanides [34]. In the present study, we will evaluate this magnetic deformation parameter in combination with DFT calculations to discern the best metal monoborides as magnetocaloric materials. We perform a first rough screening after partial substitutions in MnB. We consider either the possibility of Mn and B replacement. This latter choice has not been previously considered in the literature. For the substitutions we choose transition metals such as Fe, Co, Ni, Cr and Ti, which are very reasonable choices from the chemical point of view, together with Si and Ge, which, in principle, are more similar to boron. After identifying the most promising substitutional elements, a follow-up analysis to confirm the trend at various compositions was performed. The next step in the study involved the synthesis of samples with partial boron substitution by Si or Ge and the subsequent experimental characterization. Our experimental work demonstrates that the MCE 2 J. Phys. Energy 5(2023) 024021 C Romero-Mu˜ niz et al magnitudes of the new borides can be greater than that of the original MnB despite a relatively large fraction of secondary phases. The present study shows that computationally driven synthesis is far more efficient than traditional trial-and-error methods or simple random searches for new substitutional elements. Even if the new materials shown here have transition temperatures above those that are usually used in magnetocaloric refrigeration, once the synthesis is optimized, these could have potential applicability for refrigeration at higher temperatures and in the field of magnetocaloric energy conversion [6]. 2. Methods 2.1. Computational details The density functional calculations based on DFT were performed using a plane-wave basis set as implemented in the VASP code [35]. The basis set was constructed with an energy cutoff of 500 eV and the pseudopotentials were built using the projected-augmented wave method [36,37]. The magnetic moments of the atoms were accounted for by using a spin-polarized scheme in all the calculations. The Perdew–Burke–Ernzerhof exchange-correlation functional [38] was used on a Monkhorst–Pack grid [39] of 15 ×11 ×13 to sample the reciprocal space. Ionic relaxations were carried out under these conditions to determine the equilibrium geometry of the compounds under study. This was accomplished by employing a conjugate gradient algorithm that did not impose any symmetrical constraints and permitted changes to the volume and shape of the unit cell. The relaxations were completed when forces upon atoms were less than 0.005 eV Å−1. In each case, the unit cell provided by the FeB-type crystal structure (made up of an orthorhombic cell with four formula units; further described in section 3) served as the starting point. The isostructural parent compounds, FeB, CoB and MnB were first thoroughly analyzed (see supplementary information for details). After partial substitution of one Mn or B atom, compounds with the general formula Mn0.75M0.25B or MnB0.75M0.25 are obtained. Within this choice, there is only one way to construct the substituted compounds, as the four Mn and four B sites are equivalent and the substitution of one single atom is the same, regardless of the site chosen. Therefore, no further statistical analysis would be required. Formation energies are calculated for all compounds analyzed in the present work following the usual procedure and taking the bulk states of constituent metals as energy references. Notice that neither B nor Mn have some of the typical metal crystal structures and they have been calculated from x-ray diffraction (XRD) inputs from α-rhombohedral B [40] and cubic α-Mn [41], also known as A12 structure. All other structures were optimizing after Birch–Murnaghan fittings. A 32-atom unit cell can be built by replicating this unit cell, allowing us to evaluate the Mn1−xMxB or MnB1−xMxsystems with M/B or M/Mn atomic ratios of around 6% but the treatment of this cell is more complicated as it requires statistical analysis. This is the reason why we have focused our analysis on the 8-atom unit cells rather than on the larger cells. We have used the larger cells appearing in the supplementary information exclusively to confirm the trend on a broader range of substituting elements. In addition