Calculation for High Pressure Behaviour of Potential Solar Cell Materials Cu 2 FeSnS 4 and Cu 2 MnSnS 4

: Exploring alternatives to the Cu 2 ZnSnS 4 kesterite solar cell absorber, we have calculated ﬁrst principle enthalpies of different plausible structural models (kesterite, stannite, P ¯4 and GeSb type) for Cu 2 FeSnS 4 and Cu 2 MnSnS 4 to identify low and high pressure phases. Due to the magnetic nature of Fe and Mn atoms we included a ferromagnetic (FM) and anti-ferromagnetic (AM) phase for each structural model. For Cu 2 FeSnS 4 we predict the following transitions: P ¯4 (AM) 16.3 GPa −−−−−→ GeSb type (AM) 23.0 GPa −−−−−→ GeSb type (FM). At the ﬁrst transition the electronic structure changes from semi-conducting to metallic and remains metallic throughout the second transition. For Cu 2 MnSnS 4 , we predict a direct AM (kesterite) to FM (GeSb-type) transitions at somewhat lower pressure (12.1 GPa). The GeSb-type structure also shows metallic behaviour.


Introduction
The impending exhaustion of fossil fuel has prompted the exploration and exploitation of alternative energy resources, with the solar energy harvesting through photovoltaic devices spearheading these efforts. In an attempt to overcome the restraints of Si-based materials, the direct optical band gap of chalcogenide-based solar cells offers the benefit of higher absorption in comparison to silicon. Given that the employed chalcogenides are composed of multiple elements, one can additionally optimise the photovoltaic properties of the respective material by appropriate metal or chalcogenide substitution. Among the various chalcogenides investigated for this purpose, the quaternary semiconductor Cu 2 ZnSnS 4 has attracted considerable attention [1,2]. The suitability of this material for solar cell applications stems from its almost optimal band gap (E g ≈ 1.5 eV), its high absorption coefficient in the visible range, and its earth-abundant, low-cost, and non-toxic constituents [3][4][5] . In a previous experimental and theoretical study on Cu 2 ZnSnS 4 we have investigated the high pressure behaviour to probe its reaction to tensile stress [6]. One of the biggest issues with Cu 2 ZnSnS 4 is that it suffers from Cu-Zn cationic disorder [7]. The main reason why Cu and Zn can be interchanged easily is their similar ionic radius. The analogues Cu 2 FeSnS 4 and Cu 2 MnSnS 4 have similarly favourable properties for use as a solar cell absorber. We expect cationic disorder to be less present due to the bigger difference in size of Fe and Mn in comparison to Cu. In this work, we want use density functionalbased (DFT) first principle methods to investigate how Cu 2 FeSnS 4 and Cu 2 MnSnS 4 behave under tensile stress to understand the physical limitation of those materials.

Calculation Set-Up
The periodic density functional theory (DFT) calculations were performed with VASP 5.4.4 [8][9][10][11]. A plane wave basis set with an energy cutoff of 550 eV with the projector augmented (PAW) potentials [12,13] was used, whereby the 5s, 5p and 4d electrons of Sn, 3s, 3p electrons of S, and 4s, 3d electrons of Cu, Fe and Mn were explicitly considered. The electronic convergence criteria was set at least to 10 −5 eV, whereby the Blocked-Davidson algorithm was applied as implemented in VASP. The structural relaxation of internal and external lattice parameters was set to a force convergence of 10 −2 eV/Å 2 while the conjugate-gradient algorithm implemented in VASP was used [14]. The freedom of spin polarisation was enabled and a Gaussian smearing approach with a smearing factor σ of 0.01 eV was utilised. For all structures we simulated 16 atoms which corresponds to the number of atoms in the kesterite unit cell. The cells were fully optimised with a 8 × 8 × 4 k-grid constructed via the Monkhorst-Pack scheme [15] and centered at the Γ-point with the PBE functional [16]. The cells include two magnetic ions (Fe or Mn) which can be arranged in two different magnetic phases, ferromagnetic (FM) with parallel magnetic moments and anti-ferromagnetic (AM) with antiparallel ones. On top of the PBE-optimised structures, single point calculations for the band gap and DOS with the HSE06-functional [17][18][19][20] were performed with a 4 × 4 × 2 k-grid to account for an accurate electronic structure. The tetrahedron method with Blöchl corrections [21] was applied for band structure evaluation.
The pressure dependence was determined by selecting volume points in a range of about 50 Å 3 below the minima. This corresponds to a pressure range of 0-30 GPa. We used a step size of 8 Å 3 which lead to at least 10 volume points for each structural model. At each point we optimised the ionic positions and cell shape, while keeping the volume constant. We fitted the total energy versus volume to a Birch-Murnaghan Equation of State (B-M EoS) [22]. Then the pressure at each volume was obtained from the P(V) formulation of the same EoS (for details see Appendix A.3). Using the pressure we calculated the enthalpies (H(P) = E + PV) for each structural model and compared them over the investigated pressure range to identify the most stable structures.
All energy and enthalpy differences between different structural models in the following refer to the KS unit cell size, hence to two formula units.

