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Alena Vishina, Rebecca Clulow, Daniel Hedlund, Vitalii Shtender, Peter Svedlindh, Martin Sahlberg, Olle Eriksson, Heike C. Herper

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[MFe6X4 system (M = Mg, Sc, Zr; X = Al, Si, P, Ga, Ge, In, Sn, Sb) as possible ’gap’ magnets](https://mdr.nims.go.jp/datasets/e5895327-c8e0-4b87-987f-c623f1c82833)

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MFe6X4 system (M = Mg, Sc, Zr; X = Al, Si, P, Ga, Ge, In, Sn, Sb) aspossible ’gap’ magnetsAlena Vishinaa, Rebecca Clulowb, Daniel Hedlundc, Vitalii Shtenderb, PeterSvedlindhc, Martin Sahlbergb, Olle Erikssona,d and Heike C. HerperaaDepartment of Physics and Astronomy, Uppsala University, Box 516, SE-75120, Uppsala,Sweden; bDepartment of Chemistry - Ångström, Uppsala University, Box 538, 751 21, Uppsala,Sweden; cDepartment of Materials Science and Engineering, Uppsala University, SE-75103,Uppsala, Sweden; dSweden and Wallenberg Initiative Materials Science, WISE, UppsalaUniversity, Box 516, SE-751 20 Uppsala, SwedenARTICLE HISTORYCompiled June 18, 2025ABSTRACTLiFe6Ge4, with a theoretically predicted saturation magnetization of 1 T, a magne-tocrystalline anisotropy energy of 1.78 MJ/m3 and a Curie temperature of 620 Kwas suggested to be a promising permanent magnet as an outcome of a data-miningsearch. Magnetic measurements of the synthesized sample are reported here. Unfor-tunately, experiments revealed a weak ferromagnetic behaviour with magnetizationvalues much below that predicted by theory. This discrepancy is analyzed in detail,and is attributed to the trigonal crystal symmetry that was missed in the previouscharacterisation of the material. The correct crystal structure is R3mH (space group166) and it is found here to have an antiferromagnetic ground state, as opposed toa theoretically predicted ferromagnetic state of the previously reported monocliniccrystal structure. Theoretical calculations show that element substitution can sta-bilize a ferromagnetic state of the trigonal crystal structure, with high values ofsaturation magnetization and magnetocrystalline anisotropy. The best results areseen for the Al or Ga substitution for Ge of the LiFe6X4 compound.KEYWORDSPermanent magnets; Magnetic anisotropy; DFT; Magnetism; Rare-earth-free1. IntroductionWith the rapid growth in the number of electric vehicles and windmills required for thetransition to an electrified society and green energy solutions, there is an ever-increasingdemand for high-performance permanent magnets (PM). All the materials used inthese applications contain rare-earth (RE) elements, which are considered critical [1,2].Various materials have been investigated in an attempt to decrease the amount [3,4] ofREs or find RE-free alternatives while maintaining the necessary performance.There is also a large gap in the price-performance space between the hard ferritemagnets with their low price and low magnetization and the expensive high-performanceRE-permanent magnets [5], providing further incentive for new RE-free magneticmaterials with intermediate-performance (’gap’ magnets).When searching for materials that possess the correct magnetic properties, one shouldCorresponding author A. Vishina. Email: alena.vishina@physics.uu.selook for ferromagnetic (FM) systems with high saturation magnetization (MS), uniaxialmagnetic anisotropy with large magnetocrystalline anisotropy energy (MAE), and highCurie temperature (TC).The search for new RE-free permanent magnets is currently carried out at manylaboratories, both on experimental and theoretical fronts. Among the promising materi-als are α′′-Fe16N2 and L10-FeNi type materials [6,7], Mn-based intermetallics, such asMnBi, MnAl, MnAlGe and MnGa [8–10], Co-rich transition-metal alloys, and manymore [11]. Various computational and experimental methods have been tested, suchas high-throughput experiments [12], high-throughput computational screening [13],additive manufacturing [14], etc.The current investigation is an outcome of a high-throughput search, as described inRef. [15]. The details of the search criteria and methods were given in Refs. [16,17]. Inour data-mining approach, we filter through materials of several databases, both previ-ously synthesized (Inorganic Crystal Structure Database (ICSD) [18]) and predictedtheoretically [19]. For each entry, we calculate the required magnetic characteristics(MS , MAE, TC, etc). LiFe6Ge4 was found in the ICSD database among the materialscontaining a 3d- and a p-element of the Periodic Table [15]. It had the highest magneti-zation, magnetocrystalline anisotropy, and TC of all the promising magnetic materialsdiscovered in the investigation.Following the theoretical predictions, LiFe6Ge4 (and ZrFe6Ge4) was here synthesizedexperimentally to, firstly, attempt to reproduce the structure reported in the ICSD and,secondly, to verify the predicted magnetic properties. The experimental methods andresults are described below in detail. A discrepancy between experimental results andtheoretical predictions was observed and explained, as a different (to the ICSD entry)crystal structure was obtained in the experiment. The relative stability and propertiesof both structures were analyzed from theoretical and experimental points of