On the magnetic contribution to the inverse magnetocaloric effect in Ni-Co-Cu-Mn-Sn metamagnetic shape memory alloys

Accepted Manuscript On the magnetic contribution to the inverse magnetocaloric effect in Ni-Co-CuMn-Sn metamagnetic shape memory alloys P. Czaja, M. Kowalczyk, W. Maziarz PII: DOI: Reference:

S0304-8853(18)32735-5 https://doi.org/10.1016/j.jmmm.2018.11.071 MAGMA 64630

To appear in:

Journal of Magnetism and Magnetic Materials

Received Date: Revised Date: Accepted Date:

29 August 2018 3 November 2018 11 November 2018

Please cite this article as: P. Czaja, M. Kowalczyk, W. Maziarz, On the magnetic contribution to the inverse magnetocaloric effect in Ni-Co-Cu-Mn-Sn metamagnetic shape memory alloys, Journal of Magnetism and Magnetic Materials (2018), doi: https://doi.org/10.1016/j.jmmm.2018.11.071

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On the magnetic contribution to the inverse magnetocaloric effect in Ni-CoCu-Mn-Sn metamagnetic shape memory alloys P. Czaja1,*, M. Kowalczyk2, W. Maziarz1 1

The Aleksander Krupkowski Institute of Metallurgy and Materials Science, Polish Academy of Sciences, 25 Reymonta St., 30-059 Kraków, Poland 2 Faculty of Materials Science and Engineering, Warsaw University of Technology, 141 Wołoska St., 02-507 Warsaw, Poland

Abstract Martensitic transformation and magnetic properties in directionally solidified Ni45xCo xCu 5Mn39Sn11 (x = 0, 1, 2) alloys were studied. The martensitic transformation temperature decreases with increasing Co concentration, whereas the Curie temperature of austenite increases, what then alters the magnetic state of austenite at the onset of martensitic phase transformation. Concomitantly the effective magnetic moment of austenite increases by 0.7 μ /. . with Co substitution. Under an applied magnetic field of 5 T the peak values of the magnetic entropy changes reach 11.4 J/kgK (x = 1) and 4.5 J/kgK (x = 2). The variations in magnetic entropy are discussed in relation to a stronger ferromagnetic contribution promoted by Co in the martensite phase. Key words: Magnetic shape memory alloys, Heusler alloys, Martensitic transformation, Magnetocaloric effect, Entropy Introduction

 .

The magnetic contribution (∆ ) to the martensitic transformation (MT) entropy change (∆ ) in Ni-Mn-(In, Sn, Sb) based metamagnetic shape memory alloys (MSMA) [1,2] gives rise to a number of unique and functional phenomena including a magnetic field induced

 . reverse MT [2] and an inverse magnetocaloric effect (inverse MCE; ∆ > 0) [3,4] interesting for magnetic actuation and solid state refrigeration [5,6]. Both phenomena result in relation to entropy and magnetic discontinuity at the MT allowed by the coupling between the magnetic exchange energy and interatomic distances [3]. The coupling implies that the collapse in crystallographic symmetry coincides with symmetry diminution in a magnetic configuration, which behavior can be overturned with a magnetic field (  ∙H) induced reverse MT. In general

 . . for ferromagnetic alloys the ∆ is written as ∆ = ∆ + ∆ , where the main contribution to the overall entropy change, aside from the magnetic term, is of vibrational . (∆ ) origin with negligible influence of configurational and electronic inputs [7]. The

 . ∆ is fueled by the saturation magnetization difference (∆  ) across the MT; i.e. between the lower symmetry martensite and the parent austenite (L21; Fm3m) phase and it can   be maximized by increasing the ∆  =  −   and/or extending the temperature difference between the MT transformation temperature (TMT) and the Curie temperature of austenite ( ) ∆TT =  - TMT; e.g. by Co doping [8,9,10,11]. Interestingly the overall ∆ is

 . . found to decrease with increasing ∆TT (∆ < 0, ∆ > 0) with the chief contribution *

Corresponding author. Electronic mail: [email protected]

1

 .

ascribed in this instance to the ∆ , that itself is sensitive to the temperature dependence of magnetization [7,12,13]. In extreme scenario, under a magnetic field of high enough intensity the Δ tends to zero leading to a transformation arrest, since the thermodynamic driving force is given as: ∆ = Δ ∙ ∆, where ∆ is undercooling [14]. Similar to Co the Cu for Ni substitution in Ni-Mn-Sn alloys brings the TMT to lower values and increases the  stabilizing the ferromagnetic austenite over a wider temperature phase field [15,16,17,18,19]. Although such composition change permits to tune the ∆TT in a relatively broad temperature range it may adversely influence the ∆  , and thus infringe the driving force for reverse MT

 . simultaneously reducing the ∆ , depending on the magnetic state of martensite e.g.: antiferromagnetic (AFM) [20]; reentrant spin glass (SG) [21,22]; superparamagnetic (SPM), superspin glass (SSG) [23,24] coexisting with ferromagnetic (FM) exchange coupling in NiMn-Sn [25] and Ni-Co-Mn-Sn [26,27] based alloys. Nonetheless, despite the complexity of magnetic behavior Co and Cu, at moderate concentrations (< 9 at.%) escaping the precipitation

