The second-order magnetic phase transition and magnetocaloric effect in all-d-metal NiCoMnTi-based Heusler alloys

The novel all-d -metal Ni(Co)MnTi based magnetic Heusler alloys provide an adjustable giant magnetoca-loric effect and good mechanical properties. We report that the second-order magnetic phase transition can be tailored in this all-d -metal NiCoMnTi based Heusler system by optimizing the Mn/Ti ratio, resulting in a reversible ferromagnetic-to-paramagnetic magnetic transition. A candidate material Ni 33 Co


Introduction
The giant magnetocaloric effect (GMCE) is characterized by an adiabatic temperature change (∆T ad ) and an isothermal magnetic entropy change (∆S m ) when a magnetocaloric material (MCM) is exposed to a changing magnetic field.The GMCE can be utilized to design promising environmental-sustainable and eco-friendly applications like waste heat recovery, a thermomagnetic generator (TMG) and solid-state magnetic refrigeration (SSMR).The GMCE has been widely observed in various MCMs like Gd-Si-Ge [1], Fe 2 P-type [2], La-Fe-Si [3], Ni-Mn-X (X = In, Sn, Sb, Ga, Al) based Heusler alloys [4] and Mn-M-X based (M = Co or Ni, X = Si or Ge) ferromagnets [5].These materials demonstrate a strong first-order magnetic transition (FOMT) with a discontinuous change in the first derivative of the Gibbs free energy resulting from the coupling between the magnetic and crystal lattice degrees of freedom (in the form of a magnetoelastic or magnetostructural coupling).Even though the MCMs that show a FOMT exhibit the giant and sharp ∆S m and ∆T ad , the associated undesirable intrinsic thermal and magnetic hysteresis inevitably results in a low energy efficiency during cooling cycles as a result of the irreversibility.Furthermore, the strong crystal lattice distortion accompanied by the structural transition generally makes these MCMs subject to cracking and fatigue, which limits the lifetime of these materials.
Compared with the FOMT, the second-order magnetic transition (SOMT) with a discontinuous change in the second derivative of the Gibbs free energy show a reversible magnetic transition from the low-temperature ferromagnetic (FM) to high-temperature paramagnetic (PM) state.The SOMT materials can thereby avoid some of the intrinsic disadvantages of the FOMT materials, although the magnetocaloric performance is relatively moderate.Currently, some interesting SOMT materials like (LaSr)MnO 3 based perovskites [6], Fe-based amorphous alloys [7], AlFe 2 B 2 based intermetallic compounds [8], MnSb based half-Heusler alloys [9,10] and NiMn based Heusler alloys [11][12][13][14][15][16] have been investigated.Singh et al. found that the off-stoichiometric Ni 2 Mn 1.4 In 0.6 Heusler alloys can simultaneously demonstrate a large saturation magnetization (M S = 6.17 µ B / f.u.) and a high ∆T ad (of about 1.5 K for a field change of 0-2 T) near room temperature, which makes it competitive with some FOMT shape-memory Heusler alloys [11].Additionally, the SOMT properties of the Si substituted Ni 50 Mn 36 Sn 14-x Si x (x = 1, 2, 3) and Ni 50 Mn 35 In 15−x Si x (1 ≤ x ≤ 5) Heusler systems have been studied [12,15].Recently, the unique all-d-metal Ni(Co)MnTi based magnetic Heusler alloys have been discovered [17,18].In comparison to the traditional NiMn-X (X = In, Sn, Sb, Ga, Al) based magnetic Heusler alloys, where the 3rd element is mainly occupied by p-block elements, the structural transition temperature can be significantly decreased by introducing Ti and ferromagnetism can be established by forming strong Mn-Co-Mn magnetic interactions in these all-dmetal Ni(Co)MnTi based Heusler alloys.Like other Heusler systems, this all-d-metal Heusler alloy system also shows a large thermal hysteresis [19][20][21].Because the Ti in the system can effectively stabilize the austenite phase [22], we therefore expect that tuning the Mn/Ti ratio could decouple the first-order magnetostructural transition, resulting in a reversible SOMT.Recent studies in this Heusler system mainly focus on regulating the FOMT [19,23].Studies associated with the SOMT in this system are still scarce and could deepen our understanding of the functionality of this material system for future applications.
By optimizing the Mn/Ti ratio all-d-metal NiCoMnTi based magnetic Heusler alloys with a SOMT have been produced successfully.We systematically investigate the magnetocaloric properties (including compositional maps of T C and M S ), the structural properties and the microstructure information of these alloys by XRD, SQUID, SEM and Density functional theory (DFT).Our results show T C and M S can be controlled by adjusting the Ni/Co concentration and by doping non-magnetic Cu atoms.The present study provides new insight into the magnetic phase transition for this all-d-metal Ni(Co) MnTi based Heusler alloy system.