to the standard DFT calculations, we used the method developed by Bocarsly et al [33] to screen potential magnetocaloric compounds. In brief, they proposed that a single parameter, which they defined as the magnetic deformation parameter, ΣM, was correlated with the MCE performance of the material. This parameter can be obtained using two DFT calculations of relaxed structures with and without spin polarization. The notion behind ΣMis that it measures the amount that atomic magnetic moments deform the unit cell. Therefore, it was computed solely from the lattice vector matrices of the magnetic and non-magnetic structures AMand ANM respectively. Specifically, ΣMdepends only on the matrix P=A−1 NM ·AMthrough the following relations: ΣM=1 3qη2 1+η2 2+η2 3×100 where η1,η2,η3are the eigenvalues of the following matrix η=1 2PTP−I. The authors suggest that compounds with ΣMvalues greater than 1.5 are likely to show remarkable magnetocaloric properties. Although this criterion only provides qualitative information and might not adequately characterize complex materials, it can still be helpful in situations where experimental data are unavailable. 3 J. Phys. Energy 5(2023) 024021 C Romero-Mu˜ niz et al 2.2. Experimental The MnB, Mn50B50−xSixand Mn50B50−xGexsamples (x=3.125, 6.25 and 12.5 at. %) were prepared by arc melting pure elements (with a purity higher than 99%) in an argon-controlled environment. Five flips and remelts were performed to ensure homogeneity. An excess Mn of 10 wt. % was used to account for its ease of vaporization. The sample designation used in the work is denoted by the nominal content of the partial substitutions as: MnB, Si3.125, Si6.25, Si12.5, Ge3.125, Ge6.25 and Ge12.5 respectively. The phase compositions were characterized by XRD performed at room temperature using a Bruker D8I diffractometer with Cu-Kαradiation. The Rietveld refinement of XRD data was performed using TOPAS 6.0 software. The MCE was indirectly determined using Maxwell relation from isothermal magnetic measurements conducted in a vibrating sample magnetometer (VSM; Lake Shore Cryotronics VSM7407). 3. Results and discussion 3.1. DFT-assisted screening It is crucial to have a thorough understanding of the system we are attempting to model before carrying out a screening procedure based on DFT calculations. This includes a detailed understanding of the crystal structure of metal monoborides in order to develop a successful model. It is known that several metal monoborides crystallize in three different types of orthorhombic structures (FeB, CrB and MoB). Ferromagnetic monoborides, such as MnB and FeB, belong to the FeB-type crystal structure, which is isomorphous to other compounds like CoB, TiB or HfB. The other two crystal structures in which metal monoborides occur can essentially be interpreted as distorted variations of the FeB lattice, sharing a lot of the same characteristics. Cr–B-type compounds include CrB, NiB, NbB, TaB and VB while MoB and WB crystallize according to a MoB structure [42]. All of them are characterized by infinitely parallel zigzag chains of boron atoms. The nearest neighbors of boron are separated by about 1.8 Å while each of these atoms is coordinated by six metal atoms that are located at the vertices of a trigonal prism with metal boron distances that fall between 2.10 and 2.20 Å. In figure 1(a), we show the FeB-type crystal structure of MnB. In practice, it is unclear whether the coordination of boron atoms in this type of structure must be assigned to 6 or 7. The latter option calls for a seventh metal atom as the first neighbor, resulting in the construction of a mono-capped trigonal prism with a slight distortion as the building block of the coordination polyhedron. It should be noted that the phase shown in figure 1(a) is known as β-phase since it exists another phase labeled as αwhich displays a CrB-type structure and shares many properties with the β-phase [19,43]. This structure with different trial compositions constructs the starting point (step (i)) to perform DFT calculations attending to the schematic flowchart shown in figure 1(b). The obtained model then includes magnetic and non-magnetic elements to search in the partial substitution space for Mn or B sites in step (ii). Next, in step (iii), we evaluate for