Magnetocaloric Effect in Lightly‐Doped Fe5Si3 Single Crystals

Development of promising new materials for above room temperature magnetic cooling applications relies on careful balancing of structure and composition to maximize accessible metastable phases that can drive a strong magnetocaloric effect (MCE). However, the working temperatures of these materials may fall outside of desired application windows. In this work, it is shown that it is possible to control metastable phase stability temperatures of Fe5Si3 through selection of appropriate spin and charge doping. Here, the parent material's desired structure appears only within a narrow temperature range from 1098 to 1303 K. Doping with Mn and P is shown to allow stabilization of the parent's high temperature phase and resulting MCE to room temperature. The structural and magnetic properties, and the magnetocaloric effect of single crystal Fe4.83Mn0.16Si2.91P0.09 (FMSP) are investigated experimentally and theoretically. A first‐order magneto‐elastic transition is observed at 348 K, where magnetic onset is accompanied by a change in lattice volume without an apparent change in crystal symmetry. Although the trace Mn and P doping are found to decrease the TC, the maximum magnetic entropy change ΔSMax(T) and the relative cooling power (RCP) of FMSP are enhanced compared to polycrystalline Fe5Si3. As a result, an intrinsically broader entropy change over a larger temperature span is generated in the lightly doped single crystal of Fe5Si3. The magnetic moment of the system is also enhanced. Density functional theory (DFT) calculations are performed to gain microscopic insights into the experimental findings. The results suggest that the hexagonal Fe5Si3 is a new giant room temperature MCE material that is on par with La–Fe–Si and Fe‐Mn‐P‐Si systems.


Introduction
The magnetocaloric effect (MCE), defined as a reversible change in the magnetic component of total entropy (and temperature) of a material upon application or removal of a magnetic field, is the basis for magnetic refrigeration techniques. [1][2][3][4][5][6] Magnetic refrigeration is considered to be a new environmentally -friendly and energy -efficient alternative to conventional vapor-compression technology. In current research efforts to find the most suitable candidates for applications, both first-order and secondorder transitions have been pursued to improve efficiencies. For a material with a second-order magnetic transition, the ΔS M (T) originates from the magnetic transition only, so typically it creates a smaller − ΔS M (T). [7] In contrast, for a material exhibiting a first-order transition, the MCE can become much larger, [5,8] because its ΔS M (T) can gain considerable lattice contributions through latent heat. [2,9] So far, two types of firstorder magnetic transitions have been reported in giant MCE materials: type I is a first-order magneto-structural transition, as observed in Gd 5 Si 4-x Ge x , [10,11]  Ni-Mn-(In, Sn, Sb)-based Heusler-type magnetic shapememory alloys, [4,12,13] and MnCoGeB x ; [14,15] type II relies on a magneto-elastic transition as found in MnFeP(As, Ge), [5,16,17] LaFe 13-x Si x H, [18,19] and Fe 2 P-based Mn-Fe-P-Si systems. [20,21] Generally, type I materials offer large MCEs, however, the accompanying thermal and magnetic hysteresis inhibits applicability. The lack of thermal and magnetic hysteresis of type II MCE materials makes them more desirable potential refrigerants.
