Magnetoresistance behavior of a ferromagnetic shape memory alloy: Ni_1.75Mn_1.25Ga
S. Banik, R. Rawat, P. K. Mukhopadhyay, B. L. Ahuja, Aparna Chakrabarti, P. L. Paulose, S. Singh, A. K. Singh, D. Pandey, S. R. Barman
aa r X i v : . [ c ond - m a t . m t r l - s c i ] M a y Magnetoresistance behavior of a ferromagnetic shape memoryalloy: Ni . Mn . Ga S. Banik , R. Rawat , P. K. Mukhopadhyay , B. L. Ahuja , Aparna Chakrabarti ,P. L. Paulose , S. Singh , A. K. Singh , D. Pandey , and S. R. Barman ∗ UGC-DAE Consortium for Scientific Research,Khandwa Road, Indore, 452017, India LCMP, S. N. Bose National Centre for Basic Sciences, Kolkata, 700098, India Department of Physics, M. L. Sukhadia University, Udaipur 313001, India Raja Ramanna Centre for Advanced Technology, Indore, 452013, India Tata Institute of Fundamental Research,Homi Bhabha Road, Mumbai, 400005, India. and School of Materials Science and Technology,Banaras Hindu University, Varanasi, 221005, India.
Abstract
A negative − positive − negative switching behavior of magnetoresistance (MR) with temperatureis observed in a ferromagnetic shape memory alloy Ni . Mn . Ga. In the austenitic phase between300 and 120 K, MR is negative due to s − d scattering. Curiously, below 120 K MR is positive, whileat still lower temperatures in the martensitic phase, MR is negative again. The positive MR cannotbe explained by Lorentz contribution and is related to a magnetic transition. Evidence for this isobtained from ab initio density functional theory, a decrease in magnetization and resistivity upturnat 120 K. Theory shows that a ferrimagnetic state with anti-ferromagnetic alignment betweenthe local magnetic moments of the Mn atoms is the energetically favoured ground state. In themartensitic phase, there are two competing factors that govern the MR behavior: a dominantnegative trend up to the saturation field due to the decrease of electron scattering at twin anddomain boundaries; and a weaker positive trend due to the ferrimagnetic nature of the magneticstate. MR exhibits a hysteresis between heating and cooling that is related to the first order natureof the martensitic phase transition. PACS numbers: 73.43.Qt, 81.30.Kf, 75.47.-m, 71.15.Nc . INTRODUCTION Recent years have witnessed extensive research on magnetoresistance (MR) to understandits basic physics in metallic multilayers, transition metal oxides, etc . Ferromagnetic shapememory alloys (SMA) are of current interest because of their potential technological applica-tions and the rich physics they exhibit.
Large magnetic field induced strain(MFIS) of 10% with actuation that is faster than conventional SMA’s has been obtained inNi-Mn-Ga.
MFIS is achieved by twin boundary rearrangement in the martensitic phaseand the main driving force for twin boundary motion in the presence of a magnetic field isthe large magnetocrystalline anisotropy (MCA).
Negative MR has been observed earlier in SMA’s like Cu-Mn-Al and was associated withthe possible presence of Mn-rich clusters in the Cu AlMn structure. Recently, we havereported a negative MR of about 7.3% at 8 T at room temperature in Ni x Mn − x Ga. It was explained by s − d scattering model for a ferromagnet, while the differences in theMR behavior in the martensitic phase compared to the austenitic phase was related to twinvariant rearrangement with magnetic field. MR ranging between -1 to -4.5% has beenreported for thin films of Ni-Mn-Ga.
Recently, a large negative MR of 60-70% has beenreported for Ni-Mn-In, which has been explained by the shift of the martensitic transitiontemperature with magnetic field. Ni − y Mn y Ga with y = 0.25 i.e. Ni . Mn . Ga is one of the unique compositions inthe Ni-Mn-Ga family that has low martensitic transition temperature ( M s ) of about 76 K. This enables the study of the ferroelastic transition much below the Curie temperature( T C = 380 K). Here, part of the Mn atoms ( y = 0.25), referred to as MnI, occupy the Ni sitewhile the remaining Mn ( y = 1.0) atoms at the Mn site are referred to MnII. The MnI atoms,which are 20% of the total Mn atoms, are excess with respect to the stoichiometric Ni MnGacomposition. These excess MnI type atoms are expected to have interesting influence onthe resistivity, MR, and magnetization, since in related systems like Ni Mn . Ga . andMn NiGa their moments are reported to be anti-parallel to the MnII atoms.