 . of γ phase [28,29], apparently reductive for ∆ [30], are highly desired alloying elements not only in the view of their influence on ∆TT but also with respect to a reduced hysteresis shown by Ni45Co 5Mn40Sn10 alloy [31], as well as their impact on ductility enhancement [32,33] and 12% magnetic field induced strain yielded by ferromagnetic, non-modulated single crystalline Ni45Mn24Ga23Co 4Cu4 under low twinning stress ~1.2 MPa [34]. These are critical findings in the light of the facts that (i) due to the first order nature of the MT hysteresis losses significantly compromise the refrigeration efficiency [35] and further limit the temperature range for reverse MT [36,37]; (ii) the critical isothermally applied magnetic field needed to $ complete the reverse MT can be estimated as  ∙ "# = (&' − ' ) ∙  ∙ )"* /), where Af, Mf stand for the austenite/martensite finish temperatures and the )" * /) denotes the inverse rate of Af temperature change with applied H, what stipulates that the reduced &' − '

 .

difference lends the ability to reap the ∆ at the relatively lower  ∙H [38,39,40,41]; (iii) Ni-Mn-(In, Sn) alloys have been reported with giant baro- [42,43] and elastocaloric effects [41,44,45,46,47] what extends their unique fundamental and functional behavior offering combined multicaloric [17,48] response, provided sufficient ductility is ensured. Since, MT is diffusionless in nature the magnetic order of austenite is inherited by martensite and therefore it has a strong bearing on its magnetic response. A more detailed investigation of the real

 . magnetic landscape of the martensite around MT and its imminent influence on the ∆ and ∆ in Ni-Mn-Sn-(Co, Cu) based alloys is still needed for advanced engineering of MCE and MFIS. It is particularly vital with respect to materials (e.g. single crystalline or large grain, textured specimens – directional solidification) with extended ∆ vs. T dependence

 . beneficial for the width of the ∆ peak, and thus for the overall refrigerant capacity (RC) [49,50,51,52], which nonetheless may entail MT spread over a broad temperature regime e.g. As ≤  ≤ Af ≤  . Such temperature spread, depending on the combination of the critical temperatures, may involve in consequence severe Zeeman Energy, ZE = ∆M·H, perturbations along the complete transformation path. Therefore the current work scrutinizes the MT behavior and the evolution of the magnetic exchange across MT with their simultaneous contribution to

 . the ∆ and ∆ in directionally solidified Ni45-xCoxCu5Mn39Sn11 (x = 0, 1, 2) alloys. Experimental 2

A word on the choice of composition: in order to identify the suitable ternary Ni-Mn-Sn terminal composition the literature values for reverse MT temperature (TpM→A) and the  as a

 . function of e/a along with the ∆ dependence on the TpM→A have been plotted in Fig. 1 (a, b) and collected in Table 1 for a set of arc-melted ternary Ni-Mn-Sn and quaternary Ni-Mn-Sn  . (Co/Cu) based alloys. The ∆ has been normalized over ∆H and approximated as

 . ~∆Smag/∆H, given the fact that for a second order magnetic phase transition ∆ ∝ Hn and for T << TC, n ~ 1 [53,54]. Also taking into account some controversy related to the TMT vs. e/a behavior in Cu substituted Ni-Mn alloys [55] the calculated valence electrons include Ni (3d84s2), Mn (3d54s2), Sn (5s25p 2), Cu (3d104s1), Co (3d 74s2). From Fig. 1 (a) it is clear that the TMT is more susceptible to composition change than the  . In Fig. 1 (b) on the other hand the

 . shaded areas highlight the ultimately desirable temperature range for considerable ∆ . Based on Fig. 1 (a) and (b) as well as ref. [56] the Ni50Mn39Sn11 alloy with the TMT ~400 K has been chosen as the terminal composition. It was then substituted with 5 at.% Cu, having noted prior to substitution ca. 15 K drop per at.% in TMT in Ni50-xCuxMn38Sn12 [17]. It was then followed with further 1 and 2 at.% Co for Ni substitution in order to arrive with MT at around 300 K with simultaneous ∆M enhancement. Eventually three polycrystalline alloys with composition of Ni45-xCoxCu5Mn39Sn11 (x = 0, 1, 2) were prepared from high purity Ni, Co, Cu, Mn, Sn by induction melting. Subsequently the alloys were placed in a crucible, remelted (1570 K) and directionally solidified by the Bridgman method with the crucible pulling rate of 10 mm/h. The resultant ingots were sealed under vacuum in quartz ampules and left in a furnace at 1220 K for 72 h in order to encourage chemical homogeneity. The annealing step was then followed by slow cooling with the furnace to guarantee the maximum experimentally attainable atomic order in all three samples. The composition of alloys was examined with energy dispersive X-ray spectrometer (EDX) wedded to the FEI E-SEM XL30 scanning electron microscope (SEM). It has turned out in a good agreement with the nominal composition as follows: Ni46.2 ± 0.9Cu5.7 ± 0.2Mn37.4 ± 0.7Sn10.7 ± 0.4 (e/a = 8.294), Ni44.7 ± 0.9Co1.2 ± 0.2Cu 5.5 ± 0.2Mn38 ± 0.8Sn10.5 ± 0.4 (e/a = 8.273), Ni43.4 ± 0.9Co 2.4 ± 0.5Cu 5.8 ± 0.2Mn38.1 ± 0.8Sn10.3 ± 0.4 (e/a = 8.274). The three alloys are abbreviated herein to Co0, Co1 and Co2, accordingly. The structure has been confirmed with synchrotron high-energy X-ray radiation (87.1 keV, λ = 0.142342 Å) in a transmission geometry at the beamline Petra P07B at DESY, Germany. Thermal effects were investigated using differential scanning calorimetry (DSC) on a Mettler DSC 823 instrument in the 173–423 K temperature range. The cooling/ heating rate used throughout DSC experiments was set at 10 K/min. The (dc) mass susceptibility and magnetisation were measured in the temperature range between 0 K and 400 K and under a magnetic field between 5 mT and 5 T using the Vibrating Sample Magnetometer (VSM). Consecutive zero field cooling (ZFC), field cooling (FC) and field heating (FH) measurements were performed on decreasing and increasing temperature, respectively. All the measurements were conducted in a step mode with a stabilised temperature at each experimental point. Based on the isofield M (T) curves the

 . magnetic entropy change (∆ ) has been computed employing the Maxwell relation: ∆ = 0

/(0, )

 ∙ - 3 .

