Total Scattering Study of Local Structural Changes in MnAs 1 − x P x In ﬂ uenced by Magnetic Interactions

: The interplay between ﬂ uctuations of the local structure and magnetic interactions is of great importance for phenomena like superconductivity, colossal magnetoresistance, and frustrated magnetism. Such local distortions are often subtle and di ﬃ cult to probe. The metallic MnAs 1 − x P x ( x = 0.06, 0.12, 0.18) solid solution represents a sensitive model system, currently analyzed by variable-temperature X-ray total scattering (TS). A second-order transition ( Pnma to P 6 3 / mmc ) occurs on heating, intimately coupled to magnetic ordering at low temperatures and a temperature-induced low- to high-spin transition for manganese. Intrinsic compositional ﬂ uctuations along with a particular magneto-volumetric coupling to low- and high-spin like states triggers formation of local high-symmetry nanosized domains in an orthorhombically deformed matrix that eventually converts globally into a high-temperature hexagonal arrangement. These features are only traced by TS analyses, whereas di ﬀ raction provides a regular second-order transition with, e.g., cationic displacements de ﬁ ned by Rietveld analysis acting as order parameter. The coexistence model provides good ﬁ ts of the TS data and, on average, translates nicely into a continuous V ( T ) thermal expansion relation with maximum expansivity in the range where the TS data shows the largest di ﬀ erence between local (<20 Å) and intermediate-range (20 − 80 Å) structures. The degree of local distortions, Mn(As, P) 6 octahedra inclusive, is a result of volume-dependent electronic properties as well as magnetic interactions. This study demonstrates how X-ray TS can conveniently give essential insights into the local symmetry ﬂ uctuations from the perspective of strong magnetic interactions.


■ INTRODUCTION
Nanoscale heterogeneities, structural variations, and broken symmetry states play a ubiquitous role in emergent properties such as colossal magnetoresistance, 1 frustrated magnetism, 2,3 pseudogaps, 4 and high-temperature superconductivity. 5,6 The properties of these types of complex materials depend critically on local deviations from the long-range average structure. For example, magnetic fluctuations are considered to be responsible for slowing down the pseudogap phase of the hightemperature superconductor YBa 2 Cu 3 O y (6.72 < y < 6.95). 7 Variations in the local magnetic moments are a result of not only the exchange interactions with their neighbors but also the local effective crystal fields. The latter becomes prominent if the (anion) substructure contains atoms A and B with different effective charges. Therefore, each magnetic atom will experience a local low-symmetry crystal field in addition to the average crystal field arising from the crystal structure. 8 This random anisotropy may, in turn, influence the local atomic structure. Moreover, during a magnetic ordering transition (MT), the local change in magnetic interactions might influence the local atomic structure without entering into the situation of a simultaneous atomic structural phase transition (ASPT). Such a change in local structure will result in diffuse scattering that cannot be analyzed by conventional crystallo-graphic methods based solely on Bragg reflections. However, in total scattering (TS) methods the diffuse scattering is analyzed in parallel with Bragg scattering on an equal basis. 9 TS has, for instance, been successfully utilized to show co-emergence of magnetic order and structural fluctuations in magnetite below the Curie transition. 10 In the current article, we probe the change in the local atomic structure during a continuous magnetostructural phase transition in magnetocaloric MnAs 1−x P x (x = 0.06, 0.12, 0.18). There is recently a strong renewed interest in MnP and related transition metal pnictides with MnP-type orthorhombic structure due to the discovery of unconventional superconductivity under high pressure and upon chemical substitution. 11 The superconductivity is considered to arise from an enhanced coupling of (helimagnetic) spiral spin fluctuations and indicates that superconductivity and magnet-ism are intertwined. Fluctuation and competition between phonons and spin appear to have a direct connection to a superconducting pairing of s, p, and d character. In this context, the variation of the pitch of the incommensurate helical fluctuations provides rich grounds for local FM and intermediate-range AFM orders. On the other hand, in MnPtype CrAs, the unconventional pressure-induced superconductivity is achieved by shifting the quantum critical point (QCP) by Al substitution. 12 Magnetostructural phase transitions may be accompanied by substantial magnetocaloric (MC) effects that possibly can be exploited for room-temperature refrigeration. 13, 14 MnAs and ternary derivatives show promising behavior for such roomtemperature applications. 