Here, wereport an intriguing switching behavior of MR with temperature that is related to the oc-currence of martensitic transition at low temperature in the ferrimagnetic state. To the bestof our knowledge, such MR behavior reported here has not been observed in any magneticmaterial till date. This basically arises from the interplay of magnetism and shape mem-2ry effect. Our studies indicate possibility of new practical applications for ferromagneticSMA as magnetic sensor for data storage and encryption, whose response can be toggled bychanging the temperature. It is envisaged that the multifunctional combination of properties(magnetic sensing, magnetocaloric, actuation and shape memory effects) of the ferromag-netic SMA’s will be important for their future application.
II. METHODS
Bulk polycrystalline ingots of Ni . Mn . Ga have been prepared by the standard methodof melting appropriate quantities of Ni, Mn and Ga (99.99% purity) in an arc furnace. Theingot was annealed at 1100 K for nine days for homogeneization and subsequently quenchedin ice water.
The composition has been determined by energy dispersive analysis of x-rays using a JEOL JSM 5600 electron microscope. A superconducting magnet from OxfordInstruments Inc., U.K. was used for carrying out the longitudinal MR measurements up toa maximum magnetic field of 8 T. MR is defined as ∆ ρ m = ∆ ρρ = ( ρ H − ρ ) ρ , where ρ H and ρ are the resistivities in H and zero field, respectively. The statistical scatter of the resistivitydata is 0.03%. M ( T ) measurements were performed with Lakeshore 7404 vibrating samplemagnetometer with a close cycle refrigerator. M ( H ) measurements were done using a MPMSXL5 SQUID magnetometer. Temperature-dependent powder x-ray diffraction (XRD) datawere collected using an 18 kW copper rotating anode-based Rigaku powder diffractometerfitted with a graphite monochromator in the diffracted beam. The temperature was stablewithin ± Generalized gradient approximation for the exchange correlation was used. The muffin-tinradii were taken to be Ni: 2.1364 a.u., Mn: 2.2799 a.u., and Ga: 2.1364 a.u. The convergencecriterion for total energy was 0.1 mRy, i.e. an accuracy of ± II. RESULTS AND DISCUSSION
Fig. 1 shows the isothermal magnetoresistance (∆ ρ m ) of Ni . Mn . Ga as a function ofmagnetic field at different temperatures. It can been seen from the figure that at 300 K,the magnitude of ∆ ρ m ( H ) increases with H to -1.35% at 8 T (Fig. 1a). In order to ascer-tain the H dependence, we have fitted ∆ ρ m ( H ) by a second order polynomial of the form α H + β H (solid lines in Fig. 1). We find the second order term ( β ) to be very small, the ratio β/α being 0.02, which shows that the variation is essentially linear. Similar linear variationis obtained up to 150 K, although the magnitude of ∆ ρ m decreases to -0.3%. Linear variationof negative MR with field has been observed for Ni MnGa. Also Kataoka has calculated∆ ρ m ( H ) for ferromagnets with different electron concentrations using the s − d scatteringmodel, where the scattering of s conduction electrons by localized d spins is suppressed bythe magnetic field resulting in a decrease in ρ . Magnitude of ∆ ρ m is shown to increasealmost linearly with H for ferromagnetic materials. Since Ni . Mn . Ga has large Mn 3 d local moment with high electron concentration (valence electron to atom ratio, e/a = 7.31),negative MR in the 150-300 K range is well described by the s − d scattering model. As thetemperature is lowered, ∆ ρ m ( H ) decreases due to reduction in the spin disorder scattering.MR in Fig. 1b shows an interesting behavior: ∆ ρ m ( H ) is positive at 100 K. However,at 50 K it is