/

2 )". 0

3

Results

Fig. 1. The reverse MT temperature (TpM→A) and  vs. e/a for a number of Ni-Mn-Sn based

 . alloys (a); the magnetic entropy change averaged over ∆H as ∆ /∆H vs. TpM→A (b). The dotted lines in Fig. 1 (b) are provided for the ease of eye navigation.

Table 1. The critical Ms, Mf, As, Af,  ,  temperatures along with the transformation

 . hysteresis (Af - Ms) and the ∆ for a set of Ni-Mn-Sn based alloys. Alloy Ni50Mn50-x Snx x=15 x=13 x=10 x=5 Ni50-xMn39+xSn11 x=5 x=6 x=7 Ni50Mn36 Sn14 Ni50Mn36.5 Sn13.5 Ni50Mn37 Sn13 Ni41Mn50 Sn9 Ni43Mn46 Sn11 Ni44Mn45 Sn11 Ni43-xMn47+xSn10 x=0 x=1 x=2 x=3 x=4

e/a

Ms (K)

Mf (K)

As (K)

Af (K)

465 (K)

47 5 (K)

Af - Ms (K)

8.05 8.11 8.20 8.35

189 307 444 711

174 289 437 693

190 295 445 718

202 318 453 743

-

230 -

8.02 7.99 7.96 8.08 8.09 8.11 7.96 7.96 7.99

270 245 200 276 275 305 300 200 246

255 230 185 262 263 286 280 185 -

270 276 276 300 290 195 -

285 290 288 316 320 206 -

300 290 280 300 320 320 280 280

7.99 7.96 7.93 7.90 7.87

-

-

262 246 216 187 164

274 263 240 208 185

276 277 278 282 295

9:;.

∆874 (J· kg-1· K-1)

Ref.

13 11 9 32

14.2

[25] [25] [25] [25]

180 180 180 244 230 140 -

15 14 13 11 20 6 -

6.8 (1T) 10.1 (1T) 10.4 (1T) 12 (5T) 5.2 (1.5T) 8.3 (5T) 10.4 (1T) 31.2 (5T)

-

12 17 24 21 21

11.6 12.6 14 11 10.1

(5T) -

(1.2T) (1.2T) (1.2T) (1.2T) (1.2T)

[57] [58] [57] [59] [60] [61] [62] [63,64] [65] [66] [66] [66] [66] [66] [66]

4

x=5 Ni43Mn46Sn11 Ni40Mn50Sn10 Ni51Mn49-xSnx x=13.8 x=14 x=14.2 x=14.5 x=14.8 x=15 Ni50-xCuxMn36 Sn14 x=0 x=2 x=4 x=6 Ni50-xCuxMn38 Sn12 x=0 x=2 x=4 x=6 Ni50Mn33Cu2 Sn15 Ni44-xCoxMn45 Sn11 x=0 x=1 x=2 Ni48.75 Co1.25Mn37 Sn13 Ni50Mn37-xCoxSn13 x=1 x=3

7.84 7.96 7.90

230

8.12 8.11 8.10 8.10 8.09 8.08

185

142 195 202

280 275 266 245 222 208

164 215 242

298 293 286 265 242 230

306 280 -

-

22 12

9.4 (1.2T) 10.4 (1T) 1.63 (1T)

315 317 318 319 321 323

250 255 260 -

18 18 20 20 20 22

8.7 (1.5T) 5.3 (1.5T) 10.8 (1.5T) 8.4 (1.5T) 7.2 (1.5T) 1.1 (1.5T)

8.08 8.08 8.11 8.12

220 194 148 106

210 182 136 58

240 197 151 76

250 212 167 122

317 321 325 329

-

30 18 19 16

20.9 (5T) 13.1 (5T) -

8.14 8.16 8.18 8.20 8.13

331 309 284 238

-

-

-

313 315 321 310

175 215 240 -

-

13.5 (5T)

7.99 7.98 7.97 8.10

210

-

245 221 189 -

253 236 204 -

290 316 350 -

180 186 186 -

-

10.1 (1T) 14.4 (1T) 6.2 (1T) -

8.13 8.17

281 303

-

289 307

-

-

-

-

-

220

[66] [66] [67] [68] [68] [68] [68] [68] [68] [68] [69] [69] [69] [69] [69] [70] [70] [70] [70] [70] [15] [71] [71] [71] [71] [8] [8] [8] [8]

Fig. 2. DSC thermograms recorded on cooling and heating in the temperature range between 200 and 400 K for Co0 (a), Co1 (b) and Co2 (c) alloys; XRD patterns for the Co0 (d), Co1 (e) and Co2 (f) alloys at room temperature; SADP taken from the Co2 alloy - inset in (f) .

5

Table 2. The valence electron to atom ratio (e/a), critical Ms, Mf, As, Af,  and  temperatures, → → the peak temperatures for the forward (< ) and reverse (< ) martensitic transformation → along with the computed structural transformation entropy change on the forward (∆ ) and → reverse (∆ ) MT for the Co0, Co1 and Co2 alloys.