15,16 The transition temperature for the ordering of magnetic moments is affected by the local coordination (composition, symmetry). Furthermore, the ordering process is characterized by magnetic entropy changes (ΔS M ) across the phase transition. A giant MC effect occurs when the first-order ASPT couples with the magnetic transition. MnAs exhibits this behavior, where the first-order magnetostructural transition temperature is T C = 318 K 17 and occurs between a low-temperature ferromagnetic (FM) hexagonal NiAs-type phase (space group P6 3 /mmc) and an orthorhombic paramagnetic (PM) MnP-type phase (Pnma). 18 Substituting As with phosphorus P (MnAs 1−x P x , x = 0.06, 0.12, and 0.18) allows the MnP-type phase to stabilize at ambient conditions. The phase diagram for MnAs 1−x P x is shown in Figure 1c. On increasing temperature, a second-order MnP− PM to NiAs−PM transition occurs, increasing from 425 K for x = 0.06 to 500K for x = 0.18. This symmetry-allowed displacive transition takes place over a wide temperature range. 19 In the orthorhombic regime, the MT is decoupled from ASPT and occurs at 230, 241, and 245 K for x = 0.06, 0.12, and 0.18, respectively. Importantly, thermal expansivity and magnetic susceptibility data along with paramagnetic diffuse scattering data measured by powder neutron scattering reveal a continuous low-to high-spin conversion for the Mn sublattice (assuming Mn 3+ in the ionic limit; from S = 1 to S = 2) of MnAs 1−x P x . 20 The MnAs 1−x P x system is perfectly suited for exploring how the local structure influences the magnetic spin transition and, thereby the structural phase transition from Pnma to P6 3 /mmc. The average Mn spin state appears to be very dependent on bond distances (unit cell volume; distortions). Hence, this makes it possible to explore how distortions in the local symmetry owing to quite different Mn−As and Mn−P bond distances affect the magnetism and structure. We address this challenging issue by means of a total scattering analysis of MnAs 1−x P x and correlate the findings with magnetic susceptibility data.

■ EXPERIMENTAL SECTION
The powder samples of MnAs 1−x P x (x = 0.06, 0.12, 0.18) were prepared as earlier described. 19 The purity and homogeneity of the samples were ascertained from powder X-ray diffraction (PXRD) data recorded using a Bruker D8 Discover diffractometer with Bragg− Brentano geometry, Cu Kα1 radiation [λ = 1.540598 Å; Ge (111) monochromator], and a LynxEye detector. Total scattering PDF data were collected at the Materials Science Beamline 21 at the Swiss Light Source (SLS; Paul Scherrer Institut, Villigen). Silicon was used as a calibrant for wavelength and instrumental parameters (a Si = 5.431194 Å at 22.5°C, NIST powder diffraction standard 640c). The diffractometer was operated in Debye−Scherrer geometry with a Mythen microstrip detector and capillary spinner. The wavelength was 0.406080 Å. The Mythen microstrip detector was placed at four different 2Θ positions in order to collect a full set of angular data extending to high Q max for the subsequent PDF analysis. Samples were packed under Ar atmosphere in a 0.3 mm diameter quartz capillary and sealed to avoid any oxygen/moisture in the capillary. A liquid nitrogen flow cryostat from Oxford was used in the temperature range from 100 to 500 K. Data were collected at 25 K intervals; the total collection time at each temperature was 40 min. The diffraction data were normalized and reduced by standard routines at the beamline. The xPDFsuite 22,23 was used for Fourier transformation of the total scattering structure function S(Q) to obtain the PDF. Q min = 0.5 Å −1 and Q max = 28 Å −1 were used for the Fourier transformation. Experimental resolution parameters Q damp = 0.0038 and Q broad = 0.00229 were determined through refinements of PDF data for the Si standard. Unit cell parameters, anisotropic thermal factors, delta 2, and symmetry-allowed positions (space groups = Pnma and P6 3 / mmc) were refined to give the best fit to the experimental data. Rietveld refinements were carried out with JANA 2006. 24 For dc magnetic susceptibility and isothermal magnetization measurements, a Quantum Design Physical Property Measurement System (QD-PPMS) was used in the range 4−350 K and for applied magnetic fields of ± 9T. Polycrystalline powders of MnAs 1−x P x were loaded into plastic holders clipped onto a brass half-tube sample holder and loaded into the cryostat of the VSM-based ACMS-II unit. For dc susceptibility measurements, static fields between 0.05 and 5 T were applied. In general, zero field cooled−warming (ZFC), fieldcooled−cooling (FCC), and field-cooled−warming (FCW) cycles were followed. For dc isothermal magnetization measurements at selected temperatures, the magnetic field was ramped between 0 and ±9 T. For all measurements, samples were allowed substantial time to establish thermal equilibrium before measurements were started.  