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Magnetic glass in Shape Memory Alloy : Ni45Co5Mn38Sn12

Archana Lakhani,∗ A. Banerjee, and P. ChaddahUGC-DAE Consortium for Scientific Research, University Campus, Khandwa Road, Indore-452001,India

X. Chen and R. V. RamanujanSchool of Materials Science and Engineering, Nanyang Technological University,

N4.1-01-18, 50 Nanyang Avenue, Singapore -639798

The first order martensitic transition in the ferromagnetic shape memory alloy Ni45Co5Mn38Sn12

is also a magnetic transition and has a large field induced effect. While cooling in the presence of fieldthis first order magnetic martensite transition is kinetically arrested. Depending on the cooling field,a fraction of the arrested ferromagnetic austenite phase persists down to the lowest temperatureas a magnetic glassy state, similar to the one observed in various intermetallic alloys and in halfdoped manganites. A detailed investigation of this first order ferromagnetic austenite (FM-A) tolow magnetization martensite (LM-M) state transition as a function of temperature and field hasbeen carried out by magnetization measurements. Extensive cooling and heating in unequal field(CHUF) measurements and a novel field cooled protocol for isothermal MH measurements (FC-MH)are utilized to investigate the glass like arrested states and show a reverse martensite transition.Finally, we determine a field -temperature (HT) phase diagram of Ni45Co5Mn38Sn12 from variousmagnetization measurements which brings out the regions where thermodynamic and metastablestates co-exist in the HT space clearly depicting this system as a ’Magnetic Glass’.

PACS numbers: 75.30.Kz,75.50.-y ,75.50.Cc, 81.30.Kf

I. INTRODUCTION

The kinetics of any first order phase transition (FOPT)is governed by time required for extracting the latentheat of the system and can be arrested by rapid enoughcooling1. When a magnetic first order transition is ki-netically arrested it gives rise to the states which aremagnetically ordered metastable states and are referredas ’magnetic glasses’2.Kinetic arrest of martensite transition (MT) in ferro-

magnetic shape memory alloys (FSMAs) has been re-ported extensively in recent years, especially in NiMnInand NiMnSn based FSMAs [3-22]. Apart from thetechnological importance of FSMAs, they are also verygood candidates for the fundamental studies in field -temperature (HT) phase space since first order marten-site transition is influenced by both field and tempera-ture. The parent austenite phase shows a stronger ferro-magnetism than that of the martensite phase and at themartensitic transition temperature (Tm), a sharp changein magnetization is observed in thermo-magnetizationmeasurements. Tm decreases on increasing the magneticfield of measurement. The kinetics associated with mag-netic FOPT gets hindered in many of these materialsresulting in phase coexisting states at low temperaturewhich comprises of an arrested (metastable) state andthe transformed (stable) state. In spite of the wide rang-ing studies justifying the presence of kinetic arrest ofmartensite transformation in FSMAs, the magnetic glassconcept has been discussed only in a few In and Sn basedFSMAs [18-22].

In general, magnetic field may enhance or reduce thekinetic arrest, depending on whether the low temper-ature equilibrium state has lower or higher value ofmagnetization23,24. It has been noted that by coolingin a certain field (Hc) and then heating in a differentfield (Hw), this glass like arrested state (GLAS) can bede-arrested and on further heating a reverse magnetictransition is observed. Hence by cooling and heating inunequal fields (CHUF), a re-entrant transition can beseen but for only the appropriate sign of (Hc-Hw)

24. Inthe case of FSMAs, since the high temperature phaseis ferromagnetic austenite (FM-A) while the low tem-perature phase is low magnetization martensite (LM-M),this reentrant transition will be seen only for the positivesign of (Hc-Hw). Kainuma’s group has reported magne-tization measurements on cooling in various fields andwarming in lower fields (0.05T) on Ni50Mn34In16 alloyand observed the ‘unfreezing of P+M coexisting state’14.This ‘dearrest’ stated as ‘unfreezing’ is analogous to ‘de-vitrification’ observed in manganites with charge orderedground state [25-27]. These results are consistent withwhat is expected in a magnetic glass; however the wellestablished CHUF protocol provides a crucial test for val-idating whether the kinetically arrested state correspondsto a magnetic glass. The CHUF protocol requires thatthe measurements are done in the fields both below andabove Hc, i.e. for both positive and negative values of(Hc-Hw).