negative, but with a different H dependence compared to the s − d scatteringregime (Fig. 1a). In other ferromagnetic Heusler alloys like Ni MnSn and Pd MnSn, positiveMR has been observed and attributed to the Lorentz contribution. In such cases, ∆ ρ m ispositive at lowest temperatures and decreases as temperature increases. For example, MRis positive for Pd MnSn at 1.8 K and is negative above 60 K. In contrast, the MR variationin Ni . Mn . Ga is opposite. Lorentz contribution gives rise to a positive MR when thecondition ω C τ >> ω C and τ are cyclotron frequency and conductionelectron relaxation time, respectively. This condition is valid for extremely pure metallicsingle crystals at very low temperatures (where τ is large and ρ ≤ − Ω cm ) or at large H (where ω C is large). But for Ni . Mn . Ga, the residual resistivity is large, implying small τ so that even at 8 T the above condition is not satisfied. By the same argument, we expecta more positive contribution at 5 K compared to 50 K, since the resistivity is lower at 5 K(Fig. 2a). On the other hand, the observed data show opposite trend. Hence, the positiveMR in Ni . Mn . Ga cannot be ascribed to Lorentz force and other mechanisms need to4e explored to understand this finding.Fig. 2a shows resistivity ( ρ ( T )) at zero and 5 T magnetic field between 5 and 180 K fortwo cycles. Above 120 K, where the sample is in the austenitic phase ρ ( T ) has a positivetemperature coefficient of resistance, and the data for the different cycles overlap. Between88 and 37 K, the hysteresis in ρ ( T ) becomes highly pronounced and this is a signatureof the martensitic transition. The martensitic transition is also clearly shown by the ac-susceptibility data in Ref.26 and the low field magnetization data shown in Fig. 4a (discussedlatter). The onset of the martensitic transition is depicted by the change in slope in ρ at M s (= 76 K, in agreement with Ref.26). The other transition temperatures like martensitefinish M f = 37 K, austenitic start A s = 47 K, and austenitic finish A f = 88 K, shown in Fig. 2a,concur with the M ( T ) data to be discussed later (Fig. 4a). ρ shows a step centered around65 K. This possibly arises due to strain effect on the nucleation and growth of the martensiticphase at such low temperatures, and similar effect has been observed in Ni FeGa. In order to establish beyond any doubt that the hysteresis in ρ ( T ) is related to themartensitic transition, we show the powder XRD pattern at different temperatures in Fig. 3.To record the XRD patterns, Ni . Mn . Ga ingot was crushed to powder and annealed at773 K for 10 hrs to remove the residual stress. The L cubic austenitic phase is observed upto 100 K. There is no signature of any phase transition, related to the formation of a possiblepremartensitic phase around 120 K, which could have been responsible for the upturn in ρ ( T ). The lattice constant at 100 K turns out to be a aus = 5.83˚A. At 80 K, new peaksappear. These peaks correspond to the martensitic phase and coexist with the austenitepeaks. By 40 K, the XRD pattern shows that the martensitic transition is complete as thereis no austenite phase, in agreement with the ρ ( T ) data. The XRD patterns have been indexedby Le Bail fitting procedure; and we find that the martensitic phase is monoclinic in the P /m space group. The refined lattice constants are a = 4.22, b = 5.50 and c = 29.18 ˚A, and β = 91.13. Since c ≈ × a , a seven layer modulation may be expected, and such modulatedstructures with monoclinic or orthorhombic symmetry have been reported for Ni-Mn-Ga. Magnetic field induced strain has been observed in Ni-Mn-Ga for structures that exhibitmodulation.