Table  S1). At 425 K, phase fractions were 68.34% and 31.66% for orthorhombic and hexagonal phases, respectively. Beyond 425 K, only the hexagonal phase could be fitted to the data. Phase fraction obtained from Rietveld refinement might be misleading since there are overlapping Bragg peaks from both phases. Therefore, these Rietveld refinements could not establish the true nature of the phase transition. In these circumstances, real-space PDF refinement is advantageous to determine the phases fraction. A similar problem of overlapping Bragg peaks was observed in the case of intermetallic PtGd structure determination. Real-space PDF refinement established that the real structure crystallizes in the space group Pm-3m instead of Fm-3m determined from Rietveld refinement. 25 The PXRD data reveals that the ASPT depends strongly on composition (x) (see Supporting Information (SI) Figures S4 and S5). These observations are well in line with earlier studies as well as paramagnetic scattering data. 20 A pertinent question is now whether changes in the local coordination starts to take place prior to the crystallographically averaged structural transition as revealed by the PXRD data. At the local scale it might well be possible that there exist islands of hexagonal symmetry emerging in the orthorhombic matrix owing to compositional fluctuations and/ or slight atomic rearrangements.
A detailed analysis of the local and intermediate-range structures was carried out based on PDF data in real space. Figure 2a shows the PDF data of MnAs 0.94 P 0.06 at 100 K fitted in Pnma (R w = 15.6%) for the r range 2−80 Å. The presence of two different bond distances due to Mn−As and Mn−P local environments were investigated by a detailed analysis of the first peak at 2.48 Å, which corresponds to the first neighbor distances of Mn, i.e., the Mn(As,P) 6 octahedron. Attempting a fit with one Gaussian peak was unsatisfactory, Figure 2b. However, for the choice of two Gaussian peaks (Figure 2c), the fit improved significantly, and the derived distances of 2.507(1) and 2.426(1) Å are attributed to Mn−As and Mn−P bonds, respectively. Similarly, two Gaussian peaks were found to improve the fitting of the first peak in all other data sets in all compositions (see Figures S6−S8) until the temperature where there was no change in the local structure (discussed later). Therefore, we have direct intuitive evidence of two distinct bond distances, which implies that the situation in MnP and MnAs is transferred into the local structure of the solid solution phase. Figure 2d shows the variation of these two bond distances with respect to P substitution. The assigned Mn−P bond distance shifts toward a lower value on increasing P substitution (x), whereas the Mn−As distance shifts toward longer distance on increasing As content, approaching those of MnAs (average Mn−As bond = 2.58 Å for MnAs; average Mn−P bond = 2.36 Å for MnP). Cell parameters and the average bond distance Mn−As/P decrease with increasing P substitution following Vegard's Law. These variations suggest that the electronic state of the M atoms changes within the analyzed composition interval at room temperature. As expected, the area under Mn−P bond distances increases while the area under Mn−As peak decreases with increasing P substitution (see Figure S10). It shows qualitatively that the area under the Mn−P peak increases with increasing P substitution without considering the scattering intensity of the atoms and normalizing them with respect to the scattering intensity. Further concentration dependence of the peak widths to separate the broadening due to static atom displacements from the thermal broadening was also not considered. Therefore, the area under the peak might be overestimated. When different sized atoms are substituted in the same crystal lattice, it is expected to have different bond distances. For example, in the case of Ga 1−x In x As, highresolution PDF data clearly shows two very distinctive peaks corresponding to In−As and Ga−As at 2.65 and 2.45 Å, respectively. 26 Two Gaussian peaks were used to fit these peaks to find out the corresponding bond distances. Two peaks were clearly resolved because of the high-resolution data (Q max = 45 Å −1 ). Further, with increasing In substitution, the In−As peak intensity increases while the Ga−As peak intensity decreases. Similarly, when a smaller atom, here P in place of As, is substituted in MnAs, this is expected to give rise to two different bond distances corresponding to Mn−As and Mn−P. However, more high-resolution data are required to quantitatively show the trend by Gaussian fitting wellseparated peaks by considering instrument broadening. The resolution of PDF is defined by π/Q max , and we used a Q max of 28 Å −1 . Therefore, a shoulder is observed corresponding to the Mn−P bond left side of the Mn−As bond distance.