In this communication our studies onNi45Co5Mn38Sn12 ribbon sample demonstrate allthe features crucial to unambiguously prove the mag-netic glass state by various thermo-magnetizationmeasurements, including CHUF measurements. Besides,we highlight an important aspect that the transition

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between LM-M and FM-A phases can not be achievedat low temperature by the conventional protocol ofisothermal field variation of the ZFC state because ofthe limit of experimentally accessible field range. Byfollowing the novel protocol of field cooling and thenisothermally reducing the field we are able to observethe transition between LM-M and FM-A phases withinthe accessible field range even at the lowest temperature.We justify this by constructing the qualitative phasediagram identifying bands of supercooling (SC), super-heating (SH) and kinetic arrest (KA) from the varietyof measurements spanning the HT space and checkits self consistency. As has been discussed in detail inreference[23] the SC limit T*(H), the SH limit T**(H)and the kinetic arrest line TK(H) are broadened intobands in system with quenched disorder. Thus we showthat the technologically useful FSMAs are magneticglasses, as shown earlier in manganites.

II. EXPERIMENTAL DETAILS

The sample Ni45Co5Mn38Sn12 (Sn12) used in thisstudy is prepared by arc melting the high purity elementsinto buttons and preparing ribbons from these buttonsby melt spinning in an inert atmosphere. The compo-sition and crystal structure were determined by an en-ergy dispersive X-ray spectrometer (EDXS) attached toa scanning electron microscope (SEM), and powder X-ray diffraction (XRD). Details of sample preparation andcharacterization can be seen in reference 20. The DC-Magnetization was measured with a commercial 14 TeslaPPMS- VSM (M/s: Quantum Design).

III. RESULTS AND DISCUSSIONS

Sn12 sample exhibits a clear first order phase tran-sition with respect to field and temperature, displayingbroad hysteresis. The high magnetization ferromagneticaustenite (FM-A) phase transforms to the low magnetiza-tion martensite (LM-M) phase and vice versa on coolingand heating, respectively20,21. The first order nature ofthe martensite transition with respect to field in this sam-ple was established in our earlier work20 by performingzero field cooled Magnetization vs Field (MH) measure-ments during cooling and heating28. The MH isothermsin both the cases (cooling and heating) were completelydifferent for (T*∼75K)<T<(T**∼ 215K). Similarly, inthe plot of Magnetization v/s Temperature i.e. M(T),a broad hystersis is observed in the same temperaturerange during cooling and heating. These results signifythat the fractions of coexisting metastable martensiteand austenite phases not only vary with field and tem-perature but also depend on the path followed in the HTspace. These metastable states at low temperature aregoverned by an interplay of supercooled and kinetically

arrested states, because neither the supercooled nor ar-rested state is the equilibrium state of the system.29

Figure 1 shows magnetization as a function of temper-ature in three different measurement protocols viz: zerofield cooled warming (ZFC), field cooled cooling (FCC)and field cooled warming (FCW) at 1, 3, 5 and 9T. TheFCC and FCW curves shown here were reported in refer-ence 20 and 21. They are reproduced here in a replottedversion along with the ZFC curve to explain the thermo-magnetic irreversibility in these systems at low temper-atures. As shown in figure 1(a) the cooling and heatingcurves at 1T exhibit a clear first order phase transitionfrom FM-A phase to LM-M phase, showing a broad hys-teresis in the range of (T*∼75K)<T<(T**∼215K). Athigher fields the MT gets gradually inhibited and com-pletely arrested at 9T, as shown in figures 1(b-d). As aresult, various co-existing metastable states are observed,depending on the magnitude of the magnetic field duringcooling and heating. These ‘kinetically arrested states’are due to slowing down of growth of the martensitephase from the supercooled austenite phase, similar tothe viscous retardation in structural glasses. In struc-tural glasses the liquid to crystal freezing is arrested,while in a magnetic glass the magnetic re-ordering is ar-rested. In both cases the material is cooled through thefirst order transition temperature without extracting la-tent heat. While in a jamming process translational ki-netics is arrested; in the formation of both these glassesthe specific heat is extracted, while the latent heat (whichhas a different coupling with thermal conduction process)can not be extracted1. In both cases the higher entropyphase persists down to the lowest temperature30. In thissense the magnetic glass and the structural glass addresssimilar physics. However in structural glasses pressureis the variable parameter. The experimental advantageof magnetic field (H) over pressure (P) is that it can beeasily varied reversibly without a control medium, andits variation does not interfere with temperature control.