Experimental methods
The SOMT all-d-metal NiCoMnTi based magnetic Heusler alloys with a composition of Ni 50-x Co x Mn 30 Ti 20 (x = 11, 12, 13, 15, 17, 19, 21, 23), Ni 37 Co 13 Mn 30+x Ti 20-x (x = 1, 2), Ni 33 Co 17 Mn 30-x Ti 20+x (x = 2, 4) and Ni 37-y Co 13 Mn 30 Ti 20-x Cu x+y (x,y = 0.5, 1) samples were prepared from high-purity elements (Ni 99.99%, Co 99.9%, Mn 99.99%, Ti 99.99% and Cu 99.9%) through the arc-melting technique under Ar atmosphere.For homogenization the melted ingots were flipped and remelted for five times.An extra 4% Mn was added to compensate for evaporation losses during melting.Subsequently, the as-cast ingots were sealed into quartz ampoules under Ar atmosphere and annealed at 1173 K for 6 days followed by cold-water quenching to further enhance homogeneity and short range order.The room temperature X-ray diffraction (XRD) patterns were collected on a PANalytical X-pert Pro diffractometer with Cu-K α radiation.The crystal structure refinement of XRD patterns was performed using the Rietveld refinement method [24] implemented in the Fullprof software package.The microstructure of the alloys was analyzed by a Scanning Electron Microscope (SEM, JEOL JSM IT100LA) equipped with Energy Dispersive X-ray Spectroscopy (EDS), and line-scans were used to determine the elemental distribution of different phases.To visualize the grain boundaries of the materials two drops of etching solvent (0.5 g FeCl 3 mixed with 9.9 mL methanol (CH 3 OH)) were spread on the surface of metallographic specimens and then rapidly removed with ethanol after 15-20 s.After that, optical microscopy (Olympus Corporation) was applied.The temperature and magnetic field dependence of the magnetization curves were characterized by a superconducting quantum interference device (SQUID) magnetometer (Quantum Design MPMS 5XL) using the reciprocating sample option (RSO) mode.For measurements on the magnetic properties above 370 K a vibrating sample magnetometer (VSM, Quantum Design Versalab) was applied.The ∆S m and ∆T ad can be derived from the calorimetric measurements based on a home-built in-field DSC machine, details can be found in Ref. [25].
First-principles electronic structure calculations were performed in the framework of the density functional theory (DFT).The Vienna ab initio simulation package (VASP) [26,27] in the projector augmented wave (PAW) method [28,29] was employed to perform the DFT calculations using the generalized gradient approximation of Perdew-Burke-Ernzerhof [30] for the exchange correlation functional.The valence electron configuration was 3p 6 4s 2 3d 5 for Mn, 3p 6 4 s 2 3d 2 for Ti, 4s 2 3d 7 for Co and 4s 2 3d 8 for Ni.A 2 × 2 × 1 supercell, built from a 16-atom unit cell, was utilized in all calculations.The structural degrees of freedom were fully relaxed on a k-grid of 10 × 10 × 10.The k-space integrations were performed with the Methfessel-Paxton method [31] of second order with a smearing width of 0.05 eV.The lattice parameters and atomic positions were relaxed for a force convergence of 0.1 meV/Å, the energies were converged to 1 μeV.The kinetic energy cutoff was set at 350 eV.