Two other aspects which must be considered are the transition temperature and the moderate magnetic field needed to generate the total entropy change. [3,22] Fundamental and practical research on magnetocaloric materials intensified after the discovery of near room-temperature giant MCE compounds, such as Gd 5 Si 2 Ge 2 (≈270 K), [10,11,23] LaFe 11.4 Si 1.6 , [24] LaFe 13-x Si x H, [18,19] and Fe 2 P-based Mn-Fe-P-Si systems. [20,25,26] Nevertheless, a practically applicable MCE material comprised of earth-abundant elements and having the ability to operate in magnetic fields below 2 T is yet to be found. Fe 5 Si 3 was found as a metastable phase in the hexagonal D8 8 structure (see Figure 1) and orders ferromagnetically below 373 K. [27,[28][29][30] Fe 5 Si 3 appears within a narrow temperature range from 1098 to 1303 K, and previously only been stabilized either by quenching bulk materials or in nanostructures. Fe 5 Si 3 has interesting magnetic properties, including the coexistence of large and small magnetic moments in Fe(I) (4d) and Fe(II) (6g) sublattices, respectively. [27,31] Kanematsu theoretically discussed the crystal structure and proposed magnetic moments on the Fe(I) (2 B ) and Fe(II) (1 B ) sites with very different atomic environments. [32] Subsequent Mössbauer experiments confirmed these structures. [27] This particular crystal and magnetic structure enables easy tuning of the magnetic interactions by substituting elements. [33] Moreover, the hexagonal D8 8 structure of Fe 5 Si 3 supports uniaxial magnetocrystalline anisotropy, which is uncommon for iron-silicon systems, and is especially beneficial in applications. [28] However, the magnetic properties of Fe 5 Si 3 have not been well studied due to the difficulty in sample preparation (precipitation of the primary phase), as the phase is not thermodynamically stable at room temperature. The MCE was found in polycrystalline ingots of the pseudo binary Mn 5-x Fe x Si 3 system (x = 0, 1, 2, 3, 4, 5). [33] The x = 4 compound shows a relatively larger magnetic-entropy change compared with the x = 5 compound, which demonstrates how controlling composition of the large magnetic moment of the Mn atoms can effectively tune MCE response. [33] Here, we successfully synthesize stable magnetocaloric FMSP single crystals through light Mn-and P-doping in Fe 5 Si 3 and describe their structural, magnetic and magnetocaloric properties. A first-order magnetoelastic transition without accompanying notable hysteresis is observed at 348 K. Large anisotropy of magnetization and entropy changes indicates a strong spinlattice coupling. In combination with density function calculations, we describe the coexistence of the ferromagnetic (FM) and planar ferrimagnetic (FIM) states along with the shrinkage along 0 H//c and expansion along 0 H⊥c without an apparent change in crystal symmetry at the magnetic transition. The sensitivity of the structural stability to chemical doping and the strong contribution to the MCE effect from lattice degrees of freedom in Fe 5 Si 3 make it possible to generate exceptionally favorable roomtemperature magnetocaloric properties by optimizing the substitution elements and parameters. This work demonstrates a new route to developing MCE devices and that it opens the door to future studies using other earth abundant elements such as Mn, Cr for Fe, and P, As for Si.

Results and Discussion
The compositions of the crystals are determined to be Fe 4.83 Mn 0.16 Si 2.91 P 0.09 using Energy Dispersive X-Ray Spectroscopy (EDX). The composition is uniform around the whole sample. The X-ray diffraction (XRD) data for both room temperature and 25 K show that the FMSP single crystal is in the hexagonal D8 8 type (Space group P63/mcm) with the Fe 5 Si 3 -type structure. Figure 1a provides the XRD -2 scan of FMSP single crystals for (H 0 -H 0) reflections at room temperature. The thermal expansions along a(b) and c axes have linear behaviors in all temperature ranges except a kink ≈345 K (Figure 1b), which suggests a first-order transition. The observed smaller lattice expansion at 345 K is similar with that of Eu 2 In with the first-order transition. [34] Importantly, no significant hysteresis is observed during the cooling and heating processes. The atomically resolved annular dark-field (ADF) STEM image (Figure 1c) of the basal plane of the single crystal shows the hexagonal Fe 5 Si 3 structure, with a = 6.88 ± 0.02 Å, comparable to the XRD measurement shown in Figure 1b. The Mn and P dopants are not distinguishable because of the low concentrations. To illustrate the Fe 5 Si 3 -type hexagonal structure, the projection to the basal plane of Fe 5 Si 3 which includes two inequivalent sites of Fe, i.e., Fe(I) and Fe(II), are shown in Figure 1d and superimposed onto the image in Figure 1c.