The unit cell volume of the martensitic phase is within 2% of that of theequivalent austenitic cell given by 7 × a aus /2. This shows that the unit cell volume changeslittle between the two phases, as expected for a shape memory alloy. After establishing the existence of the structural martensitic transition from XRD, we5iscuss the details of the resistivity behavior. ρ ( T ) at 5T shows a difference in the first andsecond FH (field heating) cycles, the first cycle ρ ( T ) being higher. In the first FH cycle,the sample is subjected to a magnetic field of 5T at 5 K after ZFC (zero field cooling).Subsequently, FC data were taken and then the second cycle of FH was measured. Thus,while in FH first cycle, the magnetic field of 5 T was switched on at 5K, where as in theFH second cycle the field is on from RT. The possible reason for the difference in resistivitybetween the two FH cycles is discussed later on. In Fig. 2b, we show the MR calculatedfrom the difference between the ZFC and FC (cooling MR data) and ZFH and FH secondcycle (heating MR data). But, if the FH first cycle is considered, MR is lower by about0.4% at 5 K, which argees with the value in Fig. 1. This is because the MR in Fig. 1, ∆ ρ m is measured in a different way: at 300 K, H is varied from 0 to 8 to 0 to -8 to 0 Tesla. Then,the specimen was cooled down to the next measurement temperature of 235 K and the fieldwas varied in a similar way. For the next measurement, the sample was heated up to 300 Kand cooled under zero field condition to the temperature of measurement. Thus, for themartensitic phase, this MR data (Fig. 1) can be related to ∆ ρ m calculated from ZFH andFH first cycle ρ data (Fig. 2a).Fig. 2b clearly shows the switching effect in MR as a function of temperature. A com-parison of Fig. 2a and b shows a significant correlation between the hysteresis in MR and ρ ( T ). For the cooling cycle, MR is negative from 300 to 135 K, and exhibits a negative topositive switching at 135 K. This negative MR region is explained by s − d scattering, asdiscussed above. MR is positive between 135 to 76 K (= M s ); and this is also manifested inMR(H) data at 100 K in Fig. 1b. As discussed earlier, the positive MR cannot be assignedto Lorentz force contribution. MR exhibits a positive to negative switching at M s in thecooling cycle. MR becomes negative at M s with a shallow minimum at 73 K, shows a humpat 64 K, and then plunges to large negative values below 64 K, and finally increases slightlyto reach a temperature independent value of about -3% below 37 K (= M f ). The shape ofthe MR(T) curve in Fig. 2b during heating is very similar to that during cooling, but isshifted in temperature in the martensitic transition region due to hysteresis. Thus, hystere-sis in MR is clearly observed, which indicates the possibility of studying phase co-existenceand first order phase transition in FSMA’s using MR.Magnetization measurements have been performed to understand the magnetoresistancebehavior. A sharp decrease of magnetization at the martensitic transition (Fig. 4a) in small6elds (0.01-0.1 T) is the manifestation of large MCA in the martensitic phase. Large MCAhas been observed in different Ni-Mn-Ga alloys and is responsible for magnetic field inducedtwin variant reorientation. The magnetization in the martensitic phase decreases because inthe low field, a twinned state with moments along the easy axis ([001]) oriented in dissimilardirections for different twins is energetically favorable. The gradual decrease of magneti-zation in the austenitic phase, on the other hand, is possibly related to an increase of theaustenitic phase MCA with decreasing temperature. A step-like decrease in magnetiza-tion with distinct change of slope is evident at 120 K for both 0.01 and 0.1 T fields (inset,Fig. 4a). This decrease is significant because it suggests that the upturn in ρ (T) and positiveMR could be related to a magnetic transition that decreases the magnetization.Fig. 4b shows M ( T ) at 5 T in FC and FH. This field is much higher than the saturationfield, as shown by the isothermal M − H curves in Fig. 5. M ( T ) shows the characteristicvariation of saturation magnetization with temperature. By fitting the higher temperatureregion using the expression ( T C - T) γ (bold dashed line in Fig. 4b), we obtain an approximateestimate of T C to be 380 K. This is close to the T C of 385 K reported for Ni . Mn . Ga. Incomparison to Fig. 4a, magnetization increases by two orders of magnitude for 5 T FC andFH runs. Thus, the changes in the magnetization that are clearly visible in the low fieldmeasurement (Fig. 4a) are not evident here. For example, the large relative decrease inmagnetization in the martensitic phase (Fig. 4a) and the decrease at 120 K are not observedin Fig. 4b. Instead, the magnetization gradually increases in the martensitic phase. Thisincrease is intrinsic and is due to higher saturation magnetization in the martensitic phase.This results from alterations in interatomic bonding related to the change of structure, asalso observed in Ni MnGa.