view. Inaddition, substitutional alloying was further investigated theoretically to improve theproperties of the more stable crystal form.2. Computational methodsFor the high-throughput search, the full-potential linear muffin-tin orbital method(FP-LMTO) as implemented in the RSPt code [20,21] was used. The PBE functional[22] for exchange and correlation was employed. The results were obtained with thetetrahedron method with Blöchl correction for the Brillouin zone integration [23,24].Further details can be found in Ref. [15].Structure relaxations for element substitutions were performed using the ViennaAb Initio Simulation Package (VASP) [25,26] within the Projector Augmented Wave(PAW) method [27]. The formation enthalpy of a material was calculated as the energydifference between the material and the composition-weighted average of its elementalcomponents. For example:∆H[LiFe6Ge4] = ELiFe6Ge4 − ELi − 6EFe − 4EGe.Here ELi, EFe, and EGe are the energies per atom of alpha-samarium structured Li,body-centered cubic (bcc) iron, and diamond structured Ge, respectively. The resultsare given per atom for the elements and per formula unit for the compound.The magnetic anisotropy energy was obtained (using the RSPt code) as the energy2difference ∆E = Epl − Ec. Ec and Epl are the total energies calculated with themagnetization directed along and perpendicular to the crystallographic c-axis. A positivesign of the MAE corresponds to the required uniaxial anisotropy. A converged withrespect to the number of k-points Monkhorst-Pack mesh [28] of 20× 20× 20 was used.The Curie temperature TC was calculated employing Metropolis Monte Carlo (MC)and Atomistic Spin Dynamics (ASD) simulations as implemented within the UppsalaAtomistic Spin Dynamics (UppASD) software [29]. The simulations were performed ona 20×20×20 supercell with periodic boundary conditions. The exchange parameters Jijwere calculated with the RSPt code within the first seven coordination shells [30–32].For the case of LiFe6Ge5, Jijs were calculated for the experimental structure withthe spin-polarized Korringa-Kohn-Rostoker method [33,34] within the atomic sphereapproximation (ASA) as implemented in the SPR-KKR code [35]. Jijs were calculatedwithin a cluster of atoms with the radius of 2.5a.In addition, the Sumo package [36] and VESTA code [37] were utilized for visualisa-tion.3. Experimental methodsThe sample was synthesised by heating Fe6Ge4 powder with a 200 at% excess of Lithiumpieces (CEL, 99.8 %) in a tantalum tube at 1000 ◦C for 1 hour followed by 800 ◦C for 2days. Fe6Ge4 powder was initially prepared from alloying of Fe (Goodfellow, purity 99%) and Ge (Lesker, purity 99.999 %) using an arc furnace. The sample was remeltedthree times to ensure good homogeneity. Further preparation was conducted in a glovebox and sealed under inert conditions. The Ta tube was then sealed within a steel tubeto protect the vessel from oxidation at high temperature. The ZrFe6Ge4 sample wasprepared by arc melting stoichiometric quantities of Zr (Goodfellow, Purity 99.2 %), Feand Ge under an argon atmosphere. The sample was remelted three times to ensuregood homogeneity. The sample was wrapped in tantalum foil before annealing at 1000◦C in an evacuated silica tube for seven days. The phase purity and crystal structureof the compounds were analysed using powder X-ray diffraction using a Bruker D8diffractometer equipped with a lynx-eye position-sensitive detector (PSD) and Cukαradiation (λ = 1.54 Å). The data were analysed using the Rietveld refinement methodwithin the Topas 6 software program [38].Magnetic measurements were made using a Quantum Design MPMS XL system aswell as a LakeShore vibrating sample magnetometer.4. Results4.1. LiFe6Ge4 as the result of the high-throughput searchA high-throughput and data-mining search for rare-earth-free permanent magnets waspreviously performed among the materials containing a 3d and p-element of the PeriodicTable using the approach suggested in Ref. [16]. The details are given in Ref. [15]. Oneof the promising materials found was LiFe6Ge4. Its calculated saturation magnetization,magnetic anisotropy energy and Curie temperature are 1 T, 1.78 MJ/m3, and 620 K,respectively [16]. The ground state was found to be ferromagnetic. The monoclinic unitcell of LiFe6Ge4 (ICSD 100061) with C12/m1 (12) space group that was used in thetheoretical calculations is shown in Fig. B1.3Following the high-throughput investigation, LiFe6Ge4 was synthesized and itsmagnetic properties were investigated, to corroborate the theoretical findings. Asreported below, the magnetization was, unexpectedly, found to be much lower thanwhat the theory suggests [16]. The origin of this discrepancy was then explored and isfound to be caused by structural effects. Moreover, following the theoretical analysis,the structure reported in the ICSD does not seem to be valid. Two approaches werefurther pursued to enhance the magnetism: i) a theoretical element substitution on theLi and Ge sites of LiFe6Ge4 in order to improve the magnetic state; ii) the experimentalsubstitution of Li for Zr and Ge for Ga. Details of these results are also given below.4.2. Experiment: synthesis, structure, and magnetismLiFe6Ge4 was formed as the majority phase with LiFe6Ge5, Fe1.77Ge and Fe3Ge impurityphases. The X-ray diffraction pattern