possible new compounds for viability and their magnetic properties, then use the magnetic deformation parameter, ΣM, of values >1.5 to further screen for potential candidate compounds for experimental synthesis (step (iv)). As previously discussed, only MnB and FeB show remarkable magnetic ordering whereas CoB is regarded as weak ferromagnetic or diamagnetic material. All three possess the same crystal structure as shown in figure 1(a). For this reason, we always start our calculations with the same FeB-structure for all elemental combinations. Therefore, we have calculated these three structures to check that our DFT model reproduces the major features correctly. The calculated lattice constants of MnB, FeB and CoB in comparison to experimental data are tabulated in tables S1–S3 respectively. It is observed that the calculation results are in good agreement with experimental XRD data surveyed from literature. Furthermore, as shown in table S4, the calculated magnetic moment per metal atom is reproduced accurately. Magnetic deformation parameters of MnB and FeB (along with other magnitudes, including mass density, energy difference between magnetic and non-magnetic structures and associated volume change) are also calculated and tabulated in table S5. Our results (ΣM=1.784 (MnB) and 2.334 (FeB)) are strikingly similar to those obtained (ΣM=1.72 (MnB) and 2.17 (FeB)), which Bocarsly et al [33] identified as promising values using their proposed screening procedure. After the verification of the proposed DFT methodology in pure monoborides, it is further applied to ternary solid solution systems: Mn1−xCoxB and Mn1−xFexB (0 ⩽x⩽0.75), whose experimental reports found the largest MCE, 4.4 J kg−1K−1(1 T), for MnB [8]. As for their Curie temperatures, Fe substitution raises the Curie temperatures whereas Co substitution has the opposite effect. The simulated magnetic properties of Mn1−xCoxB and Mn1−xFexB together with their calculated magnetic deformation parameter are tabulated in table 1. With increasing Co content, saturation magnetization (Ms) of the Mn1−xCoxB series decreases monotonically (eventually vanishes for pure CoB), which is also reflected in the monotonic decrease in their ΣMvalues. On the other hand, this is not the case for Mn1−xFexB series: a non-monotonic trend in ΣMvalues is observed while Msdecreases as Fe content increases. In any case, note that all 4 J. Phys. Energy 5(2023) 024021 C Romero-Mu˜ niz et al Figure 1. (a) Schematic view of the crystal structure of MnB (FeB-type) showing boron chains parallel to each other and six-fold coordination of boron atoms with trigonal prisms. (b) A flowchart that summarizes our computational approach to the synthesis of new borides using the composition and crystal structure as inputs for the screening procedure. Table 1. Relevant data to screen the Mn1−xCoxB and Mn1−xFexB systems using our DFT methodology. They include the saturation magnetization (Ms), the mass density, the volume change between the magnetic and non-magnetic calculations (∆V) with its corresponding energy difference (ENM-M) and the magnetic deformation parameter (ΣM) used to screen potential magnetocaloric materials. The formation energy per f.u. Efor is given in the last column. MsDensity ∆VΣMENM-M Efor Compound (emu g−1) (g cm−3) (%) (%) (eV/atom) (eV/f.u.) CoB 0.0 7.48 0.038 0.007 0.0000 −0.811 Co0.75Mn0.25B 38.9 7.23 0.717 0.334 0.0093 −0.768 Co0.50Mn0.50B 80.9 6.99 1.496 0.908 0.0339 −0.793 Co0.25Mn0.75B 123.6 6.75 2.766 1.489 0.0671 −0.886 MnB 158.6 6.54 3.978 1.784 0.0975 −0.998 Mn0.75Fe0.25B 151.9 6.62 3.562 1.358 0.1075 −0.954 Mn0.50Fe0.50B 134.9 6.73 2.705 0.769 0.1055 −0.890 Mn0.25Fe0.75B 116.4 6.84 2.082 1.150 0.0892 −0.825 FeB 97.9 6.95 1.556 2.334 0.0588 −0.754 compounds display similar formation energies revealing that all solid solutions between Mn and Fe or Co are stable. Given that CoB exhibits no magnetic behavior, the observed trend in Mn1−xCoxB is straightforward: with increasing Co content, the saturation magnetization decreases, resulting in a smaller MCE. This is also consistent with the experimental report in [8]: upon partial substitution of Mn by Co, the MCE dropped dramatically to 1.3 J kg−1K−1(1 T) for Mn0.9Co0.1B and essentially vanishes for Mn0.25Co0.75B with only 0.3 J kg−1K−1. Conversely, the