The saturation moment turns out to be 3.5 µ B . The onlysignature of the martensitic transition in Fig. 4b is the hysteresis in M ( T ) during heatingand cooling cycles. However, there is hardly any change in the martensitic transitiontemperature with field. This shows that for this alloy, magnetic field does not change M s resulting in magnetic field induced martensitic transition, unlike in Ni-Mn-Sn and Ni-Mn-In. The isothermal M − H loop in Fig. 5 shows a decrease in the saturation magneticfield between the martensitic phase (20 K) and the austenitic phase (283 or 360 K). This isbecause in the austenitic phase, the MCA is very small and there is no twinning comparedto the martensitic phase with large MCA and twinning.We have calculated the magnetic ground state using ab initio , spin polarized density7unctional theory employing FPLAPW method to understand the origin of positive MRbehavior. Good agreement between experiment and theory has been obtained earlier forthe magnetic moments, lattice constants, total energies and the density of states for boththe phases. In particular, the total energies have been used to explain the phasediagram and magnetic states of Ni MnGa, Ni . Mn . Ga and Mn NiGa.
Here, we calculate the total energies of the different magnetic states of non-stoichiometricNi . Mn . Ga for the L structure (see Fig. 1 in Ref.8) with lattice constant of 5.843˚A de-termined from XRD at room temperature. The structure consists of 4 interpenetrating f.c.c.sub-lattices occupied by two Ni atoms, one Mn (MnII) and one Ga atom. To emulate thenon-stoichiometric composition, a 16 atom L super-cell is considered, where one of the eightNi atoms is replaced by one excess MnI type atom. Thus, there are seven Ni, five Mn (oneMnI and four MnII i.e. out of total Mn atoms only 20% are MnI) and four Ga atoms in thesuper cell with the chemical formula Ni Mn Ga , which is equivalent to Ni . Mn . Ga. Thetotal energy that consists of the total kinetic, potential, and exchange correlation energies ofa periodic solid with frozen nuclei has been calculated for two magnetic configurations withMnI spin moment parallel and anti-parallel to MnII. We find that the total energy is signifi-cantly lower by 16 meV/atom, when MnI is anti-parallel to MnII, compared to their parallelorientation. Anti-parallel alignment of Mn spins is energetically favored because of the directMnI-MnII nearest neighbor (at 2.53 ˚A distance) interaction, as has been shown for otherMn excess systems like Mn NiGa, Ni Mn . Ga . and Ni-Mn-Sn. The exchange pairinteraction as a function of Mn - Mn separation was calculated by a Heisenberg-like modeland an antiferromagnetic coupling at short interatomic distances was found. Enkovaara et al. reported antiferromagnetic Mn configuration in Ni Mn . Ga . from magnetizationand first principle calculations. Here for Ni . Mn . Ga, the Ni magnetic moment (0.3 µ B )is parallel to MnII. The MnI and MnII moments for the anti-parallel (parallel) orientationare unequal: -2.74 (1.9) and 3.23 (3.16) µ B , respectively. Thus, the magnetic momentof MnI is smaller than MnII. Smaller magnetic moment for MnI has also been obtained forMn NiGa, and this has been assigned to stronger hybridization between the majority-spinNi and MnII 3 d states in comparison to hybridization between Ni and MnI 3 d minority-spinstates. The difference in total energy between the paramagnetic and ferromagnetic phases ofNi MnGa was equated to k B T C . Following a similar approach, the total energy difference8etween the ferro- and ferrimagnetic states (16 meV/atom) corresponds to 186 K. As dis-cussed earlier, M ( T ) shows a decrease in magnetization at 120 K which is indicative of amagnetic transition. Since from theory, we find that the MnI atoms have magnetic momentdifferent from and anti-parallel to the MnII atom, we term the state below 120 K to be ferri-magnetic. Here, anti-parallel alignment of unequal local Mn moments would exist for thoseMnII atoms that have MnI as a nearest neighbor. The estimate of a transition temperatureof 186 K from theory can be considered to be in fair agreement with the experiment (120 K),considering that theory considers an ideal situation while the actual conditions may be morecomplicated. For example, the MnI atoms would replace the Ni atoms at random positions,and absence of any superlattice peak in the XRD pattern (Fig. 3) indeed indicates that. Thisdisorder effect in not considered in theory. Moreover, anti-site defects, possibility of cantedalignment are not considered by theory. So, in reality, the lattice sites where