Alloy Co0 Co1 Co2

e/a

Ms

Mf

As

Af

8.22 331 290 305 347 8.21 295 264 306 323 8.20 290 259 296 317

46→7 >74

47→6 >74

(K) 322 280 278

341 317 310

TCA

TCM

312* 206* 318* 218* 327* 218*

∆86→7 74

∆87→6 74

(J/kgK) 55.8 51.1 57.8 48.8 34.5 44.5

*VSM

Thermal behavior of the studied Co0, Co1 and Co2 alloys was initially monitored with DSC (Fig. 2 a-c). The characteristic martensite (austenite) start/finish Ms/Mf (As/Af) temperatures were estimated from the respective exo- (cooling) and endothermic (heating) DSC peaks by tangent method (Fig. 2 a-c). All the temperatures are collected in Table 2, which shows that the TMT decreases with increasing Co content. The change in Ms is considerable ~∆Ms = 36 K when going from the Co0 to the Co1 alloy, and then less significant upon additional substitution to 2 at.% Co (Co2). On the forward austenite → martensite transition the → temperature hysteresis, ∆?@. = Af – Ms, increases with increasing Co concentration, whereas → ← the transformation interval, ∆A. = Ms – Mf, decreases (Table 3). On the reverse MT (∆?@.

← = As – Mf; ∆A. = Af – As) the trend continues, nonetheless with seemingly much broader → → hysteresis (Table 3). The forward (< ) and reverse (< ) transformation peak ↔ temperatures as well as the magnitudes of entropy changes (∆ ) on the forward and reverse ↔ ↔ transformations, calculated as ∆ = ∆L/< , were ∆L is enthalpy, are also collected ← (Table 2). In general on the reverse MT the ∆ is found to decrease with increasing Co ↔ content. The ∆ values differ slightly for the same alloys between the forward and reverse MT, which is commonly ascribed to the presence of hysteresis and energy dissipation inseparable from the first order nature MT. The difference is more striking for the Co2 alloy exclusively upon the forward MT. All the values in Table 2 were read from the reproducible second cycle, thus the discrepancy may be related to enthalpy estimation and for discussion we ← subsequently refer to ∆ , either way more pertaining to the inverse MCE. The Curie temperatures of the austenite, visible in Fig. 2 (b, c) for the Co1 and Co2 alloys, and martensite for all the three alloys were determined from the inflection points based on the temperature dependence of magnetic susceptibility measurements (Fig. 3 a - c). As expected the  increased with increasing Co concentration. Another notable feature in the DSC curves (Fig. 2 a), is the width and tailing of the peaks, specifically at the martensite end of the MT spectrum, ↔ i.e. Mf ≤ T ≤ < . This may suggest secondary phase contributing to the transformation with a surplus energy term, nonetheless no trace of additional phases was found neither by Light Microscopy nor by SEM, TEM or XRD.

6

Table. 3. Transformation hysteresis and transformation interval on the forward (Af – Ms), (Ms – Mf) and reverse MT (As – Mf ), (Af – As) and lattice parameters for austenite (ac) and martensite (aM, cM) for the Co0, Co1 and Co2 alloys. Alloy

Af – Ms

Ms – Mf

16 28 27

41 31 31

As – Mf

Af – As

ac

15 42 37

42 17 21

5.9858 5.9858

(K) Co0 Co1 Co2

aM (Å) 6.1454 6.1461 6.1500

cM 5.6300 5.6247 5.6276

According to the high energy synchrotron X-ray radiation measurements (Fig. 2 d-f) the crystal structure of the three Co0, Co1 and Co2 alloys can be well indexed solely as a mixture of the L21 austenite (space group: 225) and the 4M martensite (space group: Pmma) phases. The satellite peaks indicated in the Fig. 2 (d) reflect the three fold periodic modulations intrinsic to the 4M martensite. The modulations are also well portrayed in the inset in the Fig. 2 (f), which shows the selected area electron diffraction pattern (SADP) taken from the Co2 sample. The SADP was successfully indexed along the [111] zone axis of the 4M martensite. The satellite peaks outlined along the [110] direction in between the main reflections, and pointed out for clearer view with red arrows, translate to the s1..3 reflections in Fig. 2 (d). The lattice parameters were evaluated and are given in Table 3. The phase volume fraction determined based on the Fig. 2 (e, f) is 71.3% martensite and 28.7% austenite in the Co1 alloy, whereas in the Co2 the phases are present in the amount of 65.5% and 34.5%, respectively. The temperature dependence of the magnetic susceptibility at 5 mT measured in ZFC, FC and FH modes for the Co0, Co1 and Co2 alloys is portrayed in Fig. 3 (a) – (c). The Fig. 3 (d) illustrates the magnetization (M) behavior, under  ∙ " = 5 T, given in µB/Mn vs. temperature measured in the ZFC mode for all the three alloys. Consistent with the DSC the evolution of χ upon heating and cooling reflects typical changes attributable to the second order magnetic and first order MT in MSMA [1]. Strikingly, whereas for the Co0 and Co1 samples the magnetic susceptibility following MT and above  drops to near zero, for the Co2 sample it decreases but seemingly remains non-zero. The changes in the peaks’ heights as well as in the width of the plateau within the Ms ≤ T ≤  temperature range, between the three investigated alloys, result from the shift in the relative proximity between the  and Ms indicating on the onset paramagnetic → paramagnetic (APM → MPM) transition in the case of the Co0 alloy and ferromagnetic → para-/ferromagnetic (AFM→ MPM/FM/?) transformation in the case of the Co1 and Co2 alloys. The splitting between the ZFC and FC curves at low temperature, well below the  , is also a common feature of MSMA originating in magnetic inhomogeneity, i.e. frequently coexisting AFM and FM exchange. The magnetic moment per Mn atom at 5 T evidently increases with Co concentration and it varies with temperature re-tracing MT (Fig. 3 d). For the Co0 alloy the magnetization of martensite below  is higher than the magnetization of austenite below  stemming, most likely, from the low fraction of FM austenite. On the contrary in the case of the Co1 and Co2 samples austenite is the stronger FM phase. While, within the MT temperature range and above the  the M response of the Co2 alloy surpasses