Structural Models
In quaternary chalcogenide semiconductors the equilibrium structure at ambient pressures in most cases are kesterite (KS, Figure 1a) or stannite (ST, Figure 1b) structures [23,24]. We include both structures as potential low pressure phases for Cu 2 FeSnS 4 and Cu 2 MnSnS 4 . Please note that in the cited work by Schorr et al. [23] besides KS and ST also three disordered structures are suggested which are very unlikely to occur in our systems due to the different ionic radii of the involved elements. In our high pressure study on Cu 2 ZnSnS 4 we found the distorted rocksalt structure (GeSb, Figure 1c) to be the most stable phase beyond 16 GPa [6]. Therefore we include GeSb as a high pressure phase in this study. We also include a tetragonal P4 structure (Figure 1d), which is discussed in literature as the thermodynamically most stable structure for Cu 2 FeSnS 4 [25][26][27].
KS, ST and P4 have a coordination number of 4, due to the same structural motif, they are close in formation energy and which structure forms depends on the crystallisation conditions. Unless the crystallisation is done carefully to enable the formation of the thermodynamic equilibrium the crystallisation process is kinetically driven, which we can not simulate in our DFT calculations. The high pressure phase GeSb has a coordination number of 6. Transitioning from a four to a six-fold coordination is a massive structural change associated with a large difference in the energy of formation. Due to the large energy difference, we can describe the pressure induced transition well in DFT.