and Rietveld refinement are shown in Fig. B2. Theestimated phase purity for LiFe6Ge4 was approximately 90 wt% from Rietveld refinementwhilst the estimated phase fractions of LiFe6Ge5, Fe1.77Ge and Fe3Ge were 7.5, 2 and0.5 wt%, respectively . The material adopts the R3mH space group with refined unitcell parameters of a = 5.0521(1) and c = 19.6755(4) Å which is in agreement with laterworks [39] rather than the C12/m1 space group identified in earlier experiments andused in the calculations for the high-throughput search. The minor phase LiFe6Ge5is crystallographically closely related to LiFe6Ge4, the unit cell length of LiFe6Ge5 isdoubled in the c direction relative to the LiFe6Ge4 compound. The presence of theimpurity phases is potentially due to inhomogeneity or Li sublimation during weldingof the Ta reaction vessels. This was minimized through the use of a large excess of Lias previously reported in the literature and care during heating [40]. X-ray diffractionpatterns were also recorded over several days to confirm the stability of the compounds.The powder X-ray diffraction pattern of the ZrFe6Ge4 compound confirms that thematerial is isostructural to the LiFe6Ge4 compound with no evidence of a secondaryphase. The results of the Rietveld refinement are shown in Fig. B3 and the refinementgave unit cell parameters of a = 5.0763(1) and c = 20.0862(3) Å. The data arein agreement with literature data previously reported for ZrFe6Ge4 [41]. Noticeablepreferred orientation was observed in both compositions which was incorporated intothe refinement and can be ascribed to the relatively long c unit cell parameter. Fulldetails of the Rietveld refinements can be found in the tables in Appendix A.The isothermal magnetization of the LiFe6Ge4 and ZrFe6Ge4 samples was measuredat T = 10 K; the results are presented in Appendix B, Fig. B11a. Moreover, thetemperature dependent magnetization in a magnetic field of µ0H = 0.5 T was measuredbetween 300 and 1100 K to investigate the influence of impurity phases such as Fe1.77Ge,Fe3Ge and Fe. The results are presented in Appendix B, Fig. B11b. The results giveevidence of a weak ferromagnetic or ferrimagnetic behaviour with a magnetic orderingtemperature above room temperature. However, the saturated magnetization of bothsamples is disappointingly small, less than 1µB per formula unit in a magnetic fieldof 5 T, a number that is considerably smaller than the value predicted by the theory.Both samples undergo significant decomposition during the measurement due to thehigh temperatures. However, no contribution from Fe was observed in either case (thedetails can be found in Appendix B).44.3. Origin of the discrepancySince the magnetization of the synthesized Li-based compound was much smaller thantheoretically predicted [16], it was necessary to investigate the origin of the discrepancy.The cause was found to be in structural effects. The space group of LiFe6Ge4, as obtainedfrom powder X-ray diffraction, is R3mH (space group (SG) 166) [39], in contrast to theC12/m1 (space group 12) [40] (Fig. B1) used in the calculations [16]. The two crystalstructures are very closely related and their diffraction patterns are almost identical,as shown in Fig. B4. The discrepancy between the two reported structures is likelythe result of missing trigonal symmetry elements used in identifying the monocolinicC12/m1 structural model, a problem previously reported in the literature for a range ofmonoclinic materials [39].LiFe6Ge4 has been reported to form both in SG 12 and SG 166; both are listed inICSD. However, in our data-mining search [16], the latter structure was discarded dueto its weak magnetic performance. To analyze the magnetism of LiFe6Ge4 (SG 166vs SG 12) and explore the feasibility of further attempts to synthesize the material(SG 12), we calculated the total energies of the magnetic states, particularly the FMand AFM states in SG 166 and the FM state of SG 12. We found the energies ofthe two magnetic phases in SG 166 to be very close to each other, with the preferredAFM orientation of the magnetic moments. The lowest energy of all the consideredantiferromagnetic configurations lies only 4 meV/atom below the FM phase.When comparing the formation enthalpy of the two structures (SG 166 vs SG 12),the trigonal phase (SG 166) was found to be more stable, with a large energy differenceof 252 meV/atom. This number discourages further attempts to produce the materialwith SC 12, proving that the ICSD 100061 entry is likely the result of a characterizationerror.4.4. Calculations: changing the magnetic stateAs the FM state of LiFe6Ge4 in SG 12 is quite promising from the magnetic pointof view, we attempted to find a way to stabilize the ferromagnetic ground state ofLiFe6Ge4 in SG 166. Keeping in mind the ferromagnetic ground state of the monoclinicphase, changing the crystal structure was explored by varying the c/a-ratio at constantvolume. The atomic positions in the unit cell were relaxed for a range of c/a-ratios withthe experimental u.c. volume fixed (V = 145.18 Å3). It can be seen in Fig. B5 thatincreasing the a lattice parameter by just 1-2 % makes the FM state more stable thanthe AFM one. At the lattice constant value where this magnetic transition occurs, atr,the system has promising magnetization of 0.94 T and the