Structural analysis
The room temperature XRD patterns for the Ni 50-x Co x Mn 30 Ti 20 (x = 12,13,15,17,19,21,23) samples are shown in Fig. 1(a).All diffraction peaks correspond with the cubic B 2 -type austenite (space group Fm-3 m) crystal structure, confirming that a stable austenite phase is formed.No signal from the modulated martensite structure or from an impurity phase was found, indicating a pure austenite phase.Wei et al. demonstrated that samples contained less than 16% Co could hold martensite at low temperatures [17], while in our case the martensite to austenite structural transition can be tuned to disappear and only the parent B 2 -type austenite is left by optimizing Mn/Ti ratio to a lower Mn level (higher Ti).The lattice parameter a decreases from 5.928 Å to 5.914 Å when the Co content increases from 12% to 23%, as illustrated in Fig. 1(b).Considering the covalent radius of Ni (1.24 Å) and Co (1.26 Å) [32], more Co with a larger radius should expand the unit-cell volume, which is in conflict with the experimental results.Similar results were also observed in Ni 50- x Co x Mn 35 Ti 15 (x = 13, 13.5) ribbon samples with a FOMT [20].This decrease in cell volume is also confirmed by our DFT calculations see below.The Rietveld refinement of the room-temperature XRD pattern for the Ni 33 Co 17 Mn 30 Ti 20 sample is presented in Fig. 1(c) and the main diffraction planes are labeled as (220), (400) and (422).In Fig. 1(d) the cubic B 2 austenite crystal structure with space group Fm-3 m is shown.The various metallic atoms follow specific crystal occupancy rules.The Ni/Co atoms occupy the 8c site at (1/4, 1/4, 1/4) and (1/4, 1/4, 3/4) while the Mn/Ti atoms occupy the 4b site at (1/2, 1/2,1/2) and the 4a site at (0, 0, 0), where Mn preferentially occupies the 4b position.