The anisotropic magnetic behavior shows clearly in the magnetization curves at 4 K for 0 H⊥c and 0 H//c, as shown in the insets of Figure 2a  , the magnetization increases sharply upon cooling near T C , then decreases upon further cooling, creates a cusp feature in the M(T) curve. At higher field (7 T), the above behavior is overturned, the two magnetization curves look more isotropic. This indicates that the magnetic transition in this compound is not a simple paramagnetic/ferromagnetic transition, and instead, a competition between ferromagnetic and antiferromagnetic or ferrimagnetic phases is involved. The T C = 348 K can be determined from the M(T) curves under 100 Oe field, at the same temperature of the thermal expansion kink in Figure 1a. The simultaneous appearance of the shifted lattice constants with unchanged crystal structure and T C at 348 K suggests a strong spin-lattice coupling in this compound. Except for the above features, Figure 2 shows no obvious thermal hysteresis between cooling and warming curves around T C in the M(T) curves for both 0 H⊥c and 0 H//c. This feature is similar to that in meltspun LaFe 13-x Si x (x < 1.6), [18,35] which is also a first-order materials with no thermal hysteresis.
To further understand the magnetic properties, the magnetization isotherms of FMSP as the field increases and decreases at different temperatures for 0 H//c and 0 H⊥c around the transition temperature of 348 K are shown in Figure 3a,b. Each isotherm shows reversible behavior for both 0 H//c and 0 H⊥c directions without obvious magnetic hysteresis. The compound behaves as a ferromagnetic material with the field in the 0 H⊥c direction and exhibits competition with magnetocrystalline anisotropy in the 0 H//c direction. Around T C , in a field of 7 T, the magnetic moment is ≈0.78 B per transition metal atom in the ferromagnetic region (the value is calculated from the 324 K M-H 0 H⊥c curve). At 4 K, the saturation magnetic moment is 1.43 B per transition metal atom from the easy axis magnetization curve. This value is slightly larger than the reported value of 1.32 B in a field of 5 T for polycrystalline Fe 5 Si 3 . [31] If we consider that the difference in the saturation moment is from the trace Mn substitution in the single crystal, by taking 1.32 B /Fe as the Fe moment in our present Fe 4.83 Mn 0.16 Si 2.19 P 0.09 compound, the magnetic moment for Mn is 4.84 B . This value is close to the moment of Mn 3+ . Given that the doping and substitutions can strengthen the magnetic interactions as evidenced both in calculations [36] and experiments, [14,20] the larger magnetic moment is well described in terms of the trace Mn and P substitution.  Figure 3c,d, respectively. The maximum values of the magnetic entropy changes are 3.4 J kg −1 K −1 for 0 H⊥c and 2.3 J kg −1 K −1 for 0 H//c for field changes from 0-5 T. This provides two major improvements compared with the reported results from polycrystalline undoped parent Fe 5 Si 3 samples. [31] First, while the peak value − ΔS M (T) in the c direction is comparable with that in polycrystalline samples, the peak value of − ΔS M (T) in the ab direction is larger. Second, the − ΔS M (T) peak is broader. As a result, the magnetic cooling efficiency is improved in the single crystal, RCP = −ΔS M × T, where T is the full-width at half-maximum. [37] The calculated RCP values for the magnetic field change of 0-5 T along the ab and c directions are 223 and 119 J kg −1 , respectively.