Equilibrium Structures
Before discussing the enthalpies we will review the equilibrium structures at zero pressure of Cu 2 FeSnS 4 and Cu 2 MnSnS 4 , obtained at the PBE level (Table 1) and compare to published crystal structures. XRD (X-ray diffraction) analysis by Brockway dating back to 1934 revealed that natural Cu 2 FeSnS 4 samples crystallise in ST structure [28]. Those results where subsequently confirmed in the 1970s by Ganiel et al., they furthermore studied the magnetic ordering via Mössbauer spectroscopy and found that it was anti-ferromagnetic [29]. In 1972 Springer studied the solution series Cu 2 Fe 1−x Zn x SnS 4 . Beyond x = 0.4 and above 680 • C he observed an ST crystal structure he labeled β-Cu 2 (Fe/Zn)SnS 4 . Below x = 0.4 and 680 • C he found another tetragonal phase he labeled α-Cu 2 (Fe/Zn)SnS 4 [25,30]. In 2000 pure α-Cu 2 FeSnS 4 was synthesised [26]. After the solid state reaction of CuFeS 2 on SnS at 1323 K in sealed graphite crucible for 24 h the product was cooled slowly over 50 h. Through the slow cooling they obtained the thermodynamically most stable αphase. Through XRD measurements the space group of the sample was determined to be P4 [26]. Those results where confirmed by Rincon et al. who furthermore studied the magnetic susceptibility and revealed that also α-Cu 2 FeSnS 4 exhibits an anti-ferromagnetic ordering [27]. Exp. [27,29] Our PBE results for Cu 2 FeSnS 4 agree very well with the experiments. We found the anti-ferromagnetic P4 (corresponding to α-Cu 2 FeSnS 4 ) structure to be most stable (Table 1). But it is only 22 meV more stable than the naturally occurring anti-ferromagnetic ST structure. The anti-ferromagnetic KS structure is another 100 meV above the antiferromagnetic ST structure. The small energy difference between ST and P4 may give an explanation why the P4 phase is hard to obtain in pure form. From the experimental results we conclude that the formation of the ST phase has to be kinetically favoured. This aspect dominates the crystallisation process if the samples are rapidly cooled. We expect the thermodynamic equilibrium to build up slowly based on the small energy difference between the P4 and ST structures, hence slow cooling is crucial to obtain α-Cu 2 FeSnS 4 . In agreement with the experimental data we find the anti-ferromagnetic ordering favoured over the ferromagnetic ordering by 82 meV and 152 meV, for ST and P4, respectively. The PBE lattice parameter for both Cu 2 FeSnS 4 phases agree reasonably well with the XRD experiments. The lattice parameters change only slightly between the magnetic phases and are within the error bars of the functional applied.
Our PBE prediction for the most stable structure for Cu 2 MnSnS 4 does not agree with experimental results. Magnetisation and neutron-diffraction measurements have shown that Cu 2 MnSnS 4 has an anti-ferromagnetic ST structure [31]. We predict the antiferromagnetic KS structure to be 35 meV more stable ( Table 2). We also tested the P4 structure and found it to be the least stable anti-ferromagnetic and ferromagnetic structure. The anti-ferromagnetic P4 structure is 17 meV less stable than the anti-ferromagnetic ST phase at the PBE level. Our results on the relative KS and ST stability agree closely with PBEsol calculations by Scragg et al [32]. The same group has also carried out HSE06 calculations and found the ST structure to be more stable than the KS structure. The difference is only 15 meV per unit cell. The error in the lattice constants of the PBE calculations is in the range of the differences between the structures and magnetic phases. The PBE lattice constants for Cu 2 MnSnS 4 show subtle interplay between magnetism and structure but all of them are close to the experimental lattice parameter of ST (AM). In contrast to the KS equilibrium structure of Cu 2 ZnSnS 4 , the compounds Cu 2 FeSnS 4 and Cu 2 MnSnS 4 experimentally favour a ST and/or P4 structure. The ST and P4 structures are group theoretically related, both structures exhibit similar cationic layers. We can rationalise the formation of ST and or P4 structures over KS by comparing the ionic crystal radii (defined according to Fumi and Tosi [33]) of the substituted bivalent elements (Zn, Fe and Mn) in chalcogenides determinded by Shannon [34].
Cu 2 ZnSnS 4 in the KS structure consists of Cu + -Zn 2+ layers and Cu + -Sn 4+ layers. The crystal radius of Zn 2+ (r c = 0.60 Å) is identical to the crystal radius of Cu + (r c = 0.60 Å), which allows them to fit in the same layer. If we replace Zn 2+ with the larger Fe 2+ (r c = 0.63 Å) or Mn 2+ (r c = 0.66 Å), a ST or P4 structure is formed. In those structures pure Cu + layers alternate with Sn 4+ -Fe 2+ /Mn 2+ layers. Like this the largest and the smallest ion (Sn 4+ , r c = 0.55 Å) are paired in one layer. In a KS structure the large bivalent cation would have to be in the same layer as the second largest Cu + ion. We suspect that this is the main reason which drives the formation of the ST and/or P4 structures for the magnetic derivates.
In contrast to Cu 2 FeSnS 4 , we do not find the ST structure to be more stable than KS in our calculations for Cu 2 MnSnS 4 , although Mn 2+ has an even larger ionic crystal radius than Fe 2+ . We found that PBE fails do describe the electron density around Mn 2+ , the charge is more smeared out than for Fe 2+ which leads to larger positive charge at Mn (for details see Table A3 in Appendix A.1).
The PBE lattice parameter a and c of the ST and P4 structure (2c for the P4 structure) for Cu 2 FeSnS 4 differ by less than 0.1 %. The differences in Cu 2 MnSnS 4 of a and c between ST and KS are larger, particularly in c where the difference is 2 %. We think that the reason must be the different composition of the cationic layers. If we compare the ST structures of both materials, we find that the size of the lattice parameters corresponds to the crystal radius of the bivalent cation. All presented structures for Cu 2 FeSnS 4 and Cu 2 MnSnS 4 have lattice parameter within 2 % of the values for the Cu 2 MnSnS 4 KS (5.485 Å and 10.94 Å [23]).