Magnetic properties and magnetic phase diagram
In Fig. 2(a) the temperature-dependent magnetization (M-T) curves of the materials that vary in Ni/Co ratio (x = 12, 13, 15, 17, 19, 21, 23) are shown.The heating and cooling curves coincide, which suggests that the transition corresponds to a SOMT.The results show that the magnetic behavior is significantly affected by its composition.For instance, a higher Co content attributes to an obvious enhancement in magnetization.By comparing the samples with the lowest Co (12%) and the highest Co (23%) it is found that the saturation magnetization shows a fivefold increment, from 32.4 to 144.5 Am 2 kg −1 .Similar to the case of all-d metal NiCoMnTi system with a FOMT, the so-called "Co-activated ferromagnetism" also plays a crucial function in the SOMT system where Co can effectively help to build a strong ferromagnetic coupling in the local Mn-Co-Mn configuration [33,34].In Fig. 2(b), the M-T curves at 0.01 T are presented.The Curie temperature T C of austenite can be determined from the maximum in |dM/dT| in these low-field M-T curves (see the inset of Fig. 2(b)).As illustrated in Fig. 2(c), it can be seen that with increasing Co content the T C of austenite increases and closely follows a linear relation of about 27 K/at% Co.Interestingly, in Fig. 2(b) we observe for almost all samples a distinct difference between zero-field-cooling (ZFC) and field-cooling (FC) curves when temperature is below 100 K.This has also been observed in other Mn-based Heusler alloys like Fe-Mn-Si [35] and Ni-Mn-In [13] and should be ascribed to magnetocrystalline anisotropy.The maximum observed in the temperature dependence of the magnetization for Co ≤ 19 should be ascribed to a change in magnetic interactions from FM at high temperatures to antiferromagnetic (AFM) at lower temperature.Note, that the parent austenite of NiMnTi based Heusler alloys is an antiferromagnet [17,19].In Fig. 2(d) the isothermal fielddependent magnetization (M-H) curves at 5 K are presented, which demonstrate that an increase in Co concentration leads to a higher magnetization.Furthermore, it can be also deduced that considerably less magnetic field is needed to reach its maximum magnetization for samples with a higher Co content.For example, the sample containing 23% Co can be saturated at around 1 T while the 15% Co sample is still not saturated at 5 T. It is worth to note that for the samples with the lowest Co content (such as 12% and 15%) the magnetization and demagnetization curves fail to overlap each other below 1 T, which should also be attributed to the magnetocrystalline anisotropy mentioned above.
Controlling T C to cover a certain temperature range is a fundamental requirement for cooling applications.The Curie temperature can be tuned via optimizing different intrinsic and extrinsic parameters, such as composition [36], particle size [37], chemical element pressure [38], electron valence [23], and external mechanical (hydrostatic) pressure [39].Within these factors, the chemical pressure, which is closely related to a change in unit-cell volume, and electron valence effects could be distinctly affected by magnetic/ non-magnetic metal substitution or interstitial (light-element) doping.For example, the substitution of Mn by Cr has been applied to tailor the magnetic and structural transitions in Mn 1−x Cr x CoGe compounds [40].Recently, it has been found that Cu substitution in Ni-Mn-In based Heusler alloys can effectively modify the FOMT [41][42][43].Therefore, we expect that T C could also be efficiently tailored through Cu substitution of Ni/Mn in the Ni-Co-Mn-Ti system with a SOMT.In Fig. 3 The reduction in T C is about 24 K/at% Cu.The shift in T C by Cu substitution could result from the weakened magnetic exchange interaction between the Mn-Co-Mn configuration, rather than the chemical pressure effect because the covalent radius of Cu (1.32 Å) is in between that of Ti (1.60 Å) and Ni (1.24 Å) [32], even though Cu (3d 10 4s 1 ) atoms have more electrons than Ti (3d 2 4s 2 )/Ni (3d 8 4s 2 ).Therefore, Cu substitution and tuning the Ni/Co ratio are both efficient ways to optimize the T C shift.In addition, Fig. 3(c) and 3(d) show the M-T curves at 1 T for the Ni 37 Co 13 Mn 30+x Ti 20-x (x = 0, 1, 2) and Ni 33 Co 17 Mn 30-x Ti 20+x (x = 0, 2, 4) samples.
From the above results it can be seen that T C and the magnetization can be regulated by composition in the Ni 50-x Co x Mn 30 Ti 20 (x = 12, 13, 15, 17, 19, 21, 23) samples with a SOMT.This indicates that Co substitution for Ni is effective in increasing T C and the magnetization for the NiCoMnTi Heusler alloys with a SOMT.This may be attributed to the strong coupling between Co and Mn atoms.A similar phenomenon was also observed in other NiMn-based Heusler alloys with a FOMT, such as Ni(Co)MnGa [44], Ni(Co)MnIn [45], Ni (Co)MnSn [46] and Ni(Co)MnSb [47].In Fig. 4(a) and 4(b) we summarized the changes in T C and magnetization as a function of Co content.Once Co content is above 12 at% T C and magnetization data show an increasing tendency with increasing Co concentration, and T C of 11% Co is close to 12% one.
To better guide the optimization of the all-d-metal NiCoMnTi magnetic Heusler alloys with a SOMT, it is useful to determine compositional maps of the saturation magnetization M S and the Curie temperature T C with respect to different Co/Ti content (in at %), as presented in Fig. 4(c) and 4(d), respectively.On the other hand, to verify the usefulness of these phase diagrams, two new alloys with a designed composition (Ni 29 Co 21 Mn 28 Ti 22 and Ni 28 Co 22 Mn 26 Ti 24 ) are utilized.For example, Fig. 5 shows the M-T   Using DFT, the calculated lattice parameter a, the total magnetic moment and the lowest formation energy have been evaluated for the Ni 50-x Co x Mn 30 Ti 20 (x = 12, 13, 15, 17, 19, 21, 23) samples, as listed in Table 1.A decrease in lattice parameter a is also observed for increasing Co content, which is in agreement with our experimental results shown in Fig. 1(b).Interestingly, the total magnetic moment (per formula unit) for this material system with a SOMT is predominantly controlled by the Co concentration and shows an increase with increasing Co content.For instance, the calculated moment was enhanced from 5.44 (x = 13) to 5.83 (x = 23) μ B /f.u.This might be because a higher Co content can more sufficiently align the Mn atoms as the local Mn-Co-Mn configuration controls the introduced strong FM, which is similar to other Co-doping NiMn-based Heusler systems.Due to the relative high M S at 1 T (102 Am 2 kg −1 ) and the near room temperature magnetic phase transition T C (275 K) the 17% Co sample (Ni 33 Co 17 Mn 30 Ti 20 ) seems to be the most promising candidate within this series for magnetic refrigeration applications.It is therefore of interest to further investigate the magnetocaloric properties of this Ni 33 Co 17 Mn 30 Ti 20 alloy in terms of the magnetic entropy change (∆S m ), adiabatic temperature change (∆T ad ) and the relative cooling power (CRP).As shown in Fig. 6(a), the isofield M-T curves from 0.1 to 5 T have been collected.From these data the ∆S m values can be calculated by using the Maxwell relation: From Fig. 6(b) it can be seen that the sample shows a conventional MCE.As expected for a material with a SOMT the ∆S m peak is obviously broad and moderate in size.For example, the maximum |∆S m | with an applied magnetic field change (∆μ 0 H) of 0-1 T can reach only 0.6 Jkg −1 K −1 which is well consistent with the value extracted from DSC-in field measurement, and |∆S m | reaches a maximum value of 1.1 and 2.3 Jkg −1 K −1 with ∆μ 0 H of 0-2 and 0-5 T, respectively.Although maximum value for |∆S m | only reaches about 22% of the value obtained for pure gadolinium (5 Jkg −1 K −1 for ∆μ 0 H = 2 T), it is comparable to other magnetic Heusler alloys with a SOMT [11][12][13][14]48,49].The coefficient of refrigerant performance (CRP) reflects the MCE performance and can be determined by the following relation [50]: is maximum peak value of |∆S m | and T ad is the maximum temperature change (extracted from in-field DSC measurements) due to an applied magnetic field (∆T ad ≈ 0.3 K for ∆μ 0 H = 1 T).Therefore, compared with commercial Gd (≈ 0.17(2) for ∆μ 0 H = 1 T) the calculated CRP value for Ni 33 Co 17 Mn 30 Ti 20 alloy is only 0.01 which means this material is not suitable for potential magnetic refrigeration application.