To analyze the nature of the phase transition and detect the magnetic entropy behavior, we investigate the universal curve for the change in the magnetic entropy and compare it with similar magnetocaloric materials. In general, the height of the − ΔS M (T) peak, i.e., −ΔS max m , increases with magnetic field H. [38,39] For materials with a first-order phase transition, the peak of ΔS M (T) would typically be broader and ΔS max m saturates under a stronger magnetic field, while the situation, in reality, is complicated and no quantitative description has been developed yet. For a magnetic system with a second-order phase transition, a universal relation:|(−ΔS) max m | ∝ H n with n = 2/3 was proposed. [40] More recently, a new scaling relation with n = 1 + −1 + has been suggested, [41,42] where and are critical exponents, being associated with the spontaneous magnetization and the critical isothermal M(H) T = T C , respectively. This expression was also extended to first-order transition materials without hysteresis, [39] and its validity for a series of melt-spun LaFe 13-x Si x samples with x varying from 1.4 to 2.0 was confirmed. [43] The lack of hysteresis enables us to treat the FMSP single crystals with the same universal MCE behavior using the following equation: where A and B are intrinsic parameters of the cooling material and H 0 is an extrinsic parameter determined by the purity and homogeneity of the sample. Figure 4a shows the ΔS max m vs H 2/3 for FMSP along 0 H⊥c and 0 H//c, respectively. The fitting curve agrees well with the experimental results for 0 H⊥c, while for 0 H//c, the fitting deviates from the experiment at lower fields (below 2.5 T field). The parameters A and B obtained from the fitting of the plots using the above equation are both bigger for 0 H⊥c than for 0 H//c, confirming the anisotropy entropy change. The H 0 value obtained in 0 H⊥c is lower than the values reported in polycrystalline Gd and LaFeSi systems, and is comparable to the value found in Gd single crystals. [39] But the H 0 value for 0 H//c is three orders of magnitude larger than that of LaFeSi systems. [39] From this point, the deviation of the fitting curves along the c direction from experimental results deserves a more thorough theoretical study, especially for the anisotropy entropy change in both directions. To further check the universal behavior for magnetic entropy and the nature of phase transition in this system, the normalized entropy change ΔS   to satisfy Figure 4b,c it can be seen that for temperature below T C , especially for ←1, the curves do not overlap and the breakdown of the universal behavior for the normalized entropy change can be observed. The results for both 0 H⊥c and 0 H//c are similar. In the above discussion, the relative cooling power (RCP) was used to evaluate the cooling efficiency, which is inadequate especially for materials with low entropy change. [44] For low entropy change materials, the temperature averaged entropy change (TEC) is an appropriate parameter compared with that of RCP. Therefore, we further estimated the TEC of FMSP according to [45] The estimated TEC for field changes of 0-0.5 to 0-1.5 T and ΔT lift of 2, 3, 6, and 9 K for both 0 H⊥c and 0 H//c are displayed in Figure 5.
Here, T mid is the temperature where ΔS max m states. It can be seen that the TEC follows the trend of ΔS max m where it increases with increasing H for both directions. The TEC at both 2 and 3 K are close to the value of ΔS max m , which has similar behavior for both 0 H⊥c and 0 H//c though the TEC are much smaller in 0 H//c than that of 0 H⊥c. Further, the TEC for this compound FSMP at 0 H⊥c: TEC(ΔT lift = 10K, ΔH = 1T) T C =348 K = 1.23 Jkg −1 K −1 is comparable to that of Gd 55 Ni 10 Co 35 : TEC (10 K, 1T) 192-212 K = 1.5, 1.58, and 1.12 J kg −1 K −1 . [46] In addition, considering the obvious anisotropy entropy change in the FMSP as analyzed above, a rotating magnetocaloric effect will be accompanied. [47] By using the equation Here, E a, 0 H and E a,0 represent magnetocrystalline anisotropy energy under a magnetic field 0 H and zero field, respectively. Figure 6b displays the ΔS R between the parallel and perpendicular directions as a function of temperature and magnetic field. The maximum ΔS R is lower than the magnetic entropy change obtained from RCP. Now we investigate the interplay between magnetism and crystal structure using DFT. We consider the FM state and the planar FIM state, representing the possible magnetic state below the transition temperature, and the non-magnetic (NM) state, representing the magnetic state above the transition temperature. The FM state and the planar FIM state represent the possible magnetic state below the transition temperature, and the NM state corresponds to the magnetic state above the transition temperature. The proposed magnetic structure models of Fe 5 Si 3 are shown in Figure 7. For the FM state, the Fe(I) and Fe (II) lattices are aligned in the ab plane (Figure 7a), while the Fe(I) and Fe(II) sublattices alternate directions within the unit for the planar FIM state (Figure 7b).