7

that of the Co1, at the low temperature martensite region the M curves for both alloys converge (Fig. 3 d). The isothermal magnetic field dependence of M for all the three alloys is given in Fig. 4. The curves were measured every 50 K in the temperature range between 50 K and 350 K under -2 T ≤  ∙ " ≤ 2 T the applied magnetic field. According to Fig. 4 (a)-(c) all the three alloys at the temperature between 50 K and up to 200 K appear FM with the M gradually decreasing as the temperature goes up and approaches the  . At 250 K, which is within the  ≤ T ≤ Mf temperature range and at 350 K, which is well above the  , the magnetization response of the Co0 and Co1 alloys appears predominantly PM, although at 250 K the curve recorded for the Co1 alloy shows a trace of a sigmoidal curvature. The Co2 alloy displays a similar PM response at 350 K, whereas at 250 K it produces a more distinct sigmoidal curve. Most interesting at 300 K, which is slightly below As for all the three alloys, the curve for the Co0 alloy remains PM, whereas the curves measured for the Co1 and Co2 alloys reveal typical metamagnetic behavior with a characteristic hysteresis loop between the field up and down curves. It is worth noting that at 300 K the magnetic moment of the Co2 alloy flies up above the M of the martensite phase at 50 K. And it is this low temperature (50 K) martensite phase which inherits the highest M value for the two remaining Co0 and Co1 alloys. For better view the temperature evolution of the M, measured at 2 T, for all the three alloys can be followed in Fig. 4 (d).

Fig. 3. Temperature dependencies of magnetic susceptibility under the applied static magnetic field of 5 mT for Co0 (a), Co1 (b) and Co2 (c); temperature dependence of magnetization under magnetic field of 5 T for Co0, Co1 and Co2 alloys (d).

8

Fig. 4. Isothermal magnetization curves measured for the Co0 (a), Co1 (b) and Co2 (c) alloys within the -2 T ≤ µ0·H ≤ 2 T applied magnetic field and at temperatures between 50 K and 350 K (400 K in the case of the Co0 alloy); magnetization M as a function of temperature for the Co0, Co1 and Co2 alloys (d).

9

Fig. 5. Temperature dependence of magnetization (isofield) under static magnetic field in the range from 0.05 to 5 T for Co1 (a) and Co2 (b) alloys; magnetic entropy changes vs. temperature and refrigerant capacity vs. magnetic field (insets) for the Co1 (c) and Co2 (d) alloys. The temperature dependence of magnetization for the Co1 and Co2 alloys in the field range between 0.05 and 5 T are shown in Fig. 5 (a) and (b). The curves were measured during isofield cooling experiments. The Co0 alloy was not qualified for this experiment since it

 . undergoes Apara →Mpara transition and therefore would not contribute significant ∆ given

 . that the ∆ ~∆M. A slight shift of the curves towards lower temperature values with increasing intensity of the magnetic field is also noted. Based on the magnetization data and

 . employing the Maxwell relation the magnetic entropy change ∆ was computed and it is shown Fig. 5 (c) and (d) vs. temperature dependence for the Co1 and the Co2 alloys. The

 . negative ∆ peak at higher temperature corresponds to direct MCE near the  , whereas

 . at lower temperature the ∆ > 0 is owed to the inverse MCE around MT. Irrespective of

 . the sign the ∆ increases with increasing magnetic field and at 5 T it reaches 11.4 J/kg·K

 . for the Co1 and 4.5 J/kg·K for the Co2 alloys. Both ∆ > 0 peaks show tailing, more pronounced with the Co2 alloy. The RC values for both alloys were calculated by integrating

 . the area under the positive ∆ peak and they are shown vs. the magnetic field dependence for both alloys in the inset figures in Fig. 5 (c) and (d). At 5 T the RC for the Co1 alloys is 192.6 J/kg, whereas for the Co2 alloy it amounts to 114.4 J/kg. Discussion

10

From the inspection of the Fig. 3 (a) – (c) it appears that in the case of the Co0 alloy the austenite phase is paramagnetic at the onset of MT and it transforms into a PM martensite Apara ↔ Mpara with some incipient FM along the transformation, since Mf < As <  . Whereas the Co1 and Co2 alloys transform from FM austenite to PM Aferro ↔ Mpara and weakly magnetic Aferro ↔ Mweak magnetic martensite, respectively. The  is best divorced from the MT for the Co2 alloy, the Ms and  are in this instance spread apart by 37 K, and therefore it can be easily noticed protruding from the baseline as marked in Fig. 2 (c). Under the condition Mf ≤  ≤ Ms  the ferromagnetic fraction of austenite ('D$. ) undergoing MT in the case of the Co0 alloy  estimated according to: 'D$. =  − ' E − ' , is equal to 54%. The complete sequence

of the critical transition temperatures for all the three alloys can thus be given as: Co0:  < Mf < As <  < Ms < Af; Co1:  < Mf < Ms
the application of the Curie-Weiss law: G = HI to the inverse of χ →

J

K

=

H L 

. Both PM

austenite and PM/weak magnetic martensite show linear behaviors in their respective temperature ranges (not shown). The linear extrapolation to zero allows for determination of their PM Curie temperatures (θ), which are collected in Table 4. Overall the measured PM MK

temperatures for austenite (θ A) are in line with the  determined from the minimum of the M

for each sample. On the other hand the θM temperatures show more scatter relative to the respective  indicating that martensite transforms to a more complex magnetic state. From the linear fit to 1/χ vs. T we have determined the effective magnetic moment (μNOO) in the PM parent and martensite phases according to: μPNOO =

QRS  T U VW

, where M is the molecular mass, X is

the Boltzmann’s constant, μ is the permeability of vacuum, Y is the Avogadro’s number and Z is the fitted Curie constant. The μNOO values are given in Table 4. Table 4. Effective magnetic moments in μ /. . and the Curie temperatures for austenite (θA) and martensite (θM) determined from the linear fits to the G HJ (T) for the Co0, Co1 and Co2 alloys. Alloy

^ [\]] ([_ /`. a.)