Microstructural information
If the crystal structure and the macroscopic property change, then it is useful to obtain a deeper insight into the microstructure.For some traditional NiMn-X (X = In, Sn, Sb, Ga, Al) based magnetic Heusler alloys, the average grain size can reach several hundreds of μm up to the mm-range [23].As demonstrated in Fig. 7(a), the grain boundaries of the material are distinguishable in the optical microscopy image, and the average grain size is approximately 100-200 µm.Compared with other NiMn-X (X = In, Sn, Sb, Ga, Al) based Heusler alloys, this grain size is significantly smaller.Considering the Hall-Petch relation (inverse relation between the grain size and the material strength) [51] the noticeable reduction in grain size for the NiCoMnTi MCMs with a SOMT could lead to an enhanced mechanical strength.Grain refinement has been utilized in Ni-CoMnTi ribbon samples with a FOMT to improve micro-hardness [20].Additionally, as shown in the SEM image of Fig. 7(b), pure austenite is observed and there is no slat-like martensite at room temperature.Worth mentioning is the presence of several μm (below 10 µm) secondary phase precipitates within the main matrix.Because the concentration of precipitates is very limited (< 1%), it is insufficient to be detected by XRD.EDS measurements were utilized to determine the composition of main matrix phase and the secondary phase, as illustrated in Table 2 (a), the M-T curves at 1 T for the Ni 37- y Co 13 Mn 30 Ti 20-x Cu x+y (x,y = 0, 0.5, 1) samples are presented.It is observed that the magnetization decreases when Cu replaces Ti or Ni.In Fig. 3(b) it is shown that compared with the parent Ni 37 Co 13 Mn 30 Ti 20 (T C = 202 K) alloy, Cu substitution of Ti shows a remarkable decrease in T C .A substitution of 0.5% Cu shifted T C to 179 K (and 1% Cu to 171 K), while a 0.5% Cu substitution of Ni results in a reduction in T C to 190 K (and 1% Cu to 178 K).