As the first order MT gets arrested in presence of field,the low temperature states turn out to be non-ergodic.At 1T, there is no significant difference between ZFCand FCW curves as shown in figure 1(a). However, atfield above 1T, the hysteresis width △T does not changesignificantly but the area enclosed by the hysteresis re-duces and the difference between MZFC and MFCW atlow temperature increases. This difference is known asthermomagnetic irreversibility (TMI), which is defined asTMI= MFCW -MZFC at 5K. The TMI at low tempera-tures could be due to spin glass behavior, pinning of vari-ants, hindrance of domain motion or glass like arrest ofdynamics. Nevertheless for the first three cases, this irre-versibility decreases with increasing field; hence the ZFCand FCW magnetization curves would merge, in contrastto the present case. Here, TMI increases with increase infield as shown in the inset of figure 1(d). This rise in ther-momagnetic irreversibility is due to the kinetic arrest ofthe martensite phase transition at the low temperatureswhich gives rise to non-ergodic states having coexisting

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FIG. 1: (Color online)(a-d) M vs T plots for Sn-12 sampleobtained in ZFC, FCC and FCW mode in applied fields of H= 1, 3, 5 and 9T respectively. FCC and FCW data are takenfrom ref. 20 and 21.

FM-A and LM-M phases. We have almost 100% LM-Mphase fraction when cooled in zero field but on increas-ing the cooling field the ferromagnetic austenite fractionincreases. We have estimated this phase fraction by as-suming the field cooled magnetization values at 5K and9T as 100% FM-A as there is no FM-A to LM-M tran-sition on heating and cooling at this field21. The TMIat 5K gives an amount of the fraction of arrested FM-Amixed with the LM-M phase. This attribute classifiesthis system as a magnetic glass.

This system undergoes a complete transformation be-low 1T (H1), while above 8T (H2) the martensite trans-formation is almost hindered resulting in a completelyaustenite phase at low temperature. However at fieldvalues between H1 and H2, we achieve a fraction of trans-formed martensite phase along with an arrested austen-ite phase at low temperatures21. In the earlier studies ofmanganites and intermetallic alloys [25-28,33], referred asmagnetic glasses, the arrest of kinetics across the first or-der phase transformation is established from the fact thatthe virgin MH curve lies outside the envelope curve in theisothermal magnetization curves at lowest temperatures.In these cases, the samples have undergone a first ordertransformation within the available field and temperaturerange and the observed low temperature anomaly is in-ferred as the arrested kinetics of the first order transition.In all these cases, the virgin state considered are the zerofield cooled state from well above the superheating limitof the samples. They have also shown a non monotonicbehavior of metamagnetic transition field with respect totemperature in zero field cooled MH isotherms, which isan important experimental method of studying the ar-rested kinetics in these samples.