[b \]] ([_ /`. a.)

c^ (K)

cb (K)

Co0 Co1 Co2

1.7 ± 0.1 2.3 ± 0.2 2.4 ± 0.3

2.6 ± 0.3 3.8 ± 0.4 7.9 ± 1.2

313 ± 0.3 324 ± 0.5 332 ± 0.5

231 ± 0.2 227 ± 0.2 211 ± 0.4

The μNOO in austenite increases with increasing Co content (Table 4) and its values are consistent with literature [16]. Noteworthy μNOO similarly increases in the martensite phase but it is higher than in the austenite suggesting that there exists a stronger FM contribution to μNOO in the PM/weak magnetic martensite than in the PM austenite. We have thus additionally performed the Curie-Weiss fit above the Af and Mf temperatures in order to discriminate any interference from MT and establish the sensitivity on  ∙ ". The magnetizations vs. e

(T 0)

U temperature were fitted according to the formula:  = d Qgf μPNOO H ; where n is the number h

L

11

of moles of Mn per gram-atom, TC is the fitted Curie temperature and μNOO is given as μNOO =

gμj kl(l + 1); where g is the Lande’s factor (g = 2) and J is the fitted angular momentum. The fitted curves for PM austenite are shown in Fig. 6 and the results are collected in Table 5, whereas the results for martensite fitted below Mf for the Co1 alloy are shown in Fig. 7 (a) along with the evolution of J as a function of  ∙ " for the Co1 (Fig. 7 b) and Co2 (Fig. 7 c) alloys. In general the thermomagnetic data fits reasonably well with the Curie-Weiss equation with some deviation polluting the fit at higher Co content. Simultaneously J increases with increasing Co concentration and  ∙ ". This suggests that clearly J depends on the interaction between Mn and Co, and thus the magnetism in the present system at higher Co content results from the interaction between both magnetic elements, most likely through indirect RKKY type interaction. Frequently in MSMA where Mn is the chief donor of the magnetic moment ol  = 4  per Mn ion, and hence the lower values of J may indicate a stronger AFM exchange in the Co0 and Co1 alloys, partially dismissed in favor of the FM interaction in the Co2. In fact the low temperature (<  ) ZFC-FC splitting, often used for exposing the mixed AFM and FM interactions, initially increases with Co1 and then decreases with Co2 relative to the Co0 sample (Fig. 3), which is in consistence with J evolution as a function of Co concentration. The separation takes place below the Tp temperature, which is equal to 208 K, 214 K and 211 K for the Co0, Co1 and Co2 alloys, respectively.

Fig. 6. Isofield heating thermomagnetization measurements above Af and under  ∙ ∆" = 5 mT and  ∙ ∆" = 5 T together the corresponding Curie-Weiss fit for the Co0, Co1 and Co2 alloys. 12

Table 5. Applied magnetic field (  ∙ ∆"), austenite finish temperature (Af), the Curie temperature of austenite determined from the M (T) measurements, and the Curie temperature of austenite (∗ ) and angular momentum (J) obtained from the fitting of M (T) to the CurieWeiss equation. Alloys Co0 Co1 Co2

μ0·H (T) 5 × 10HQ 5 5 × 10HQ 5 5 × 10HQ 5

Af (K) 347 323 317 -

465 (K) 312 344 318 313 327 -

46∗ 5 (K) 319 ± 0.2 309 ± 0.4 331 ± 0.2 314 ± 0.6 337 ± 0.1 314 ± 0.9

J 0.188 ± 0.001 0.285 ± 0.002 0.306 ± 0.002 0.493 ± 0.005 0.370 ± 0.003 0.606 ± 0.009

Fig. 7. Isofield heating thermomagnetization measurements below Mf and under increasing  ∙ ∆" from 5 mT to 5 T and the corresponding Curie-Weiss fitted curves for the Co1 alloy (a); the evolution of J with increasing  ∙ ∆" for the Co1 (b) and Co2 (c) alloys. Since considerable μNOO above Tp may also suggest a superparamagnetic behavior in the next step, in an attempt to test the presence of superparamagnetism, we have examined the isothermal M vs. µ0·∆H curves measured at 250 K, 300 K and 350 K (Fig. 8) according to the modified Langevin model, which describes the magnetization behavior od FM clusters with V

density N and an average magnetic moment µ dispersed in a paramagnetic matrix:  (") = ∙ t

u(v) + G", where ρ is the alloy’s density and u(v) = coth(v) − 1/v is the Langevin function, 13

where v =  "⁄X  . Based on the refined parameters (Table 6) it is found that the magnetic moment is large and the cluster density is low relative to more typical superparamagnetic MSMA [22,23]. In this case it then leads to a picture of large, sparsely distributed FM clusters and eventually undermines the evidence for existence of SPM at the investigated temperatures.