In order to clarify local departures from the average picture provided by Bragg diffraction, PDF refinements were carried out for a local structure confined to the r range 2−20 Å and an intermediate-range structure for the r range 20−80 Å. At temperatures below 175 K, the local PDF structure was satisfactorily described based on the orthorhombic structure (R w = 10.5% for MnAs 0.94 P 0.06 ). At 175 K and higher temperatures, this type of fit (Pmna) leads to increasing values for R w , Figure 3a. However, when adding a local component with a hexagonal structure to the refinement, the fit improved significantly. Figure 3a shows the variation of R w with temperature. Hence, there are indications of a change in the local structure already at 175−200 K. At this temperature hexagonal domains appear locally. However, the average structure remains orthorhombic as shown by the diffraction data with a transition temperature of 425 K. On the other hand, the PDF intermediate-range picture (20−80 Å) indicates a decrease in the phase fraction of orthorhombic domains above 275 K, Figure 3b. To investigate the dependency of the hexagonal domain in orthorhombic matrix, PDF refinement was carried out with different r ranges. When the PDF refinement was restricted to the r range of 2−10 Å, there was no significant difference observed in the phase fractions compared to an r range of 2−20 Å. When the refinement range was increased to 2−30 Å, the change in the local structure was observed between 200 and 225 K (Figure 3 b). This is in line with the change in the intermediate-range structure (20−80 Å) where the change occurs beyond 275 K. Interestingly, although PXRD (average structure) suggests that the structural phase transition is complete at 425 K, the PDF refinement indicates that orthorhombic domains prevail even up to around 500 K. A similar behavior was found for the more P-rich compositions: MnAs 0.88 P 0.12 and MnAs 0.82 P 0.18 . For these, the onset of changes in the local structure (i.e., two-phase model required) is around 225 and 250 K, respectively. However, for the latter samples, the orthorhombic phase is stabilized owing to the smaller unit cell volume imposed by the higher P content. Hence, the phase transition to hexagonal symmetry is not complete at neither the local nor the average scale at 500 K (MnAs 0.88 P 0.12 orthorhombic = 10.5%; MnAs 0.82 P 0.18 orthorhombic = 76.9%).
These findings corroborate the previous observation of the paramagnetic scattering, which proved the magnetic low-to high-spin transition took place over the same wide temperature range. 20 For the MnAs 1−x P x solid solution phase, the temperature-dependent structural deformations (ASPT) is accompanied by a change in the magnetic properties of Chemistry of Materials pubs.acs.org/cm Article manganese from a low-spin configuration (at 10 K) to a highspin configuration (at 500 K). The complex magnetic and structural properties have a pronounced effect on heat capacity, which shows three major anomalies: spin disorder; low-to high-spin conversion, and structural phase transition (MnP− PM to NiAs−PM). 27,28 Susceptibility measurements do not give useful information in the temperature range for the low-to high-spin transition. However, from the observed Curie−Weiss relationship observed for the hexagonal high-temperature phase, the measured effective paramagnetic moment of μ eff = 4.6 μ B corresponds to S = 1.85 (spin-only approximation). The variation in S is well described based on paramagnetic scattering data. 20 The total scattering analysis indicates that there exist different structural domains, and the relative phase fraction is temperature dependent and correlates with the continuous spin transition at the average scale. A local highspin situation is likely to be favored by a local hexagonal environment, whereas a local low-spin state is favored by a distorted orthorhombic environment. Although the emphasis is made synthetically to achieve a homogeneous