MAE of 1.44 MJ/m3, whichconstitutes promising magnetic material for permanent magnet applications.Since the magnetic state of LiFe6Ge4 is very sensitive to the change in the c/a-ratioand since this change can be achieved by element substitution, we considered replacingGe fully with the neighbouring elements in the Periodic Table (with the exception ofAs), to pursue futther theoretical calculations. Relaxed crystal structure parameters,along with the experiential data from the current work and other available sources, arelisted in Table B1. All structures were relaxed and tested for stability by calculatingthe formation enthalpy with respect to their elemental components (for details see theComputational methods section). A more sophisticated analysis which takes into accountbinary phases was beyond the scope of the underlying high-throughput study. LiFe6X4with X= {Si, P, Sb} (space group 166) are found to be AFM, while for X = {Al, Ga,In, Sn} the preferred ground state is FM. As an example, we show the difference in5energy between the lowest in energy AFM (several AFM configurations were tested)and FM states of LiFe6Ga4 with the change in volume in Fig. B6. For each of the fourmaterials, formation enthalpy, magnetic moment, and MAE were also calculated andare listed in Table B2. The Curie temperatures are given only for the systems withlarge uniaxial MAE and a non-collinear state is noted with NC.LiFe6Al4 and LiFe6Ga4 are the most promising materials magnetically, as LiFe6Sn4 isquite low in magnetocrystalline anisotropy while LiFe6In4 has negative MAE (and is un-stable). Partial substitution was also attempted, to investigate if lower percentages weresufficient to stabilize the ferromagnetic state. LiFe6(Ge0.5Al0.5)4 and LiFe6(Ge0.5Ga0.5)4unit cells were constructed by substituting two of the Ge atoms with Al and Ga andchoosing the positions lowest in energy out of all possible combinations, see Fig. B7. Thestructures were relaxed and their magnetic properties are listed in Table B2. At 50%substitution of Al and Ga, the materials are ferromagnetic in their ground state, showinghigh magnetization and uniaxial magnetocrystalline anisotropy. Unfortunately, whenperforming finite temperature simulations with the ASD package, LiFe6(Ge0.5Al0.5)4appears to be non-collinear. Similar calculations were performed for LiFe6Ge3Ga. As canbe seen from Table B2, substituting 25% of Ge with Ga is not sufficient. Even thoughthe ground state of the material is FM, it is non-collinear at higher temperatures.Synthesis of the LiFe6(Ge0.5Ga0.5)4 and LiFe6Ga4 compounds highlighted was alsoattempted to validate these findings using the same synthesis method described above forthe LiFe6Ge4, however, the syntheses did not yield the desired phase and instead formeda mixture of LiGa, Fe3Ga; Fe3Ge and other phases. However, given the comparablecalculated values of formation enthalpy for the Ga-containing compounds, alternativesynthesis methods should be explored as part of a follow up study. [42].Trying to stabilize the FM ground state and to decrease the amount of Li in thecompound, Li substitution with Zr was tested. Replacing Li fully makes the groundstate FM and the MAE increases considerably. However, the atomistic spin-dynamicscalculations show ZrFe6Ge4 to be non-collinear at finite temperatures, see Table B2.ZrFe6Ga4 has a low TC = 15 K and loses the high value of the MAE.Replacing Fe with its neighbouring 3d magnetic elements was also attempted in thetheoretical calculations to stabilize the FM ground state. The unit cells of LiX6Ge4 (X= Mn, Co) were relaxed both in volume and a/c-ratio. Unfortunately, both materialspreserve the AFM ground state. On the other hand, replacing just one Fe with Cr orMn makes the material FM, although the ∆EFM−AFM values of -20 meV/atom and-10 meV/atom are not large enough to yield the desired high Curie temperature.In Ref. [43], another material of the same family, ScFe6Ge4 (SG 166), is reported.The authors synthesised the compound and performed magnetic measurements alongwith computational simulations of the ground state. They also suggested MgFe6Ge4 tobe a promising material, though investigated computationally only. To complement ourwork, we performed DFT calculations for the ground state of these two materials andthe ASD simulations for the higher temperatures. The results show that even thoughboth materials have high magnetization and MAE at 0 K, they show non-collinear spinstructures when ASD calculations at elevated temperatures are performed.As approximately 7% of the here synthesized Li-sample is LiFe6Ge5, we performedadditional magnetic calculations for this compound. Similar to LiFe6Ge4, ICSD suggeststwo possible crystal structures for LiFe6Ge5, namely, R3mH (SG 166) and C12/m1 (SG12). Unlike LiFe6Ge4, however, the ground states of the two structures appear to beextremely close in energy, with C12/m1 higher by 0.05 meV/u.c. only. The magneticproperties of both phases are almost the same: M166S = 0.742 T with MAE166 = 0.89MJ/m3 and M12S = 0.744 T with MAE12 = 0.93 MJ/m3. As the unit cell here is doubled6making it cumbersome to calculate the Jijs, we use the mean-field approximation forthe TC calculation, as implemented in the SPRKKR code (see the Methods section). ForLiFe6Ge5 in SG 12, a Curie temperature of 1104.7 