Fig. 8. Isothermal magnetization measurements as a function of  ∙ ∆" for the Co0, Co1 and Co2 alloys at temperatures of 250 K, 300 K and 350 K (inset). Table 6. Refined average magnetic moment (µ), FM clusters density (N) and the magnetic susceptibility (χ0) parameters obtained from the fitting of M (  ∙ ∆") to the Langevin model. Alloys T (K) 250 Co0 300 250 Co1 300 250 Co2 300 350

µ (µB) 1.7 × 10 4 ± 34.4 15.9 × 10 4 ± 822.2 1.7 × 10 4 ± 33.8 16.4 × 10 4 ± 478.1 2.5 × 10 4 ± 57.1 21.9 × 10 4 ± 754.5 7.4 × 10 2 ± 33.2

N (m-3) 2.1 × 10 20 ± 7.5 × 1018 6.9 × 10 18 ± 4.1 × 1017 3.5 × 10 20 ± 1.2 × 1019 6.7 × 10 19 ± 2.2 × 1018 2.4 × 10 20 ± 8.6 × 1018 1.7 × 10 20 ± 6.2 × 1018 2.2 × 10 21 ± 3.0 × 1020

χ0 (m3kg -1) 2.1 × 10 -6 ± 3.1 × 10 -8 2.2 × 10 -6 ± 8.6 × 10 -9 3.2 × 10 -6 ± 5.0 × 10 -8 2.7 × 10 -6 ± 4.9 × 10 -8 3.6 × 10 -6 ± 4.9 × 10 -8 2.6 × 10 -6 ± 1.6 × 10 -7 4.6 × 10 -6 ± 4.5 × 10 -7

14

Fig. 9. The TMT and  (inflection points) temperature dependencies on the applied magnetic

 . → field for the Co1 and Co2 alloys (a); the ratio between the ∆ and the ∆ taken on the → reverse MT vs. applied magnetic field (b); transformation entropy ∆ vs. | = ( −  )⁄ – inset in (b). The magnetic state of the system across MT may be also well inferred from the sensitivity of the TMT temperature to the applied magnetic field (Fig. 9 a). The MT temperature change (∆T) induced by the magnetic field (∆H) may be then approximated from the ClausiusClapeyron relationship:

M0 M

=

∆}~ €

, and thus Δ ≈ .

∆

∆}~

2 ∆". Estimating ∆M from Fig. 5 (a)

and (b) around the corresponding Ms and Mf temperatures and substituting ∆ according to the DSC results (Table 2), the Δ at  ∙ ∆" = 5 T is estimated for the Co1 alloy at about #‚#. ∆$J = 3.6 K and it is in agreement with the experimentally elaborated result (4.9 K), #‚#. whereas for the Co2 alloy the calculated ∆$P = 2.3 K and it is less than the experimental result (6.2 K). Nonetheless, the sensitivity of the MT temperature the magnetic field in the studied system is not significant (Fig. 9 a), it is less than the sensitivity of the  in the same alloys which under the same magnetic field (  ∙ ∆" = 5 T) shifts by 10.5 K (Co1) and 12.2 K (Co2), and it is much less than the temperature sensitivity of e.g. Ni-Mn-In, yet it resonates with other Ni-Mn-Sn based systems [72]. Since according to the Clausius-Clapeyron relationship

 . the field induced magnetic entropy change ∆ (H) ~ dTM/dH, it would suggest a greater

 . ∆ in the Co1 alloy, consistent with the theoretical calculations. For illustration the ratio

 . → between the ∆ and the ∆ taken on the reverse MT is shown in Fig. 9 (b). The

 . → ∆ /∆ for the Co1 alloy increases linearly with the applied magnetic field, where the 15

 .

→ limit is ∆ = ∆ , and it is higher than for the Co2 alloy for which also the ratio appears → to deviate from linearity at higher magnetic field [73]. The inset shows the ∆ dependence    on the relative proximity between  and the  ; i.e. ( −  )⁄ , from which it is visible → that the structural transformation entropy change ∆ decreases with increasing Co concentration, due to a stronger FM contribution in austenite. Since MT is diffusionless these results may also indicate a stronger FM coupling, consistent with previous findings, in the martensite phase in the Co2 alloy relative to the Co1, which on the on the one hand may

 . diminish the ∆M and thus cripple the ∆ , and on the other may impair the thermodynamic driving force for reverse MT under the applied magnetic field effectively leading to a partial stabilization of martensite. On the whole the results are in agreement with literature on MSMA. The general experimental findings have it that the MT temperature is sensitive to the presence of Cu and depending on the substituted element it either decreases, when Cu replaces Ni, e.g. Ni50xCu xMn36Sn14 [74], Ni50-xCux Mn38Sn12 [75], Ni49-xCuxMn38Sn13[76], Mn50Ni40-xCuxSn10 [77], or increases when Cu is introduced at the cost of Mn e.g. Ni50Mn35-xCuxSn15 [78], Ni44Mn45xSn11Cu x [79], Mn48-xCuxNi42Sn10 [80] or Sn e.g. Ni47Mn40Sn13-xCux [81]. Somewhat puzzling at higher Cu concentration the TMT in Ni50Mn35-xCu xSn15 is reported to stray from the monotonic behavior and, whereas initially TMT increases with x = 2 it then rapidly drops at x= 5 and is finally completely suppressed at x = 10 [78,80,81]. On the other hand the  either increases [74,75,78,79] or remains vaguely affected [76,77] by the Cu content. Simultaneously the magnetization difference ∆M = M(Af) – M(As) between martensite and austenite, in Ni-Mn-Sn systems with well-defined Ms and  temperatures, has been reported to predominantly suffer from the incipient AFM exchange seemingly boosted by Cu doping [77]. This may suggest that the introduction of Cu, if not favors, does not at the least visibly upset the FM ordering in the austenite phase. Its effect on the exchange coupling in the martensite state, eventually leading to AFM exchange, may then result from the amplification of lattice distortion due to shearing invited upon the diffusionless MT. In general terms these observations relate to a more widely established dependence of the MT temperature on the electronic band structure changes spurred either by (i) lattice contraction – chemical pressure effect - or (ii) the valence electron concentration - e/a [82,83]. Both factors can be inflicted, often in tandem and thus frequently conflictingly - spare the isoelectronic substitution, through compositional adjustments [84]. Alternatively the hybridization between the Mn and Ni 3d states, which seems to be particularly relevant in the case of Mn – rich alloys, is eagerly brought forward in a situation where the general linear MT dependence on e/a falls short to account for the MT change against the e/a or the volume trend [85,86]. In agreement with these findings the introduction of 5 at. % Cu, in the present work, instead of Ni into Ni50Mn39Sn11 brought the MT from around 400 K to 322 K despite the reduction in the unit cell volume and increasing e/a. The MT temperature drop may therefore be understood in connection with the AFM coupling setting in due lattice contraction (RNi - 0.162 nm; RCu – 0.157 nm) combined with potential antisite atom location, e.g. Cu displacing Ni into Mn sites. It would then alter the dMn-d Mn interatomic distance and thus the Ni-Mn 3d hybridization states, whereby the strengthened hybridization would stabilize the covalent bond and thus extend the austenite phase to a lower temperature range. This argument turns out ever more plausible in the light of the weakening ∆M with increasing Cu content