effects of partial substitution of Fe on the behavior of Mn1−xFexB is less straightforward to rationalize: since FeB exhibits no magnetoelastic coupling during phase transition, it exhibits a lower MCE than MnB, according to Ma et al [16]. The increase of Fe content results in non-monotonic behavior of the MCE of Mn1−xFexB, as indicated in their experimental results: the MCE decreases as Fe is added but that of Mn0.5Fe0.5B (1.3 J kg−1K−1, 1 T) is significantly larger than those of Mn0.4Fe0.6B and Mn0.6Fe0.4B (slightly lower compared to pure FeB). It is also observed that their ΣMvalues follow a non-monotonic trend with increasing Fe content, and their relatively low magnitudes are consistent with their reported low MCE. The main discrepancy in the ΣMof this series lies in the larger ΣMvalue for FeB than MnB (2.334 vs 1.784), whose MCE is significantly smaller. This inconsistency can be attributed to the qualitative information provided by the magnetic deformation parameter, which prevents us from carrying out a purely quantitative analysis. In any case, the ΣMparameter is likely to exhibit a strong correlation with the MCE of metal monoborides and values greater than 1.5 probably indicate the presence of materials with remarkable MCE. 5 J. Phys. Energy 5(2023) 024021 C Romero-Mu˜ niz et al Table 2. Relevant data to screen new monoborides using DFT calculations. They include the saturation magnetization (Ms), the mass density, the volume change between the magnetic and non-magnetic calculations (∆V) with its corresponding energy difference (ENM-M) and the magnetic deformation parameter (ΣM). Note that the absence of ΣMvalues indicate that the compound is not stable according to DFT prediction. The formation energy per f.u. Efor is given in the last column. MsDensity ∆VΣMENM-M Efor Compound (emu g−1) (g cm−3) (%) (%) (eV/atom) (eV/f.u.) Mn0.75Fe0.25B 151.9 6.62 3.562 1.358 0.1075 −0.954 MnFe0.25B0.75 69.8 7.11 1.865 0.422 0.0137 −0.341 Mn0.75Co0.25B 123.6 6.75 2.766 1.489 0.0671 −0.886 MnCo0.25B0.75 90.4 7.14 2.350 0.994 0.0213 −0.366 Mn0.75Ni0.25B 105.9 6.71 2.518 1.300 0.0396 −0.824 MnNi0.25B0.75 128.4 6.94 4.395 1.430 0.0256 −0.375 Mn0.75Cr0.25B 131.2 6.44 3.051 1.285 0.0645 −0.958 MnCr0.25B0.75 48.3 6.96 1.640 — 0.0092 — Mn0.75Ti0.25B 92.9 6.05 1.875 0.735 0.0316 −1.118 MnTi0.25B0.75 31.3 6.57 0.551 — 0.0734 — Mn0.75Ge0.25B 91.1 6.46 3.341 — 0.0296 — MnGe0.25B0.75 130.7 6.91 4.052 2.397 0.0951 −0.366 Mn0.75Si0.25B 73.9 5.94 1.100 0.603 0.0230 −0.479 MnSi0.25B0.75 148.2 6.22 3.954 2.504 0.0927 −0.671 3.2. Screening the elemental substitution search space for possible (un-synthesized) alloys The aim of the present work is to go one step beyond and find new borides which exhibit a better MCE. For this task, we employ DFT calculations and the screening procedure verified for the Mn1−xCoxB and Mn1−xFexB systems explained above. Since MnB exhibits the largest MCE magnitude among the monoborides, we start from that structure and consider if partial substitutions of Mn or B atoms lead to an enhancement of the MCE. In this task, we evaluate the ΣMvalues for the new compounds with various magnetic and non-magnetic elements partially substituting 25% of either Mn or B atoms. These elements of consideration are Co, Fe, Ni, Cr, Ti, Si and Ge. The first three are the typical ferromagnetic atoms while Cr and Mn often exhibit similar magnetic behavior when combined with other elements. For Ti, it can be found in a TiB compound that is isomorphous with the FeB-type crystal structure. The selection of non-magnetic Si and Ge atoms are suitable alternatives to boron. The calculated results of the new compounds (un-synthesized) are tabulated in table 2. When Mn is partially substituted by other ferromagnetic atoms, such as Fe or Co, our calculations show stable structures with saturation magnetization and ΣMvalues similar to those of MnB since CoB and FeB are isomorphic to MnB. However, as mentioned before, these substitutions significantly affect the MCE behavior of the material: while the Co substitution results in a non-magnetic compound, the presence of Fe atoms alters the magnetoelastic coupling, both leading to a drastic decrease in the overall MCE as experimentally demonstrated in [8]. In the case of partial substitutions of Mn by Ni or Cr, whose monoborides