Pressure-Dependent Enthalpies
If we plot and compare the enthalpies for Cu 2 FeSnS 4 ( Figure 2a,b) we find the antiferromagentic P4 structure to be most stable up to 16.3 GPa. Throughout this pressure range the anti-ferromagentic ST structures is only 22 to 40 meV less stable. The anti-ferromagentic KS structure is even less stable than the ferromagnetic ST structure which is about 100 meV above the P4 structure. The energy splitting between AM and FM increases from the KS over the ST to the P4 structure. As a consequence the ferromagnetic P4 structure is as unstable as the ferromagnetic KS structure in the investigated pressure range. At 16.3 GPa, we find a transition from the P4 structure to the GeSb structure. Its purely a structural transition, the magnetic phase remains anti-ferromagnetic. The cell volume decreases by 13% (Table 3) through the transition. At 23.0 GPa we predict a magnetic phase transition of GeSb to ferromagnetic. The energy difference between the two different magnetic phases is very small, at the structural transition pressure it is 15 meV and decreases up to the magnetic transition pressure. Afterwards it increases again, but the difference remains small, at 25 GPa it amounts to 75 meV. The anti-ferromagnetic modification for KS and ST is more stable than the ferromagnetic modification over the whole pressure range. As pointed out for the equilibrium structures, the anti-ferromagnetic P4 structure and the ST structure can be observed experimentally, depending on the preparation method. Due to the small energy difference between both structures also at the transition pressure, we predict that an ST-to-GeSb transition would also appear at a very similar pressure as the P4-to-GeSb transition.   [6] 16.0 KS → GeSb 280 240 −15.2% The enthalpy for Cu 2 MnSnS 4 (Figure 3a,b) indicates that anti-ferromagnetic KS is most stable at ambient conditions and up to 12.1 GPa, where we predict a KS-to-GeSb phase transition. The structural phase transition is accompanied by a magnetic phase transition from anti-ferromagnetic to ferromagnetic. The cell volume decreases by 14% (Table 3) through the transition. At the transition pressure the ferromagnetic GeSb modification is 66 meV more stable than the anti-ferromagnetic modification. With increasing pressure the difference is nearly constant, at 20 GPa it amounts to 73 meV. For the KS structure the antiferromagnetic modification remains more stable than the ferromagnetic modification by over 40 meV throughout the whole pressure range. For the ST structure the ferromagnetic modification becomes more stable around 12 GPa. The difference between both magnetic phases is much lower than for KS and remains below 20 meV throughout the whole pressure range. The anti-ferromagnetic P4 has a very similar stability as the ferromagnetic ST structure. The splitting between AM and FM is the largest, rendering the ferromagnetic P4 structure the least stable through the whole pressure range. As pointed out above, the relative stability of KS and ST is wrong at the PBE level. Over the whole pressure range the difference in energy between KS and ST stays below 50 meV. In comparison to the energy change induced by the structural phase transition (already 1 eV at 5 GPa above phase transition), this energy difference is small. That is why we think we can still predict a phase transition around 12 GPa. But experimentally we expect a ST(AM)-to-GeSb(FM) transition instead of the KS-to-GeSb phase transition our calculations suggest.

Electronic Structure
We investigated the electronic band structure for equilibrium and high-pressure structures for both compounds at the equilibrium and at the transition pressure with the HSE06 hybrid functional [17].
For Cu 2 FeSnS 4 , we predicted the band gap of the anti-ferromagnetic ST structure to be 1.3 eV (Table 4). Based on absorption spectra, the band gap was determined to be 1.6 eV [35]. We think that the difference from our prediction is largely due to the fact that we only optimised our structures at the PBE level but also partly due to the error of the HSE06 functional in reproducing band gaps. In an earlier study within our group we obtained similar results for Cu 2 ZnSnS 4 KS. Experimentally the Cu 2 ZnSnS 4 KS band gap is determined to be 1.5 eV [6]. The HSE06 band gap for the PBE optimised structure is 1.2 eV. Only if the structure is also optimised at the HSE06 level, we obtain the experimental band gap [36]. The HSE06 band gap deviation for Cu 2 ZnSnS 4 of the PBE structure is −0.3 eV. We expect it to have similar magnitude for Cu 2 FeSnS 4 and Cu 2 MnSnS 4 . The HSE06 band gap for the most stable anti-ferromagnetic P4 structure of Cu 2 FeSnS 4 is 1 eV. For P4 and ST Cu 2 FeSnS 4 the anti-ferromagnetic modification has an 0.2 and 0.3 eV larger band gap than the ferromagnetic modification.
For Cu 2 MnSnS 4 we predicted an equilibrium band gap for ST of 1.1 eV (Table 4). Experimental measurements by Raudsich et al. of Cu 2 MnSnS 4 indicate a band gap of 1.42 to 1.79 eV. All measured samples contained Cu 2 MnSn 3 S 8 as a secondary phase. They also calculated the band gap at the HSE06 level which they reported to be 1.5 eV. Again the deviation to our result must be due to the fact that they also carried out the optimisation at the HSE06 level while we restricted ourselves to PBE optimisations.
To understand the change of the electronic structures under pressure, we also calculated the DOS at the transition pressures for both systems. For the P4 structure of Cu 2 FeSnS 4 at the transition pressure the band gap is widened to 1.4 eV (Figure 4). For the naturally occurring ST structure (AM) the band gap is widened to 1.5 eV (for DOS see Appendix A.4.2). After the transition to the anti-ferromagnetic GeSb structure the band gap closes completely. In the DOS plot for anti-ferromagnetic GeSb at the transition pressure we can see that all bands from the valence band now extend in the region from 0 eV to 1.5 eV which is the band gap region for the P4 structure. Thus we predict a change from semi-conducting to metallic behaviour. The band gap stays zero with the second magnetic transition from anti-ferromagnetic to ferromagnetic.
For Cu 2 MnSnS 4 we find the same behaviour concerning the electronic structure at the transition pressure, a closing of the gap and a metallic character above the transition pressure ( Figure 4). During the structural transition, the magnetic structure changes from AM to FM. We are confident that this also holds for the ST (AM) to GeSb (FM) transition we expect based on the observation that the experimental equilibrium structure for Cu 2 MnSnS 4 is the anti-ferromagnetic ST structure. To verify this assumption we also calculated the DOS for ST at the transition pressure, its band gap is 1.2 eV (for DOS see Appendix A.4.2). This confirms that also for the ST (AM) to GeSb (FM) transition the electronic structure would change from semi-conducting to metallic.
Both materials show similar electronic structure changes at the transition pressure as Cu 2 ZnSnS 4 , which changes from semi-conducting to metallic at 16 GPa (for details see Appendix A.4.2). Energies (eV)