anti-parallelalignment between MnI and MnII moments occurs would be random and the moment ofMnI could be less than what is calculated. In fact, this is indicated by the underestimationof the total moment by theory (3.1 µ B ) compared to the experimental value of 3.5 µ B (Fig. 4b).To explain the positive MR shown in Figs. 1 and 2, we note that the application ofmagnetic field to a state with partial antiferromagnetic alignment of moments (MnI andMnII in this case) would induce spin fluctuations, thus increasing the spin disorder and henceresistivity that would result in positive MR. In Eu . Fe Sb , large positive MR has beenassigned to a ferrimagnetic or canted magnetic phase. We also find that for Ni . Mn . Gapositive MR increases linearly with field. In many antiferromagnetic intermetallic alloyspositive MR has been observed to increase linearly with H. For Eu . Fe Sb , at lowtemperatures a H / variation was observed. Linear positive MR has been recently reportedfor Fe, Co and Ni thin films up to 60 T and has been explained by quantum electron-electroninteraction theory. To the best of our knowledge, no theoretical prediction exists aboutMR behavior for a ferrimagnet with disordered antiferromagnetic alignment of a fraction ofthe local moments. To understand the linear MR variation in Ni . Mn . Ga, measurementswith higher fields would constitute an interesting study.In the martensitic phase, MR is negative and its magnitude increases up to the saturationfield (5 and 50 K data in Fig. 1b). But the behavior is clearly different from the austeniticphase: the slope of MR(H) does not change with temperature between 0 to 2 T (see the9 and 50 K plots in Fig. 1b). In contrast, the slope changes between 300, 235 and 150 Kdata in the austenitic phase where s - d scattering dominates. This indicates that the originof negative MR is different in the martensitic phase. Unlike in Ni MnGa, here the T C (= 380 K) is much higher than M s (= 76 K) and so the effect of s − d scattering in themartensitic phase is not visible.One of the reasons for the increase in ρ in the martensitic phase is the scattering of theBloch wave functions at the twin boundaries (TB), which are known to increase the defectdensity and hence resistivity; and this has been reported earlier for FSMA’s. The originof negative MR in the martensitic phase that leads to positive to negative switching of MRwhile cooling (Fig. 1b and 2b) possibly arises from the decrease in electron scattering due todecrease in the density of twin boundaries and domain walls with the application of externalmagnetic field. These are oriented in dissimilar directions at zero field and would tend toform larger twin variants and domains as the saturation field is reached. This will havesmaller resistivity compared to the twinned state with small sized twins and domains at H = 0. Negative MR due to domain wall scattering has been observed in ferromagneticthin films.
The hysteresis normally observed in domain wall MR is related to thehysteresis of the M − H curve. However, for Ni . Mn . Ga the M − H curves hardly exhibitany hysteresis (Fig. 5). For Ni . Mn . Ga, the observation that the increase in the negativeMR magnitude occurs for fields less than equal to the saturation field (arrow, Fig. 1b),suggests that its origin is linked with the twin and domain rearrangement.Twin boundary motion occurs when twinning stress is small and MCA is high governedby the condition
K > ǫ σ tw , where K is the magnetic anisotropy energy density, σ tw isthe twinning stress and ǫ is the maximal strain given by (1 − c/a ). For this specimen,high MCA is expected because M s is much lower than T C and this is supported by magne-tization data in Fig. 4a. In fact, the decrease in magnetization at M s gives rise to inversemagnetocaloric effect, and its magnetic field dependence has been explained by twin vari-ant reorientation. From XRD, we find that the unit cell volume remains similar acrossthe martensitic transition and the structure is modulated in the martensitic phase (Fig. 3).Modulated structures have lower twinning stress and hence are expected to exhibit twinboundary motion. These indicate that Ni . Mn . Ga would have small twinning stressand thus exhibit twin boundary motion. In fact, highest MFIS of 10% has been reportedin a Mn excess specimen with composition of Ni . Mn . Ga . that exhibits seven layer10odulated structure and a low twinning stress of 2 MPa. MFIS has been reported to occurin polycrystals that are textured and with large grain size, in trained samples, and also infine grained systems.