are not isomorphous to MnB, the ΣMvalues are slightly lower than 1.5. Besides, the saturation magnetization values clearly decrease because Ti and Ni atoms do not contribute to the total magnetic moment of the compounds (see the atomic magnetic moment distribution in table S8 of the supplementary information). When Mn is substituted with Ti, very poor ΣMand much lower saturation magnetization values are observed. The incorporation of the semimetal elements Si or Ge does not lead to suitable results because they are either unstable (Ge) or have a very low ΣMvalue (Si). However, this is not the case when these partial element substitutions occur on boron atoms. The transition metal elements are no longer viable candidates for this. Due to the larger atomic radii of Cr and Ti compared to the much smaller boron atoms, their substitutions are no longer possible in terms of structure. Although it is quite possible to substitute the ferromagnetic atoms, Fe, Co and Ni, with boron because their atomic radii differ by a small amount, the ΣMparameter is smaller than 1 in the case of Fe and Co. Moreover, the newly added Fe or Co atoms weaken the magnetic moment of Mn atoms leading to a significant decrease in saturation magnetization as shown in table S8. Conversely, for Ni substitution, these negative effects are not found, which makes it more promising: saturation magnetization remains similar and the ΣMvalue is around 1.5. However, the formation energies for Fe, Co and Ni B-substituted compounds are much smaller compared to those of Mn-substitution, suggesting a poor stability. Given that the semimetal elements, Si and Ge, are suitable boron substitutes, our calculations demonstrate that they can produce promising compounds with ΣMvalues up to ∼2.5,whose magnitudes are comparable to those of MnB and FeB. Furthermore, their saturation magnetization values are very similar to that of MnB and the local magnetic moments of Mn atoms are enhanced with the presence of Si or Ge (see table S8). Our calculations show that 6 J. Phys. Energy 5(2023) 024021 C Romero-Mu˜ niz et al Figure 2. (a) X-ray diffraction patterns of the synthesized monoboride samples with partial replacement of boron by germanium (warm colors, upper part) and silicon (cold colors, lower part). The original MnB phase is plotted in black for comparison and the gray dashed vertical lines indicate the diffraction peaks of this phase. The main secondary phases are also identified and indexed for each case (see small purple bars). (b) Compositional dependence of the FeB-type phase (in weight percent) of in the synthesized MnB1−xSixand MnB1−xGexsamples. among the promising candidates, the Si and Ge substitutions with boron atoms further stand out. Additional calculations for the MnB1−xSixand MnB1−xGexsystems for various xvalues are included in tables S6 and S7 in the supplementary information but the qualitative nature of the ΣMparameter limits further insights for predicting the optimal Ge or Si content to maximize the MCE of the series. It is observed that increasing xin the ternary compositions, Msand ΣMdecrease. According to our computational approach, manganese monoborides with partial substitution of boron by semimetal atoms, like Si or Ge, are the most promising compounds to be synthesized. This is because they display an encouraging value of ΣM∼2.5 while retaining the high saturation magnetization found in the original MnB. This finding might appear counterintuitive at first glance since all the efforts made so far to tune the magnetic properties of MnB have been focused on substituting other metals for Mn [8,17–20,44]. This choice has the additional advantage that the Curie temperature will not change significantly, as it does when substituting Mn atoms for other magnetic atoms. In the next section, we experimentally explore this novel way to modify the magnetic properties of metal monoborides. 