K is obtained. The nearest-neighbourexchange interactions are strongly FM (e.g. 38 meV around 0.29a for one type of Featoms), although there are also AFM exchange couplings further away (-8.5 meV at0.46a). Similar AFM couplings cause ZrFe6Ge4 to be NC, as we show further in theDiscussion. Indeed, after performing the ASD simulations, we can see the non-collinearstructure with a small non-zero net magnetic moment (up to 0.22 µB/at.) in LiFe6Ge5at higher temperatures.5. DiscussionLiFe6Ge4 was identified as the promising candidate for PM applications in the high-throughput search. A sample was synthesized to confirm these findings with magneticmeasurements. The diffraction data revealed that the compound was isostructural,adopting the R3mH space group rather than the monoclinic C12/m1 space groupreported in the ICSD. Further analysis showed that the crystal structure reported inthe ICSD as LiFe6Ge4 with space group 12 may be the result of missed symmetryelements during earlier analysis. Our calculations show, that SG 166 is by a largemargin energetically favorable. LiFe6Ge4 (SG 166), unlike LiFe6Ge4 (SG 12), exhibitsan AFM ground state. The magnetic ground state, however, can be changed by applyingexternal pressure or by element substitution. We investigated the effect of elementreplacement on LiFe6Ge4’s magnetic properties, substituting Ge with its neighboringelements, Fe with Co and Mn, and Li with Zr, Sc, and Mg. All the crystal structureswere relaxed and their formation enthalpies were calculated. Where the experimentaldata is available, our relaxed crystal structure parameters are in good agreement withthe experimental data, see Table B1.In case of LiFe6X4, the dopants with fewer valence electrons per atom (e/a) than Gewere found to favor FM ground states, see Fig. B8. Replacing, for example, half of Ge byGa lowers the energy of the FM state relative to the AFM state by around 50 meV/atom.Adding electrons, by doping with P or Sb, has the opposite effect, i.e. the AFM orat least non-FM structures are more likely. The DFT calculations were restricted tocollinear spin configurations and the subsequent finite temperature ASD calculationsrevealed an even more complex picture, see the discussion below. Independent of thee/a of the dopant, when substituting Ge with heavier elements that have filled 4d shells,i.e. In, Sn, and Sb, the material becomes unstable, see Table B2.Since the choice of the magnetic element has a significant impact on the magneticorder, Fe substitution with Co and Mn was also tested. In both cases, the magneticground state remains AFM.The saturation magnetization and the MAE of some of the materials investigatedhere are shown in Fig. B9 as a function of the energy difference between the FMconfiguration and the lowest-energy AFM state. We can see that below ∆EFM−AFM ≈-40 meV/at, LiFe6X4 is a stable FM system, while above that energy difference thematerials show non-collinear structures at finite temperatures (according to the ASDsimulations). All the materials keep similar saturation magnetization, while the MAEvaries considerably, with the highest values observed for Al and Ge. For the magneticproperties, Ge substitutions with Al or Ga seem to be the most promising options, asthey keep the high magnetization and uniaxial magnetocrystalline anisotropy, and areferromagnetic with the TC above 800 K.7Exchange parameters Jij for LiFe6X4 (X = Al, Ga, Ge) and ZrFe6Ge4 are shownin Fig. B10. The nearest-neighbour short-distance interactions (within the Fe planes)are FM for all four materials. However, the ground state is considerably affected bythe long-distance (interplane) AFM terms. These AFM Jijs are present for the AFMmaterial LiFe6Ge4 and the NC ZrFe6Ge4 system, while they are not observed for theFM LiFe6Al4 and LiFe6Ga4. Hence, for these materials, looking at the long-distanceJijs can be a useful criterion to predict their magnetic behavior at higher temperatures.The synthesis of ScFe6Ge4 and the results from magnetic measurements in thetemperature range 3-600 K were reported in Ref.[43]. The authors also presentedthe results of their DFT structure relaxation (using VASP) and electron structureand chemical bonding calculations (applying the augmented spherical wave method).The experimental results revealed a magnetic moment considerably smaller than thetheoretical 0 K value. The authors suggest that the discrepancy may be attributed tothe polycrystalline nature of the samples. We propose an alternative explanation of thedata. In our higher-temperature ASD simulations, a non-collinear orientation of thespins is observed with a small non-zero total moment. The material was also recentlyinvestigated in Ref. [44] as a promising topological magnet, with the experimental dataand DFT calculation pointing to an AFM ground state.Magnetic properties of a hypothetical compound MgFe6Ge4 were also studied inRef. [43]. The material compound was found promising due to its negative formationenergy and FM ground state. However, we find that the material exhibits non-collinearbehaviour when ASD simulations are performed, hence, it can not be used for PMapplications.We would like to stress that the case of LiFe6Ge4 shows the importance of an extrastep being added to the high-throughput searches. For the materials reported in severalcrystal