solid solution by prolonged annealing, there will always exist different types of local coordination for the MnX 6 octahedra, i.e., MnAs 6 , MnAs 5 P, and MnAs 4 P 2 , but probably not more P-rich situations for a well-annealed sample in which compositional fluctuations are at a minimum. A high-spin situation will be most favored by MnAs 6 and least by MnAs 4 P 2 . Our current analysis shows that there is a gradual change in the phase fraction of two local structure regimes throughout the electronic and structural phase transitions. Further, the magnetic interaction between neighboring and next-nearest  Figure 3c shows the change in the unit cell volume of the orthorhombic phase (obtained from the intermediate-range structure PDF refinement) for all compositions as a function of temperature. The continuous volume change reiterates that the nature of the structural phase transition is second order. 19,20,30,31 There is an excellent agreement in the volume change for the local and intermediate-range structure descriptions for the orthorhombic phase (see SI, Figure  S14). A similar good agreement is found for the unit cell volume of the hexagonal phase. The high uncertainty for the 175 K data point is attributed to the fact that this is the very first and weak appearance of the local hexagonal structure and corresponds to a nucleation process within an orthorhombic matrix. This parallels what is observed in the synthesis of nanoparticles. At very small particle sizes, nucleation is ongoing, the unit cell volume may deviate from that of larger crystalline particles, regular diffraction analysis is not applicable, and PDF analysis is required. 32,33 An anomaly in unit cell volume is also observed for the orthorhombic phase at 500 K, where the orthorhombic phase exists only locally, and uncertainty in the analysis becomes enhanced. Isotropic thermal parameters (U iso ) for both Mn and As increase with increasing temperature. However, a small change in slope can be seen in the temperature region 250−275 K, where the intermediate range structure starts to change ( Figure S15). A similar change of slope in delta 2 is observed within this temperature window ( Figure S16).

■ MAGNETIC PROPERTIES
The magnetic properties of MnAs 1−x P x are extraordinarily sensitive to changes in unit cell volume and interatomic distances, including chemical bonding. The reason is a volumedependent low-to high-spin transition for the Mn atoms and changes in the Mn−Mn bonding as a result of the progressing structural phase transition. In this respect, the local structure is one more key parameter. However, individual effects are hard to separate. At low temperatures, where low-spin Mn is anticipated for the x = 0.06−0.18 samples, we nevertheless note a high complexity due to competing magnetic interactions. We illustrate this by data for x = 0.06. From earlier works, an antiferromagnetic double spiral H a -type ordering was proved by single-crystal neutron diffraction for MnAs 0.925 P 0.075 , 34 whereas powder neutron diffraction (PND) showed that the H a helimagnetic structure disappears at fields above 1 T. However, the emergence of new magnetic peaks is indicative of a different incommensurate structure with long periodicity. For MnAs 0.90 P 0.10 , PND shows that ferromagnetism occurs in an intermediate temperature range, with H a order below and above, whereas MnAs 0.82 P 0.18 is fully ferromagnetic below T C 31 with a moment of 1.46 μ B aligned along [010]. 19 For H a , the spins rotate in the bc plane (easy plane of magnetization in MnAs) with spiral propagation along [100] (hard axis). Early works show clearly that sample quality (annealing conditions) has a significant impact on measured magnetic features. This is likely caused by differences in the local structure and local clustering as revealed in the current PDF study, even for long-term annealed samples, with implications for spin transitions and magnetic short-and long-range interactions.