Since the magnetic and crystal structures are expected to play important roles in MCE, we first carry out the full structural optimization considering the three magnetic states. The optimized lattice parameters are a = b = 6.559 Å, c = 4.718 Å for the NM state, a = b = 6.695 Å, c = 4.681 Å for the FM state, and a = b = 6.684 Å, c = 4.696 Å for the FIM state, without an apparent change in crystal symmetry. This suggests that the crystal shrinks along the c direction ( 0 H//c) and expands along with the a and b directions ( 0 H⊥c) at the magnetic transition irrespective of the magnetic pattern at low temperatures. We note that the previous DFT work on Fe 5 Si 3 [48] reported the stable volume V = 175.7 Å 3 . This value is closest to our value for the NM state, V =175.78 Å 3 , but smaller than that for FM state V = 181.71 Å 3 or the FIM state  Figures 8a-c show the partial density of states (DOS) for Fe d states in the FM state, FIM state and NM state, respectively, without considering the SOC. The NM DOS have large intensity at the Fermi level that might lead to the Stoner instability. In-between the PM state and the FM (or FIM) state, the Fe DOS and the electron density around both the Fe (I) and Fe (II) sites change drastically, giving rise to the structural instability discussed above. These results clearly indicate the typical firstorder magneto-elastic transition during the magnetic transition in the hexagonal Fe 5 Si 3 system, leading to a large MCE from the spin and structural coupling, as also observed in MnFeP 1-x Si x and LaFe 13-x Si x compounds. [2,20] In the FM state, the magnetic moments on the Fe(I) site and Fe(II) site are found to be 1.84 and 1.31 B , respectively. In the FIM state, the magnetic moments on the Fe(I) and Fe(II) sites are 1.88 and 0.81 B , respectively. While the local magnetic moments and the total magnetic moment per unit formula of the FIM state are close to Mössbauer [27] and magnetization studies of polycrystalline samples, [31] the total energy of the FM state (E = − 60.5361 eV per formula unit) is found to be slightly lower than that of the FIM state (E = − 60.3586 eV). This discrepancy may be attributed to the inaccuracy of DFT without the U correction describing the coupling among magnetism, electron and lattice. It is also possible that the actual magnetic ordering might be more complicated. Further, trace Mn and P doping which is not included in the calculation may alter the delicate balance between the FM and the FIM states. We further introduced SOC to examine the magnetic anisotropy. Spin moments and electron density are hardly affected by SOC. While the precise direction of the magnetic easy axis remains to be determined, the FM (FIM) state with the Fe moments along the a direction is found to be lower in energy than that with the Fe moments along the c direction by 1.1 (1.7) meV per formula unit with a 12 × 12 × 12 k-point mesh and by 1.2 (1.7) meV with a 16 × 16 × 16 k-point mesh. Thus, because of the hexagonal symmetry, the leading anisotropy (proportional to |S| 2 ) would be of easy-plane type. This is consistent with our experimental results as shown in Figures 2 and 3. Our DFT calculations suggest that the observed complicated magnetic properties of Fe 5 Si 3 might be induced by the competition between the proposed two magnetic models (planar FIM and the FM states).
The observations on the magneto-elastic transition, the anisotropy MCE and the coexistence of Fe(I) and Fe(II) sites are in parallel to those observed in hexagonal Fe 2 P compounds. [49,50] Fe 5 Si 3 with a hexagonal structure is found to have stronger anisotropy than Fe 2 P based compounds. Compared to polycrystalline Fe 5 Si 3 samples, trace doping of FMSP single crystals exhibit an MCE spread over a wider temperature span and higher ΔS value in ab direction. A higher RCP value means that for a large temperature difference between a hot and a cold reservoir it is possible to extract a significantly larger amount of heat. Based on the structural sensitivity of Fe 5 Si 3 based compounds, our results suggest that the stronger first-order characteristics such as a giant entropy change, and larger volume changes are expected in the more optimally doped Fe 5 Si 3 systems than that investigated in this work. [36]

Conclusions
In summary, the rich structural, magnetic and magnetocaloric effects in FMSP single crystals have been investigated. An anisotropic magnetization and MCE effect between 0 H⊥c and 0 H//c are observed. The breakdown of a universal ΔS Max (T) versus H relationship indicates a first order transition. Density functional theory calculations confirmed the coexistence of large and small Fe moments and the first-order magnetic phase transition accompanying the structural transition, where the crystal shrinks along the c direction and expands along with the a and b directions. This indicates that the MCE originates from the spin-lattice coupling in this system. Our results suggest that Fe 5 Si 3 -type is a new MCE model material with potential in magnetic refrigerators due to its structural sensitivity and magneto-lattice coupling.