structures, the relative stability of those phases should be investigated, includingthe effect crystal structure has on the desired properties.6. ConclusionTo conclude, we discovered and explained the discrepancy between the magneticproperties of LiFe6Ge4 reported in the data-mining search [16] and experimentalmeasurements. A different crystal structure was synthesized. Further investigationsuggests that the ICSD database entry overlooks the correct crystal structure and is,hence, incorrect. This outcome suggests the necessity of an extra step being added tothe data-mining investigations, where the related crystal structures should analyzed.With its AFM ground state, LiFe6Ge4 (SG 166) can not be used for permanentmagnet applications. However, we find that elemental substitution can induce thepromising FM ground state, thus providing the desired magnetic characteristics, withthe substitution of Al or Ga for Ge providing the highest benefit.At the same time, the LiFe6Ge4 itself can be interesting to consider for otherapplications, as its magnetic ground state can be easily affected by, for example, appliedpressure or a slight change in its lattice parameters. This property has potential inmagneto-strictive applications, including magnetocalorics.87. AcknowledgementThe authors would like to acknowledge the support of the Swedish Foundation forStrategic Research, the Swedish Energy Agency, the Swedish Research Council (grantnumber 2022-03069), The Knut and Alice Wallenberg Foundation, eSSENCE, StandUp,the CSC IT Centre for Science, and the ERC (synergy grant FASTCORR, project854843), MaMMoS (EU HORIZON, project no. 101135546). O.E. also acknowledgessupport from The Wallenberg Initiative Materials Science for Sustainability (WISE)funded by the Knut and Alice Wallenberg Foundation.In addition, we acknowledge the support from the National Academic Infrastruc-ture for Supercomputing in Sweden (NAISS) for the computation resources (projectsNAISS2023/5-322, NAISS2024-5-75, and SNIC 2024/1-18).8. Competing interestsThe authors declare no competing interests.References[1] R. Skomski, J. M. D. Coey, Permanent magnetism, Institute of Physics Publishing, Bristol,UK, 1999.[2] E. 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Rietveld refinementThe refined parameters for LiFe6Ge4 and ZrFe6Ge4 are given in Table B3 and Table B4respectively.Appendix B. Experiment: magnetismIsothermal magnetization curves at 10 K of the LiFe6Ge4 and ZrFe6Ge4 samples areshown in Fig. B11. The results give evidence of a weak ferromagnetic or ferrimagneticbehaviour. However, the saturated magnetic moment of both samples is disappointinglysmall, less than 1 µB per formula unit in a magnetic field of 5 T, a number that isconsiderably smaller than the value predicted by the theory.The magnetic properties of the LiFe6Ge4 and ZrFe6Ge4 samples were also measuredin a magnetic field 0.5 T between 300 and 1100 K to investigate possible contributionsfrom impurity phases such as Fe1.77Ge, Fe3Ge and Fe. Both samples undergo significantdecomposition during the magnetometry measurements due to the high temperatures,which makes further analysis of the magnetic behavior challenging. The decompositionwas confirmed by X-ray diffraction after magnetometry measurements and differentialscanning calorimetry measurements of pristine samples following the same temperatureprotocol.The temperature dependent magnetization of the ZrFe6Ge4 sample revealed threemagnetic transition events upon warming, two of which correspond to the known Curietemperatures of Fe1.77Ge (490 K) and Fe3Ge (650 K). These phases emerge duringthe heating and were not observed in the initial X-ray diffraction measurements. Athird weaker change in magnetisation was observed at around 805 K, however, it ischallenging to identify the phase formed during this stage of the decomposition. Nocontribution from Fe was observed in the magnetometry data or in the X-ray diffractionresults. Upon cooling from 1100 K, the result from the magnetometry measurementrevealed only one magnetic transition at about 460 K, indicating single phase behaviorand complete decomposition of the ZrFe6Ge4 and Fe3Ge phases.Similarly, the LiFe6Ge4 sample underwent decomposition and Li loss during the hightemperature magnetometry. After the magnetic measurement, X-ray diffraction revealedthat the desired LiFe6Ge4 phase had entirely decomposed. However, the magnetic curvemeasured upon heating revealed two magnetic transitions (∼ 575K and ∼ 650K). Thefirst transition most probably relates to an Fe2−xGe phase [45] or a decompositionproduct, while the second transition corresponds to the Fe3Ge phase, also observed inthe ZrFe6Ge4 sample.Using results from the Rietveld refinement of the LiFe6Ge4 sample and publisheddata for the saturation magnetization at 300 K of the ferromagnetic impurity phasesFe1.77Ge (∼ 80 Am2/kg) and Fe3Ge (∼ 140 Am2/kg) [45,46], it is possible to estimatetheir contribution to the measured magnetic moment at room temperature. With 2and 0.5 wt% of Fe1.77Ge and Fe3Ge, respectively the contribution of the ferromagneticimpurity phases to the measured magnetic moment at 300 K amounts to approx 35 %.13List of FiguresB1 (Color online) The unit cell of LiFe6Ge4, space group 12. Iron atoms areshown with brown spheres, Ge atoms are small violet spheres, and Li isdenoted with large green spheres. . . . . . . . . . . . . . . . . . . . . . 