The isothermal magnetization data, exemplified with MnAs 0.94 P 0.06 , see Figure 4 d, document this complexity. Except for the paramagnetic state at 300 K, the M(H) curves show a hysteresis loop at intermediate (2−8 T) fields. These features, not earlier clearly revealed, indicate a field-induced magnetic state, which indeed could represent the mentioned field-induced incommensurate structure. At high fields, the helical state transforms into a commensurate ferromagnetic (FM) state, μ sat ≈ 1.50 μ B /fu (x = 0.06). In very high pulsed fields up to 30 T, a discontinuous volume expansion occurs caused by a first-order magnetic phase transition from the (low-spin) MnP type to the (high-spin) NiAs type along with a transition from para/heli-to ferromagnetism. 35 This transition exhibits similar ΔV and ΔS as reported for binary MnAs and is interesting as a magneto/barocaloric system. 18 The isofield susceptibilities, Figure 4a and 4b, show complex behavior both below and above the ordering temperatures. The existence of a field-induced intermediate (probably incommensurate) magnetic state is evidenced also by the inverse susceptibility data (Figure 4 b; highlighted in gray), where the field-induced transition shifts from ∼165 K at 3 T to ∼200 K at 5 T. Further insight into the effect of the external field is provided in Figure 4c, showing the temperature dependence of irreversible susceptibility, M irr = M FC − M ZFC for samples measured in different fields on heating. The positive M irr below T N ≈ 230 K indicates stabilization of field-nucleated collinear ferromagnetic (FM) phase. The noticeable M irr peaks suggest that MnAs 0.94 P 0.06 is subject to competing interactions between a magnetic incommensurate AFM helicoidal phase and a ferromagnetic phase where the energy balance is dictated by the strength of the applied magnetic field. In the narrow interval, 230−275 K, the inverse susceptibility (μ 0 H = 0.05 T) follows the Curie−Weiss law with an effective paramagnetic magnetic moment of 2.01 μB and θ CW = +215 K, indicating ferromagnetic interactions. The μ eff corresponds to 2S ≈ 1.5, in line with the observed ordered moments and the claim of lowspin Mn (III). The anomalous 1/χ(T) behavior at higher temperatures in Figure 4b is caused by the low-to high-spin continuous spin conversion during which we currently observe major changes in the local and intermediate-range structure, while a regular Curie−Weiss region again occurs in the hexagonal NiAs-type high-temperature phase (not shown). Corresponding data for MnAs 0.88 P 0.12 and MnAs 0.82 P 0.18 are shown in the SI.
The total scattering analysis reveals structural changes, locally and on intermediate range, in the temperature range of magnetic anomalies and phase transitions as well in connection with the major changes in susceptibility related to the low-to high-spin conversion. The local spin interactions between Mn atoms are susceptible to local distortions that are expectedly manifested by diffuse scattering and correlate with current findings of the TS analysis. A similar behavior is observed for all samples. A small unit cell volume per formula unit favors low spin rather than high spin. Magnetic analysis (neutron diffraction, saturation magnetization, CW regimes) documents the spin situation at certain conditions. In this context, the current PDF data adds insight to the paramagnetic low-to high-spin transition that couples to the second-order structural phase transition (from Pnma to P6 3 /mmc). The best data for the variation of the spin moment is assumingly obtained from paramagnetic neutron scattering. 20 In Figure 5 we plot how this derived spin moment S correlates with the average Mn−P/ As bond distances of the octahedra in the composite mixture of orthorhombic and hexagonal phases, as revealed by TS analysis. The kink in the scattering data at ca. 230 K corresponds to the magnetic ordering transition. When exploring a solid solution, as currently exemplified by the pseudobinary MnAs 1−x P x phase, one will synthetically normally strive for maximum homogeneity at all length scales and thereby be able to fully study in detail how the physicochemical properties vary with parameters like the average electronegativity, electron concentration, chemical pressure, charge states, and more. For certain materials systems, the effect of tuning chemical substitution has a pronounced effect on the structure and properties. This is indeed the case for MnAs 1−x P x , where the Mn electronic state and thereby the "atomic size" (unit cell volume; symmetry) are sensitive parameters to be tuned and explored.
The current total scattering analysis shows that the individual Mn−As and Mn−P bonds differ significantly in lengths, as one may expect from simple atomic size arguments. However, since a given nonmetal atom (P, As) in the NiAstype and the distorted MnP-type structures connects to six Mn atoms (octahedra), displacements/deformations and strain are very likely to occur at the local scale. In an ionic picture, this will lead to different local crystal fields with an impact on the d-electron levels. In metallic MnAs 1−x P x , the orthorhombic distortion directly leads to the establishment of new metal− metal interactions (bonds) and to changes in the DOS at the Fermi level, including spin-up and spin-down bands. These changes correspond in the ionic limit to a low-(S = 1) to highspin (S = 2) transition. The structural implication of islands with NiAs-like local structure in a matrix of deformed MnPtype is visualized in Figure 6. This corresponds to the current findings in the PDF analysis of the paramagnetic phase that undergoes a low-to high-spin transition.