Experimental Section
Single Crystal Synthesis and Quality Characterization: The high-quality Fe 4.83 Mn 0.16 Si 2.91 P 0.09 single-crystals were grown using a tin flux method in an alumina crucible that was sealed under vacuum in a quartz ampoule. The samples were needle-shaped with clear hexagonal facets seen in the optical microscope. The composition of the crystals was determined using a JEOL JSM-840 scanning electron microscope with an EDX brand energy-dispersive X-ray spectroscopy system. The phase purity and crystal quality also were examined with temperature-dependent single crystal x-ray diffraction.
X-ray Diffraction: The sample was mounted using epoxy resin to the cold finger of a closed-cycle He refrigerator equipped with a hemispherical Be window and mounted on a 4-circle diffractometer. Incident radiation was provided by a Cu rotating-anode generator operating at 5 kW. A graphite (0002) monochromator selected Cu K a radiation. The incident x-ray beam was collimated with a single slit, while the diffracted beam was collimated with Soller slits in order to reduce errors due to sample displacement. X rays were counted using a NaI(Tl) scintillator. Theta-twotheta profiles of the (4 0-4 0) and (2 1-3 3) reflections were scanned at each temperature [the (0 0 0 1) direction being geometrically inaccessible], and fit with Pearson-VII K a1 /K a2 profiles. The a and c lattice parameters were calculated from the peak centers.

STEM (Scanning Transmission Electron Microscopy)Imaging and Analysis:
The cross-sectional ab basal plane STEM specimens of the FMSP single crystal samples were prepared by the lift-out technique using a multi-beam focused beam (FIB) system (JEOL, JIB-4600F). Structural and chemical characterization of FMSP at the atomic scale were performed using STEM with aberration correction and low-loss electron energy loss spectroscopy (EELS). ADF STEM images for the sample were recorded using aberrationcorrected scanning transmission electron microscopes (VG Microscopes HB603U operating at 300 kV and Nion UltraSTEM operating at 100 kV).
DFT Calculations: The projector augmented wave (PAW) approach [51] with the generalized gradient approximation in the parametrization of Perdew, Burke, and Ernzerhof [52] for exchange correlation as implemented in the Vienna Ab initio Simulation Package (VASP) [53,54] version 5.4.4 with the hexagonal structure (space group P6 3 mcm ) was used, a regular 6 × 6 × 6 k-point mesh centered at the Γ point, an energy convergence criterion 10 −6 eV, and an energy cutoff 500 eV. For both Fe and Si, a standard PAW potentials Fe and Si in the VASP distribution were used. Using the reported structural data, [55] the full structural optimization was performed considering three different magnetic states, non-magnetic state, ferromagnetic state, as well as planar ferrimagnetic state, where Fe ordered moments alternate along the c direction, without the spin-orbit coupling (SOC) so that all forces are less than 0.0001 eV Å −1 . Obtained atomic positions were shown in Table 1. After the structural optimization, a denser 12 × 12 × 12 kpoint mesh was used to compute the DOS without the SOC or to examine the spin anisotropy including the SOC. A denser 16 × 16 × 16 k-point mesh was also used and confirmed that the spin anisotropy was well converged.
Magnetic Measurements: Magnetic measurements were carried out using the reciprocating sample option (RSO) mode in a superconducting quantum interference device (SQUID) magnetometer (Quantum Design MPMS).