We performed similar zero field cooled isothermal mag-

netization (ZFC-MH) experiments in the range of 5-150K, as shown by the symbols (green) in figure 2(a-h).The sample is cooled from temperatures well above MTtemperature. After cooling in zero field, the low tem-perature state of the sample is in a low magnetizationmartensite (LM-M) phase, as seen by dashed lines in fig-ure 2(a). The initial field increasing cycle at 5, 15 and25K shows a sharp increase in magnetization up to ∼1Tand then almost saturates, while the return cycle followsthe same path indicating the soft ferromagnetic behav-ior. However, we did not observe the reverse marten-site transition (RMT) at low temperatures up to 14T.For temperatures above 75K, the rise in magnetizationin the forward field cycle followed by an opening of hys-teresis indicates the onset of the martensite to austenitephase transformation, which confirms the RMT in thetemperature range of 75-150K. Therefore to investigatethe absence of such RMT at low temperature, which weattribute to kinetic arrest in this system, we designed anovel protocol of field cooled MH isotherms (FC-MH),as shown by the solid lines (red) in figure 2(a-h). ForFC-MH measurements, we cooled the sample in 8T from350K, which is well above the superheating limit (∼210K)of the sample, and considered the field cooled state as theinitial state of the sample. On cooling in 8T, the sam-ple acquires maximum fraction of FM-A phase as an ar-rested phase. In each case, the sample is cooled in 8T tothe respective temperatures, and then magnetization ismeasured while isothermally raising the field up to 12T,subsequently cycling from 12T → 0 → (−12T ) → 0T .

We explain these measurements by the schematic banddiagram specified for magnetic glasses shown in figure2(i). Since FOPT (here MT) induced by field and tem-perature is broadened in HT space, as a result the sharplines corresponding to the transition temperature (hereTm) as well as the spinodal lines of supercooling (H*T*)and superheating (H**, T**) broaden into bands29,31,32.As discussed earlier24,25,28,33, if kinetic arrest occurs be-low (Hk,Tk) line in a pure system, the disordered systemwould have an (Hk,Tk) band. The kinetic arrest band inthe HT space contains a set of lines below which the dy-namics of MT is hindered on the time scales of the exper-iments, as in structural glasses. These lines in the bandwould correspond to a local region of the sample andtherefore a correlation between the positions of (Hk,Tk)and (H*,T*) bands can be established. An anticorre-lation between the supercooled and kinetically arrestedregions has been proposed and experimentally confirmedin many materials termed as magnetic glasses having firstorder magnetic transitions [23-28,33,34].

On reducing the field from point A(5K,12T), ap-proached by following the path XA, to point D(5K,0T)as shown in the HT phase diagram in figure 2(i), we ob-serve a step at 1.5T in MH curve (figure 2(a)), which isexpected to be due to the de-arrest of arrested high tem-perature phase as it crosses the KA band23. At highertemperatures, e.g., 15K, a signature of dearrest of FM-A phase at the field marked by a circle in figure 2(b) is

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observed by a clear slope increase at dearrest field Hd.This field Hd marked by circles in figure 2 increases onincreasing the temperature and the dearrested fractionalso increases upto 75K. At temperatures greater than75K, δM (estimated by the drop that occurs with thisincreased slope) decreases and we observe smaller frac-tion of the dearrested phase. The corresponding arrestedFM-A phase is reduced due to the presence of higher su-percooled fraction at temperatures between T= 75-150K.Hence, the width of the linear slope in the return fieldcycle increases from 5K-75K and then decreases up to150K. Considering T=150K at point C in the schematicdiagram 2(i), if we traverse on the field axis, we observea completely symmetrical and reversible MH curve asshown in figure 2(h). At this temperature whether weapproach by zero field cooling (from point F) or coolingin a finite field (from point C), one would get the samebehavior, since 150K lies outside the (Hk,Tk) band.

Since ZFC -MH shows a fully martensite state and FC-MH shows fully arrested metastable state at 5K, we canestimate the arrested FM-A fraction from the differencein magnetization (△M) between FC-MH and ZFC-MHat 8T for various temperatures as shown in the inset ofFig 2(h). After cooling in 8T field, the arrested FM-Afraction is almost constant below 75K, which is T* at 8Tfor this sample. Thereafter, due to the presence of su-percooled austenite fraction △M gradually decreases andalmost vanishes on heating above 150K. At T∼150K thekinetic arrest and the supercooled band tend to overlap.Hence, FC-MH measurements demonstrate the de-arrestof the glass like arrested metastable FM-A states below150K.