Fig. 4 .
Fig. 4. Effect of the Co concentration on the (a) saturation magnetization and (b) transition temperature at 5 K derived from M-T measurements.Effect of the amount of Co and Ti substitution on (c) the saturation magnetization and (d) the phase transition temperature the 2D compositional maps.The black marks indicate which compositions were measured, and ( ?), ( ?) in the top corner stands for two test samples to confirm the trends.

Fig. 5 .
Fig. 5. Isofield M-T curves at 1 T for the Ni 29 Co 21 Mn 28 Ti 22 and Ni 28 Co 22 Mn 26 Ti 24 samples.The inset corresponds to the M-T curves at 0.01 T for these two alloys.
. The chemical composition of the main matrix phase (Ni 32.57Co 16.33 Mn 31.87Ti 19.06 ) is close to the nominal composition (Ni 33 Co 17 Mn 30 Ti 20 ).Meanwhile, the small fraction of precipitates corresponds to a Ti-rich impurity (Ni 2.69 Co 1.33 Mn 4.76 Ti 91.22 ).The concentration of Ti-rich second phase particles can be controlled by the annealing conditions.For instance, a lower heat-treatment temperature would generate more Ti-rich impurities.The enlarged SEM image in Fig. 7(c) shows the morphology of the Ti-rich secondary phase.In the SEM figure of Fig. 7(c) a line scan measurement was performed at various locations along the yellow dashed line to confirm the elemental distribution of the main matrix phase and the Ti-rich secondary phase, as shown in Fig. 7(d).The line scans indicate that the Ti-rich impurities are quite homogeneous.

Fig. 6 .
Fig. 6.(a) Isofield M-T curves between 0.1 and 5 T for the Ni 33 Co 17 Mn 30 Ti 20 sample.(b) Magnetic entropy change ∆S m for different magnetic field changes as a function of temperature for the Ni 33 Co 17 Mn 30 Ti 20 sample.The black solid curve was derived from DSC-in field measurement with ∆μ 0 H = 1 T.

Fig. 7 .
Fig. 7. (a) Optical microscope image for the etched Ni 33 Co 17 Mn 30 Ti 20 sample.(b) Back-scattered SEM image for the Ni 33 Co 17 Mn 30 Ti 20 sample.(c) Enlarged back-scattered SEM image for the Ni 33 Co 17 Mn 30 Ti 20 sample.(d) SEM line scan measurements based on (c) for the Ni 33 Co 17 Mn 30 Ti 20 sample.

Table 2
Elemental composition of the Ni 33 Co 17 Mn 30 Ti 20 alloy determined by EDS measurements.