16B2 Powder X-ray diffraction pattern (λ = 1.54 Å) and Rietveld refinement ofLiFe6Ge4 and LiFe6Ge5. Rwp 7.48 and χ2 3.34. The measured diffractiondata is shown in black,the calculated diffraction curve based on thestructural model in red and the difference between the calculated andmeasured data in blue. The tick marks indicate the expected peakpositions for LiFe6Ge4, LiFe6Ge5, Fe1.77Ge and Fe3Ge compounds. . . . 17B3 Powder Xray diffraction pattern (λ = 1.54 Å) and Rietveld refinementof ZrFe6Ge4. Rwp 6.86 and χ2 3.11. The measured diffraction data isshown in black,the calculated diffraction curve based on the structuralmodel in red and the difference between the calculated and measureddata in blue. The tick marks indicate the expected peak positions forZrFe6Ge4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18B4 Comparison of the simulated X-ray diffraction patterns of LiFe6Ge4generated using the R3mH and C12/m1 space groups with the observeddata for the LiFe6Ge4 sample. The black boxes highlight regions ofinterest in the diffraction pattern. . . . . . . . . . . . . . . . . . . . . . . 19B5 (Color online) The total energies of the FM and AFM states of LiFe6Ge4-166 at different values of a with a constant experimental volume of V =145.18 Å3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20B6 (Color online) The total energies of the FM and AFM states of LiFe6Ga4in SG 166 at different volumes along with the magnetic moments atminimum volume and the difference in energy between the AFM andFM minima. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21B7 (Color online) The relaxed unit cell of LiFe6Al2Ge2, space group 166.The positions of Al (yellow atoms) are chosen to minimise the energy.Iron atoms are shown with the brown spheres, Ge atoms are small violetspheres, Li is denoted by the large green spheres. . . . . . . . . . . . . . 22B8 (Color online) Energy difference for different dopants X in LiFe6X4depending on the number of valence electrons (e/a) in the dopant X.Thick blue (thin black) circles denote systems with negative (positive)formation enthalpy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23B9 (Color online) Saturation magnetization (bars) and MAE are (black dots)plotted against the difference in energy between the FM and lowest inenergy AFM states for LiFe6X4 (X = Al, Si, P, Ga, Ge, In, Sn, Sb, andcombinations thereof) and several Zn-based compounds. The bordersbetween AFM, non-collinear, and FM states are shown for the Li-basedmaterials. The AFM materials with X = Si, P, Ge are noted withsmall bars to mark their locations. Spatial distributions of the magneticmoments in the FM LiFe6(Ga0.5Ge0.5)4 and non-collinear LiFe6Ge4 at 2K (as the result of the ASD simulations) are demonstrated in the insetabove the plot. The length of the bars is proportional to the number ofFe moments with a specific orientation and c-axis is directed along θ =0 and ϕ = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2414B10 (Color online) Fe-Fe exchange parameters Jij derived from first-principlescalculation for the ferromagnetic LiFe6Al4 and LiFe6Ga4, non-collinear(in ASD) ZrFe6Ge4, and AFM LiFe6Ge4. . . . . . . . . . . . . . . . . . . 25B11 (Color online) (a) Magnetization versus magnetic field for the LiFe6Ge4and ZrFe6Ge4 samples measured at 10 K. (b) Magnetization versustemperature for the LiFe6Ge4 and ZrFe6Ge4 samples in the tempera-ture range 300 − 1000 K during heating (black symbols) and cooling(red symbols) of the samples. Note that heating during the magnetome-try measurements led to the decomposition of the samples; for details,Appendix B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2615Figure B1.: (Color online) The unit cell of LiFe6Ge4, space group 12. Iron atoms areshown with brown spheres, Ge atoms are small violet spheres, and Li is denoted withlarge green spheres.16Figure B2.: Powder X-ray diffraction pattern (λ = 1.54 Å) and Rietveld refinement ofLiFe6Ge4 and LiFe6Ge5. Rwp 7.48 and χ2 3.34. The measured diffraction data is shownin black,the calculated diffraction curve based on the structural model in red and thedifference between the calculated and measured data in blue. The tick marks indicatethe expected peak positions for LiFe6Ge4, LiFe6Ge5, Fe1.77Ge and Fe3Ge compounds.17Figure B3.: Powder Xray diffraction pattern (λ = 1.54 Å) and Rietveld refinement ofZrFe6Ge4. Rwp 6.86 and χ2 3.11. The measured diffraction data is shown in black,thecalculated diffraction curve based on the structural model in red and the differencebetween the calculated and measured data in blue. The tick marks indicate the expectedpeak positions for ZrFe6Ge4.181 2 3 4 5 6Intensity (a.u.)Q  ( Å - 1 ) C 1 2 / m 1 R 3 m H O b s e r v e dFigure B4.: Comparison of the simulated X-ray diffraction patterns of LiFe6Ge4 gener-ated using the R3mH and C12/m1 space groups with the observed data for the LiFe6Ge4sample. The black boxes highlight regions of interest in the diffraction pattern.19Figure B5.: (Color online) The total energies of the FM and AFM states of LiFe6Ge4-166at different values of a with a constant experimental volume of V = 145.18 Å3.20Figure B6.: (Color online) The total energies of the FM and AFM states of LiFe6Ga4in