3.3. Experimental validation Based on the results of the computational screening, Mn50B50−xSixand Mn50B50−xGexsystems with x=3.125, 6.250 and 12.5 are selected for experimental validation. Their XRD results presented in figure 2(a) reveal the FeB-type crystal structure (depicted as the gray dashed lines) for x=0, the MnB compound, which is preserved after partial boron replacement by Si or Ge (check the values of new lattice parameters in figure S1(b) of supplementary information). As a result of the high chemical reactivity of Mn and B in these systems, they tend to form secondary phases when Si and Ge are added, especially in the latter case. These secondary phases are either other borides (MnB2or Mn2B) or germanides/silicides (Mn23Ge9, Mn5Ge3, Mn5Si3and MnSi). As shown in the compositional dependence of the FeB-type phase content in figure 2(b), it is clearly the majority, with over 80% content, for low Si/Ge content. However, with increasing Si and Ge contents, the proportion of secondary phases grows. See figure S1(a) for more details about proportion of secondary phases. The MCE displayed by these monoborides can be observed in figures 3(a) and (b) where the measured isothermal magnetic entropy changes of the samples are shown. They were calculated after magnetization measurements as pointed out in section 2. See figure S2 to see the M(T) curves for the different samples. The 7 J. Phys. Energy 5(2023) 024021 C Romero-Mu˜ niz et al Figure 3. The isothermal magnetic entropy change (applied field of 1 T) of the different synthetized samples with partial boron substitution by silicon (a) and germanium (b), compared to the parent compound MnB, plotted in black squares. (c) The compositional dependence of  ∆Smax isothermal values for 2 T (solid symbols) and further normalized by the FeB-type phase content results (open symbols). MnB sample (represented by black and square symbols) yields a maximum isothermal magnetic entropy change ( ∆Smax isothermal ) of 3.36 J kg−1K−1at 572 K (1 T), which amounts to 6.0 J kg−1K−1when extrapolated to 2 T using power law fits to the magnetic field dependence of |∆Sisothermal| (which was reported and verified in [45–47]). These values are similar to those reported in [8]. The influence of Si content (triangle symbols) on the MCE of Mn50B50−xSixas shown in figure 3(a) yields a non-monotonic trend: it increases to 4.31 →decreases to 3.62 →2.76 J kg−1K−1for 1 T (7.5 →6.0 →4.9 J kg−1K−1for 2 T). For xup to 6.25 in Mn50B50−xSix, the MCE is optimized compared to MnB. On the other hand, the observed non-monotonic trend in MCE of Mn50B50−xGex(circle symbols) is as follows: it raises to 3.32 →3.83 →and finally falls to 2.40 for 1 T (6.0 →6.6 →3.9 J kg−1K−1for 2 T). The enhancement in the MCE Mn50B50−xGexis less than that observed in the Si-series. The transition temperature is barely affected by the incorporation of Si or Ge. The  ∆Smax isothermal values for 2 T of the Mn50B50−xSixand Mn50B50−xGexsamples are presented as a function of xin figure 3(b). In addition, these values were further normalized by the FeB-type phase content and presented in the same figure as open symbols. This shows that, considering the response of the pure phase, Ge substitution significantly increases the MCE of the compound, while Si is less effective in that sense. 4. Conclusions In this work, we have carried out the computationally directed synthesis of new metal monoborides Mn50B50−xSixand Mn50B50−xGex. They exhibit a remarkable MCE greater than the original MnB compound while maintaining nearly the same Curie temperature, even with the presence of some secondary phases. The selection of Si and Ge as alloying elements to substitute boron was carried out following a computational screening procedure based on DFT calculations. Our theoretical selection protocol allows us to consider many candidate elements with different atomic configurations. In addition, we can carefully check each step of the selection process, discarding or suggesting target compounds for magnetocaloric applications, before carrying out the experimental synthesis of the samples, which is more expensive and time-consuming. The successful experimental confirmation of the properties predicted by our model demonstrates that it is able to provide robust selection criteria based mainly on chemical arguments. We conclude that the computationally driven synthesis of new compounds, even when following a straightforward procedure like the one presented here, is more efficient than bare trial-and-error approaches or a purely random search for new substitutional elements. In the particular case of metal monoborides, the first-principles calculations have shown that the 8