Cooling and heating in unequal field (CHUF) mea-surements confirm the kinetically arrested metastablestates at low temperatures by observing the de-arrest ofarrested phase34,35. They are also used to distinguishthe equilibrium phase from glass like arrested co-existingphases33,35. To verify GLAS at low temperatures by ob-serving the de-arrest on warming, we have carried outfour sets of CHUF measurements. In the first two setof measurements, magnetization is performed by coolingin a constant cooling field (Hc), in various different mea-suring fields (Hw) for both Hc<Hw and Hc>Hw. In theother two sets, the sample is cooled in various differentfields and the measurement field is kept constant dur-ing heating. The CHUF set is said to be complete whenthe measurements are performed in the field below andabove the cooling and/or warming field. To confirm there-entrant transition mentioned above for demonstratingthe glass like arrested state, a complete set of CHUFmeasurements is required.

In the first two sets of CHUF measurements, the con-stant cooling fields (Hc) of 6T and 3T is chosen, for whichone observes a finite fraction of both arrested and trans-formed phases at low temperature (figure 3(a) and (b)).In each case the sample is cooled from 350K down to 10K.At 10 K, the field is reduced isothermally to the respec-tive measuring field (Hw) and measurement is done while

heating. For the other two set of measurements (figure3(c)and(d)), the sample is cooled in various fields (Hc)ranging from 0T to 8T down to 10K and then the field isisothermally increased or decreased to the constant mea-suring field (Hw) of 4T and 1T, M(T) is measured whileheating.

As shown by M(T) in figure 3(a) when system is cooledin 6T and heated in 0.5, 1, 2, 3, and 4T an initial drop isobserved in magnetization and this drop is more profoundwhen the difference between Hc and Hw is large. Similartrend is observed in fig 3(b) when system is cooled in3T and warmed in 0.5, 1 and 2T, except that the initialarrested fraction is smaller. The fall in magnetizationon increasing the temperature indicates the de-arrest ofFM-A to LM-M state, i.e., the arrested FM-A phase (un-transformed phase during cooling in 6T/3T) transforms

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to the LM-M phase on heating in lower fields. On theother hand, if the warming field is kept constant whilethe sample was cooled in different fields, a clear drop inmagnetization in figures 3(c and d) indicates the tran-sition to LM-M state when Hc>Hw i.e., for the positivevalues of (Hc-Hw). Only one transition back to the FM-A state is observed at higher temperature while warmingin 4T after cooling in 0, 1, 2 and 3T as well as duringwarming in 1T after cooling in 0T. This also shows thatthe LM-M is an equilibrium state and FM-A state is aglass like arrested state (GLAS).

For the systems, where Tm (and T*) falls with increasein magnetic field, Hc>Hw is required for observing thede-arrest; T* would be lower during cooling in Hc andhigher during warming in Hw. Such a transformation tothe low temperature equilibrium phase caused by ther-mal energy is analogous to the phenomenon of devitrifica-tion of the glassy phase, which has been demonstrated inhalf doped manganites and in many intermetallic alloysclassified as magnetic glasses. Devitrification of glasseshas been used as evidence for metallic glasses36. An-other transition of LM-M phase back to FM-A phase athigher temperatures is analogous to the melting of de-vitrified crystalline equilibrium phase on increasing tem-perature. Both these transitions are seen only when thedifference between cooling field and warming field is pos-itive. Hence, the de-arrest of FM-A to LM-M is observedwhen Hc>Hw and when the difference between coolingand heating field (Hc - Hw) decreases, dearrest starts athigher temperatures. Hence, regions which have higherT* will have lower Tk. This relation is universal for all