Mechanical Properties
Finally we want to analyse how the bulk modulus changes due to the phase transitions in the magnetic materials Cu 2 FeSnS 4 and Cu 2 MnSnS 4 and compare to Cu 2 ZnSnS 4 . In the used equation of states the equilibrium volume, the bulk modulus and its pressure dependence are fit parameters.
First of all it strikes that regardless of the composition all tetragonal anti-ferromagnetic structures (KS, ST or P4) have very similar bulk moduli ranging within 2 GPa around the value for Cu 2 ZnSnS 4 KS ( Table 5). The first derivative B 0 shows larger differences, the values for Cu 2 FeSnS 4 and Cu 2 MnSnS 4 are 7 % and 10 % lower than for the KS Cu 2 ZnSnS 4 material. Without an error analysis we can not determine whether the differences in B 0 are significant. At zero pressure the P4 (AM) structure of Cu 2 FeSnS 4 has a higher bulk modulus than the ST (AM) structure, but at higher pressures eventually it flips due to the larger first derivative for the ST (AM) structure. If we compare the same structure ST(AM) for all three materials, the bulk modulus of Mn over Zn to Fe are slightly increasing, but only in a range where it would not be measurable experimentally. All bulk moduli for the anti-ferromagnetic GeSb structures are in the range of 77.8-85.8 GPa, thus each about 15 % larger than their tetragonal counterparts. In all cases the phase transition leads to stiffer materials. The bulk modulus of GeSb is smallest for Cu 2 MnSnS 4 (AM), followed by Cu 2 ZnSnS 4 and largest for Cu 2 FeSnS 4 (AM). This is the same ordering we observe for the ST (AM) phases.

Conclusions
We calculated first principle enthalpies with PBE for different structural models for Cu 2 FeSnS 4 and Cu 2 MnSnS 4 to identify low and high-pressure modifications. Thereby, we probed ferromagnetic and anti-ferromagnetic phases.
In agreement with experimental findings, we found the anti-ferromagnetic P4 structure to be the most stable for Cu 2 FeSnS 4 at ambient pressure. We additionally confirmed that the naturally occurring ST (AM) is nearly as stable until the following transition. At 16.3 GPa, we predict a structural transition to the anti-ferromagnetic GeSb structure, thereby, the coordination number of the metal ions changes from 4 to 6. The structural transition is accompanied by a change of the electronic structure from semi-conducting to metallic. At 23.0 GPa, we found a magnetic phase transition from anti-ferromagnetic to ferromagnetic, the electronic structure remains metallic.
Due to the deficits of the used density functional, we failed to identify the correct equilibrium structure for Cu 2 MnSnS 4 . All possible low pressure phases are in a small energy window, and PBE predicts the KS (AM) structure as most stable. Experimental data and HSE06 optimisations indicate that anti-ferromagnetic ST structure is present under ambient conditions. At the HS06 level the difference is only 15 meV per unit cell [32], and also at the PBE level the difference is small (under 50 meV over the whole pressure range). All four-fold coordinated anti-ferromagnetic structures show a structural and magnetic phase transition to GeSb (FM) around 12 GPa. This transition also leads to a change of the electronic structure from semi-conducting to metallic.
The results for both materials are similar to our findings for Cu 2 ZnSnS 4 , where we observe a KS-to-GeSb transition around 16 GPa [6]. Also in Cu 2 ZnSnS 4 this transition leads to a change of the electronic structure from semi-conducting to metallic. Only taking into account the band gaps and the predicted transition pressures, we conclude that the magnetic material Cu 2 FeSnS 4 is similarly suited for the use in thin film solar cells as Cu 2 ZnSnS 4 . Cu 2 MnSnS 4 also has a band gap in the desired range for a solar cell absorber but is less resistant against tensile stress than Cu 2 ZnSnS 4 and Cu 2 FeSnS 4 .