16

whilst simultaneously the Cu introduction exerts marginal or escalating influence on the  [74,77]. Similarly the introduction of a ferromagnetic Co may enhance the FM exchange in the austenite phase shipping the  to higher values and decreasing the TMT with overall enhancement in ∆M [87,88,89]. Larger ∆M entails greater driving force for reverse MT, since the Zeeman energy is given as ZE = ∆M·H, and simultaneously greater MCE, since ∆ ∆

3ƒ„.

∆}~ ∆0

=

. In this work we replaced Ni with 1 and 2 at.% Co and in accordance with our expectations

and the above discussion the TMT decreased, while the  increased. Interestingly the forward MT temperature increases abruptly with 1 at. % Co relative to the host composition and then only marginally with further increase to 2 at.% of Co. Similar behavior is noted for the  , whereas the  changes more steadily (Table 2). An overview of the temperature changes with Co content is provided in Fig. 10, which shows a magnetic quasi phase diagram for the studied Ni45-xCoxCu5Mn39Sn11 (x = 0, 1, 2) system. The results are in line with a previous

 . communication on Co for Ni substituted Ni44-xCoxMn45Sn11 (x = 0, 1, 2), whereby the +∆





 under µ0·∆H = 10 kOe changes in the following order of x: ∆ ; †‡P < ∆ ; †‡ < ∆ ; †‡J

[88]. The authors attribute this change to an increase in the FM coupling in martensite around MT (As <  ) at x = 2, which implies Aferro→Mferro and hence lower ∆M as compared to Aferro→Mpara/weakly magnetic MT noticed for x = 0, 1. In general these results agree with theoretical FPP calculations on the effect of 3d transition element partially replacing Ni in Ni-Mn-Sn [90]. Among different substituents Cu is predicated to favor AFM Mn-Mn coupling in the L2 1 parent phase with minor coupling contribution from Ni(Cu) towards neighboring Mn atoms due to insignificant µNi(Cu) ~0.1 µB. Conversely Co promotes FM coupling in the same structure and donates a stronger µCo~1.4 µB implying more significant mutual Co-Mn coupling interaction [91,92]. On the whole lattice constants of the L21 systems with FM state are larger than those featuring AFM exchange [81] and the sensitivity of structural and magnetic properties to dMnd Mn interatomic distance is a commonly acknowledged phenomenon [3]. Overall the present study shows that simultaneous Co and Cu incorporation into the NiMn-Sn system may promote FM exchange in the martensite phase opening up an avenue for magnetic field assisted martensite variant reorientation (MFIS) in MSMA.

17

Fig. 10. Magnetic quasi phase diagram for the Ni45-xCoxCu 5Mn39Sn11 (x = 0, 1, 2) system. Concluding remarks Three alloys from the series Ni45-xCo xCu5Mn39Sn11 (x = 0, 1, 2) were produced by directional solidification and investigated in terms of the martensitic transformation behavior and magnetic properties evolution with Co content. It is found that the martensitic transformation temperature decreases with increasing Co concentration, whereas the Curie temperature of austenite increases. The extending structural and magnetic transition temperature gap then alters the magnetic state of the transforming austenite from para- to ferromagnetic. The effective magnetic moment of austenite increases with Co substitution. Under an applied magnetic field of 5 T the peak values of the magnetic entropy changes come up to 11.4 J/kgK for the Ni44Co1Cu 5Mn39Sn11 and 4.5 J/kgK for the Ni43Co2Cu 5Mn39Sn11 alloys, whereas the refrigerant capacity is 192.6 J/kg and 114.4 J/kg, respectively. The decrease in magnetic entropy changes with increasing Co concentration is related to a stronger ferromagnetic exchange in martensite across the martensitic transformation. A magnetic quasi phase diagram is devised for the studied system. Acknowledgement Financial support by the Polish National Centre for Research and Development (Project number: PBS/A5/36/2013) is gratefully acknowledged. Dr. Robert Chulist (IMMS PAS) is

18

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Highlights for review -

Ni45-xCoxCu5Mn39Sn11 (x = 0, 1, 2) alloys were studied;

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Magnetic moment of austenite increases by Co for Ni substitution;

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Martensitic transformation temperature decreases with Co content;

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Magnetic entropy changes in response to altered magnetic state of martensite.

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