magnetic glasses23,37.Based on the results from all the magnetization mea-

surements, we have developed a quantitative phase dia-gram shown in figure 4, similar to the one given for themagnetic glasses mentioned above. The filled squaresrepresent the supercooling limit for the correspondingfields obtained from the peak points of FCC magneti-zation data and empty squares are taken from the pointsof slope change in the return envelope curve of ZFC- MHmeasurements. The triangular symbols represent the su-perheating limit for various fields obtained from differentmeasurements, as indicated in the legends of figure 4 andexplained in the figure caption. The filled and emptycircles correspond to the limit of kinetic arrest acquiredfrom CHUF magnetization measurements performed forHc = 6T and 3T respectively. Star symbols representthe upper limit of kinetic arrest band obtained from FC-MH isotherms. We observe that the temperature andfields corresponding to the superheating and supercool-ing limits obtained from diverse measurements like FCW-MT, ZFC-MH, ZFC-MT, 3/6T cooled CHUF and FCC-MT, fall uniformly in the respective bands. Similarly,field and temperatures corresponding to the kinetic ar-rest edges obtained by quite different sets of measure-ments mentioned above, are consistent. Hence, validityof our phenomenological model is reinforced by the re-sults obtained from the various measurement protocolsfalling in the same bands. This phase diagram gives thequantitative information about the phase fraction kinet-ically arrested across the HkTk band on cooling and/orapplying the field as well as about the de-arrested frac-tion on warming and/or reducing the field. This phasediagram also illustrates that, although the metamagnetictransition from FM-A to LM-M state at the lowest tem-perature takes place at ∼30T for this sample, which isfar above the available field range of measurements, wecan visualize these features at much lower fields in thefield reducing cycle of FC-MH by observing the de-arrestof FM-A state to LM-M state.The formation of magnetic glass in Ni50Mn50−xSnx

FSMAs could be related to the mechanism of struc-turally modulated phases observed experimentally be-low MT. The true structural ground state in these al-loys is found to be experimentally ambiguous at lowtemperatures as various modulated states are observedwhich are metastable and vary with x concentration38,39.Therefore as the degeneracy in structure of FSMAs isaffected by small variation of Sn/Mn concentration, var-ious metastable magnetic states can be formed by thekinetic arrest of MT in varying magnetic fields, leadingto the formation of magnetic glass.

IV. CONCLUSION

We have performed a comprehensive study of fieldinduced first order FM-A to LM-M transition with re-spect to temperature and field by variety of magnetiza-

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FIG. 4: (Color online) Schematic H-T Phase diagram show-ing supercooling (Blue), superheating (red) and kinetic arrestbands (wine) obtained from various measurement protocolsfor Ni45Co5Mn38Sn12 ribbon. FCC-MT: Magnetization w.r.ttemperature during field cooled cooling, FCW-MT: Magne-tization vs temperature during field cooled warming, ZFC-MT: Magnetization w.r.t temperature after zero field cooling.ZFC-MH: Isothermal magnetization vs field after zero fieldcooling. CHUF-3T/6T: M w.r.t T in various fields after cool-ing in 3T/6T. FC-MH: Isothermal magnetization w.r.t fieldafter cooling in 8T. Peak points of M in the MT curves andpoints of slope change in MH isotherms are taken as the rep-resentative limiting points for SC, SH and KA bands

tion measurements on the ferromagnetic shape memoryalloy ribbons of Ni45Co5Mn38Sn12. The kinetically ar-rested glass like metastable states are revealed by coolingand/or applying the field and their de-arrest is observedon warming and/or reducing the field by various thermo-magnetic measurements. This phenomenon is validatedby a CHUF protocol to study the arrested high tempera-ture phase and observe the re-entrant transition for pos-itive values of Hc-Hw. The co-existing states have beenproduced and higher arrested fraction at higher coolingfields has been confirmed by the novel protocol of ‘fieldcooled MH isotherms’ where the 8T field cooled state isconsidered as the initial state of the system. Based onthese measurements we regard this ferromagnetic shapememory alloy system as a ‘Magnetic Glass’, similar tocharge ordered ground state manganites.

V. ACKNOWLEDGMENT

We thank S. Dash for help in magnetization measure-ments. RVR and CX acknowledge support from NationalResearch Foundation, Singapore through the CREATEprogram on Nanomaterials for Energy and Water Man-agement.

∗ Electronic address: archnalakhani@csr.res.in1 P. Chaddah and A. Banerjee, arXiv:1004.3116v2, (2012)and references therein.

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