The total scattering analyses reveal interesting features connected with temperature-induced electronic and structural phase transitions. The high-spin state is governed by high local symmetry; there are no metal atom displacements that would impose new metal−metal bonds (in the ac plane; Pnma) and a large local volume for the Mn coordination polyhedron (i.e., Mn−As rather than Mn−P coordination). The current data indicates that nanodomains develop in the structural transition region. There appear to be domains of higher symmetry (modeled as NiAs-type arrangement) along with orthorhombic domains. Such a coexistence model was required to obtain acceptable fits of the TS data in the transition regions. On average, this translates nicely into a continuous V(T) thermal expansion relation with a maximum in thermal expansivity in the temperature range where the total scattering data shows the largest difference between local (<20 Å) and intermediaterange (20−80 Å) structures. This is consistent with the continuous variation in the displacement (and order) parameter |1/4 − z Mn | (being a measure of new Mn−Mn "bonds" formed) as as revealed from variable-temperature neutron diffraction studies. 19 The observed temperatureinduced changes in the local structure are very similar for all three investigated samples of MnAs 1−x P x (x = 0.06, 0.12, 0.18) and hence probably of quite generic validity. The electronic low-to high-spin transition takes place over a large temperature interval. We suggest that this is indeed due to the existence of a wide distribution of local coordinations for the Mn atoms with respect to the nearest and next-nearest neighbor P and As atoms. Hence, we immediately recognize that sample homogeneity is essential for structural and electronic properties. Only a homogeneous sample at all length scales will give sharp DSC (differential scanning calorimetry) signals for the enthalpy changes of relevant transitions. The MnAs 1−x P x system is extraordinary by showing an unusually strong coupling between local structure, average structure, and magnetism. It is therefore very well suited for exploring phenomena that otherwise easily escape detection yet being of high generic importance for solid solutions and materials science.
The current studies, as well as the literature, suggest a thermodynamically second-order phase transition. Pure structural MnP-to NiAs-type transitions are known for, e.g., CrAs with no coupling to any magnetic transition. The situation for Mn−As-P is significantly different since the temperature-induced changes in the average unit cell volume correlate with a conversion from a low-to a high-spin situation for the Mn atoms. In this respect, the local symmetry and the local Mn−(P, As) distances/environment become a real factor for spin conversion and probably also for the structural phase transition. An intriguing question is what drives the secondorder phase transition in this system. Parameters like impurities, strain, and grain boundaries could impact the transition. However, care has been taken to minimize these potential parameters in the synthesis; using ultrapure elements as reactants and repeated crushing and long-term annealing are conducted to achieve a high level of P, As homogeneity. The sluggishness of the phase transition allowed us to probe the local picture. PDF analysis indicates that the material is not uniform during the phase transition. Locally some Mn−As-P atoms arrange themselves in a hexagonal-like manner while others remain in an orthorhombic arrangement. In a solid solution, there will be certain distributions of the atoms at the Chemistry of Materials pubs.acs.org/cm Article local level. In the NiAs-type structure, Mn sits in octahedral (P, As) coordination with 6 + 2 Mn next-nearest neighbors. Each P, As bonds to six Mn neighbors (trigonal prismatic coordination). Therefore, the local structure of the Mn−(P, As) 6 octahedra will depend on the level of the P substitution and the distortion relative to the next-nearest metal atom neighbors. PDF indicates that these distorted octahedra behave differently on heating the material. Some remain distorted, probably due to their vicinity to P atoms and possibly also grain boundaries. Other octahedra change their spin and turn into a high-spin local situation which requires a simultaneous increase in the local symmetry. An interesting question is whether similar features can occur for other solid solution phases that undergo second-order phase transitions. These findings are interesting and provide new insight into phase transition. This brings about a tantalizing possibility where one could imagine phase transitions not as globally abrupt and/or starting and finishing where major entropy changes start and stop but rather as coexisting local structures competing energetically for dominance.
Rietveld refinement parameters and pattern for MnAs 0.94 P 0.06 ; atomic coordinates obtained from both PDF and Rietveld refinement; variable-temperature PXRD of MnAs 0.88 P 0.12 and MnAs 0.82 P 0.18 ; Gaussian peak fitting of the first PDF peak of all three compositions and silicon; variation of the normalized area under the individual peak of Mn−P and Mn−A; variation of cell parameters and bond lengths with respect to P substitution; fitted PDF pattern at 175 and 250 K with both hexagonal and orthorhombic phase; comparison of volume change in PDF refinement between local and intermediate-range structure; isotropic thermal parameter and delta2 variation with temperature; phase fraction of the orthorhombic structure at local and intermediate-range structure; magnetic data for MnAs 0.88 P 0.12 and MnAs 0.82 P 0.18 (PDF)