SG 166 at different volumes along with the magnetic moments at minimum volumeand the difference in energy between the AFM and FM minima.21Figure B7.: (Color online) The relaxed unit cell of LiFe6Al2Ge2, space group 166. Thepositions of Al (yellow atoms) are chosen to minimise the energy. Iron atoms are shownwith the brown spheres, Ge atoms are small violet spheres, Li is denoted by the largegreen spheres.22Figure B8.: (Color online) Energy difference for different dopants X in LiFe6X4 dependingon the number of valence electrons (e/a) in the dopant X. Thick blue (thin black) circlesdenote systems with negative (positive) formation enthalpy.23Figure B9.: (Color online) Saturation magnetization (bars) and MAE are (black dots)plotted against the difference in energy between the FM and lowest in energy AFMstates for LiFe6X4 (X = Al, Si, P, Ga, Ge, In, Sn, Sb, and combinations thereof) andseveral Zn-based compounds. The borders between AFM, non-collinear, and FM statesare shown for the Li-based materials. The AFM materials with X = Si, P, Ge are notedwith small bars to mark their locations. Spatial distributions of the magnetic momentsin the FM LiFe6(Ga0.5Ge0.5)4 and non-collinear LiFe6Ge4 at 2 K (as the result of theASD simulations) are demonstrated in the inset above the plot. The length of the barsis proportional to the number of Fe moments with a specific orientation and c-axis isdirected along θ = 0 and ϕ = 0.24Figure B10.: (Color online) Fe-Fe exchange parameters Jij derived from first-principlescalculation for the ferromagnetic LiFe6Al4 and LiFe6Ga4, non-collinear (in ASD)ZrFe6Ge4, and AFM LiFe6Ge4.25Figure B11.: (Color online) (a) Magnetization versus magnetic field for the LiFe6Ge4and ZrFe6Ge4 samples measured at 10 K. (b) Magnetization versus temperature forthe LiFe6Ge4 and ZrFe6Ge4 samples in the temperature range 300 − 1000 K duringheating (black symbols) and cooling (red symbols) of the samples. Note that heatingduring the magnetometry measurements led to the decomposition of the samples; fordetails, Appendix B.26List of TablesB1 Calculated and experimental lattice parameters for LiFe6Ge4-type com-pounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28B2 Magnetic ground state, calculated saturation magnetization, MAE, Curietemperature (calculated with ASD), formation enthalpy, and the energydifference between the FM and AFM states for LiFe6X4 (X = Al, Si, Ga,Ge, Ga/Ge, In, Sn, and Sb) and ZrFe6Z4 (Z = Ga and Ge), ScFe6Ge4,and MgFe6Ge4. NC stands for the non-collinear magnetic structure. . . . 29B3 Refined parameters for LiFe6Ge4 derived from powder X-ray diffractiondata and Rietveld refinement. . . . . . . . . . . . . . . . . . . . . . . . . 30B4 Refined parameters for ZrFe6Ge4 derived from powder X-ray diffractiondata and Rietveld refinement. . . . . . . . . . . . . . . . . . . . . . . . . 3127Table B1.: Calculated and experimental lattice parameters for LiFe6Ge4-type com-pounds.Material a c V ReferenceÅ Å Å3LiFe6Al4 5.017 19.67 429.0 current work (calc)LiFe6Si4 4.879 18.87 389.0 current work (calc)LiFe6P4 4.877 18.03 371.3 current work (calc)LiFe6Ga4 5.040 19.66 432.4 current work (calc)LiFe6Ge4 5.0521(1) 19.6755(4) 434.915(17) current work (exp)LiFe6Ge4 5.045 19.66 433.4 [39,40]LiFe6(Ge0.5Al0.5)4 4.995 19.77 427.2 current work (calc)LiFe6(Ge0.5Ga0.5)4 5.007 19.74 428.6 current work (calc)LiFe6Ge3Ga 5.026 19.62 429.2 current work (calc)LiFe6In4 5.379 20.95 525.0 current work (calc)LiFe6Sn4 5.375 20.76 519.4 current work (calc)LiFe6Sb4 current work (calc)ZrFe6Ge4 5.061 20.19 447.9 current work (calc)ZrFe6Ge4 5.0763(1) 20.0862(3) 448.245(14) current work (exp)ZrFe6Ge4 5.073 20.10 448.0 [47]ZrFe6Ga4 5.061 20.17 447.5 current work (calc)ScFe6Ge4 5.055 20.02 443.1 current work (calc)ScFe6Ge4 5.066 20.01 444.8 [48]ScFe6Ge4 5.079 20.01 447.0 [43]MgFe6Ge4 5.065 19.86 441.3 current work (calc)28Table B2.: Magnetic ground state, calculated saturation magnetization, MAE, Curietemperature (calculated with ASD), formation enthalpy, and the energy differencebetween the FM and AFM states for LiFe6X4 (X = Al, Si, Ga, Ge, Ga/Ge, In, Sn,and Sb) and ZrFe6Z4 (Z = Ga and Ge), ScFe6Ge4, and MgFe6Ge4. NC stands for thenon-collinear magnetic structure.Material Ground MS MAE TC ∆H ∆EFM−AFMstate T MJ/m3 K meV/at meV/atLiFe6Al4 FM 0.92 1.11 850 -155.5 -46LiFe6Si4 AFM -361.7 +4LiFe6P4 AFM -373.1 +2LiFe6Ga4 FM 0.95 0.68 885 -120.9 -45LiFe6Ge4 AFM +5LiFe6(Ge0.5Al0.5)4 FM 0.88 1.75 NC -205.7 -35LiFe6(Ge0.5Ga0.5)4 FM 0.89 1.09 820 -157.6 -50LiFe6Ge3Ga FM 0.93 1.27 NC -197.5 -18LiFe6In4 FM 0.87 -0.83 730 98 -55LiFe6Sn4 FM 0.86 0.39 NC 51.4 -16LiFe6Sb4 AFM 47.5 +3ZrFe6Ge4 FM 1.05 2.71 NC -92.4 -44ZrFe6Ga4 FM 0.99 0.79 15 -37ScFe6Ge4 FM 1.00 1.87 NC -263.9 -67MgFe6Ge4 FM 0.93 1.87 NC -110.1 -7029Table B3.: Refined parameters for LiFe6Ge4 derived from powder X-ray diffraction dataand Rietveld refinement.Atom Wyckoff Position x y z Occupancy beqLi 3a 0 0 0 1 1Fe 18h 0.4992(3) -0.4992(3) 0.1047(1) 1 3.971(75)Ge1 6c 0 0 0.1259(2) 1 2.931(91)Ge2 6c 0 0 0.3316(2) 1 2.931(91)30Table B4.: Refined parameters for ZrFe6Ge4 derived from powder X-ray diffraction dataand Rietveld refinement.Atom Wyckoff Position x y z Occupancy beqZr 3a 0 0 0 1 0.970(57)Fe 18h 0.4965(3) -0.4965(3) 0.1025(1) 1 1.754(42)Ge1 6c 0 0 0.1318(9) 1 0.904(35)Ge2 6c 0 0 0.3328(9) 1 0.904(35)31