In our case, the specimen has been annealed for more thana week at 1100 K, and that leads to the growth of large grains (200-500 µ m). On the otherhand, in the absence of field, the width of the twins is only a few microns. Thus, withina grain the twins are ubiquitous and twin boundary rearrangement can occur due to externalmagnetic field. Coarse grained Ni-Mn-Ga is known to show larger MFIS, while annealing ofNi-Mn-Ga ribbons is reported to increase the MFIS by an order of magnitude. Sozinov et al. obtained single variant state for polycrystalline Ni-Mn-Ga at 1 T. For polycrystals,since the grains are oriented randomly, which lead to internal geometric constraints, forexample, the motion of the twin boundaries would be suppressed by the grain boundaries,the macroscopic strain is small. However, at the microscopic level within a grain the twinboundary motion is expected to occur in Ni . Mn . Ga and this is what is important inthe present context to explain the negative MR behavior in the martensitic phase. Thecharacteristic shape of the MR curve in the martensitic phase in polycrystalline Ni-Mn-Gahas been explained by twin variant rearrangement with magnetic field. The difference in resistivity between the first and second FH cycles (Fig. 2) can be relatedto the extent of twin boundary rearrangement. Lower values of ρ ( T ) in second FH cycle,which is recorded after cooling in presence of magnetic field across the martensitic transitionfrom 300 K, indicate that the field would more effectively reorient the twins as soon as theseare formed below M s . On the other hand, for FH first cycle where ρ is higher the magneticfield is switched on at 5 K. Thus, although MCA increases with decreasing temperature, twinning stress may also increase limiting the extent of twin variant rearrangement forminglarger twins. The variation of negative MR with temperature in the martensitic phase shownin Fig. 2b is significant because the heating and cooling data are very similar. This maybe related to the microscopic details of the domain and twin variant reorientation withtemperature and further studies are required to explain this.Another interesting observation in the MR of the martensitic phase is as follows: abovethe saturation field although MR is negative, a positive component is evident from its gradualincrease with field (see Fig. 1b). For example, at 50 K MR increases from -0.2% at 1 T to-0.1% at 8 T. A weakly increasing MR is also observed for the 5 K data, but its slope isless compared to 50 K. This shows that at lower temperatures where thermal fluctuations11ecrease, higher field would be required to induce spin disorder in the ferrimagnetic statefor causing similar increase in MR. This, in turn, supports the argument that below 120 Kthe magnetic state is ferrimagnetic in nature. Thus, there are two competing effects thatgovern MR in the martensitic phase with increasing field: a dominant negative trend due tothe formation of larger size twin variants and domains and a weaker positive trend due tothe ferrimagnetic nature of the magnetic state. While the first effect is present only up tothe saturation field, the second effect becomes visible only above the saturation field. IV. CONCLUSION
The switching of MR from negative to positive and back to negative values with decreasingtemperature is observed in a Mn excess ferromagnetic shape memory alloy Ni . Mn . Ga.Positive MR below 120 K in the austenitic phase is related to a ferrimagnetic state wherethe excess Mn atoms (MnI) at Ni site are antiferromagnetically oriented with the Mn atomsat Mn site (MnII). The existence of the ferrimagnetic state is shown by density functionaltheory, and experimental evidence is obtained from a decrease in magnetization and resis-tivity upturn at 120 K. In the martensitic phase, negative MR arises due to decrease inelectron scattering related to reduction in the density of twin boundaries and domain wallswith the application of external magnetic field. This effect is visible up to the saturationmagnetic field. Above this, a weaker positive trend due to the ferrimagnetic nature of themagnetic state is visible. On the other hand, negative MR above 120 K in the ferromagneticaustenitic phase is explained by the s − d scattering model. The hysteresis in MR(T) is amanifestation of the first order nature of the martensitic phase transition. V. ACKNOWLEDGMENT
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40 42 44 46 66 68 112 114 A ( ) (x 5)A ( ) (x 4) i n t e n s it y ( a r b . un it ) (x 12) MA MMM (/ 2)AM
MMM M M (- )( )( )(- )(- ) (x 3)M (- ) θθ