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript: DFT density functional theory KS kesterite ST stannite AM anti-ferromagnetic FM ferromagnetic XRD x-ray diffraction DOS density of states Appendix A.

Appendix A.1. Equilibrium Optimisations
To understand why PBE predicts the correct stability of the equilibrium structures for Cu 2 FeSnS 4 but not for Cu 2 MnSnS 4 we calculated the Bader charges [37] at the PBE (fully optimised) and HSE06 level (only single point calculation on top of PBE structure) for anti-ferromagnetic KS and ST (Table A3).
We can see that for both materials and structures PBE assigns about 0.2 e − less electron density than HSE06 to Fe or Mn ions. If we look closer we can see that the difference for Mn is slightly smaller than for Fe. It is −0.16 and −0.17 e − for KS and ST respectively, while it is −0.19 e − for Fe in KS and ST. That means that in PBE the charge is a little more smeared out with reference to the HSE06 charge in Cu 2 MnSnS 4 compared to Cu 2 FeSnS 4 . We suspect that this is the reason for the stabilisation of KS over ST at the PBE level. Table A1. Optimized lattice parameter a and c (in Å) for Cu 2 FeSnS 4 for the listed structural (Struc.) models and magnetic (Mag.) phases at the PBE level of theory. µ Fe refers to the magnitude of the magnetic moment at Fe (in µ B ) and E tot denotes the total energy (in eV). For GeSb and P4 the lenght of 2c is listed for better comparison.

Struc.
Mag Appendix A.2. Volume Scan Data Table A4. Optimized lattice parameter a and c (in Å) for Cu 2 FeSnS 4 for the listed structural (Struc.) models and magnetic (Mag.) phases with the given volume V (in Å 3 ) at the PBE level of theory.
µ Fe refers to the magnitude of the magnetic moment at Fe (in µ B ) and E tot denotes the total energy (in eV). For GeSb and P4 the lenght of 2c is listed for better comparison.

Struc
. E 0 denotes the energy per unit cell at zero pressure, B 0 the bulk modulus at zero pressure, V 0 the reference volume at zero pressure; B 0 , pressure derivative of the bulk modulus at zero pressure. The corresponding Birch-Murnaghan pressure function can be calculated as follows:  Figure A1) we can see that the differences are small in the total DOS. In all three materials the valence band is dominated by the Cu 3d and S 3p bands. In the magnetic materials additionally the 3d bands of Fe and Mn contribute significantly to the valence band, but their DOS is much smaller than for Cu and S bands. The conduction band for Cu 2 ZnSnS 4 KS and ST is dominated by the Sn 5s and the S 3p bands. In Cu 2 FeSnS 4 and Cu 2 MnSnS 4 this also holds true. In the magnetic materials additionally the 3d bands of Fe and Mn contribute significantly to the conduction band. The DOS of the P4 symmetric structure for Cu 2 FeSnS 4 looks nearly identical to the ST (AM) DOS, which is not surprising because they have a very similar structure (same cationic layers). Comparing the DOS of both magnetic materials to their parent Cu 2 ZnSnS 4 KS material DOS ( Figure A3), we find that also in Cu 2 ZnSnS 4 the former band gap region (0 to 2 eV) in GeSb consist of the same bands as the valence band. The most striking difference is that in Cu 2 ZnSnS 4 GeSb the former band gap region has two dedicated peaks at 0.6 and 1.6 eV, while in the magnetic cases the DOS amplitude stays relatively constant throughout the whole band gap region.