Effect of twin boundaries on electrical transport in a Ni-Mn-Ga single crystal

Effect of twin boundaries on electrical transport in a Ni-Mn-Ga single crystal
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  Effect of twin boundaries on electrical transport in a Ni–Mn–Gasingle crystal Vijay Kumar Srivastava and Ratnamala Chatterjee a  Physics Department, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India R. C. O’Handley  Department of Materials Science and Engineering, MIT, Cambridge, Massachusetts 02139-4307   Received 22 August 2006; accepted 18 October 2006; published online 29 November 2006  Detailed electrical resistivity measurements for different twin configurations and crystallographicdirections on Ni 49 Mn 29 Ga 22  Heusler alloy are presented. Important results of these measurementsare   i   the resistivity of the crystal is not related to the number of twin boundaries present   aspreviously reported   but instead depends upon the local environment of the atoms   c   long directionor  c  long direction   in the crystal. The crystallographic anisotropy of the resistivity is appreciable   c   I     c   I  .   ii   Intermartensitic transition temperature is strongly affected by the twin configurationand suppressed for the twinned state as compared to the single-variant states. ©  2006 American Institute of Physics .   DOI: 10.1063/1.2397541  In recent years Ni–Mn–Ga   Refs. 1–3   Heusler alloysclose to stoichiometric composition have drawn attention of the research community. Mostly the work in this field of ferromagnetic shape memory alloys has focused on the over-all strain obtained at a given field or at a given temperature,neglecting the effect of twin boundary motion that enablesthese crystals to strain under the action of a field or appliedstress. As pointed by Marioni  et al. , 4 the stochastic nature of the pinning process can profoundly affect the performancesof small Ni–Mn–Ga based devices. Conflicting reports on theeffect of twin boundary on resistance in Ni–Mn–Ga alloysexist in literature. Jin  et al. . 5 demonstrated a 12% increase inthe resistance in Ni–Mn–Ga on transformation from austen-ite to martensite and explained this in terms of electron scat-tering at twin boundaries present in the crystal. Later, they 6 reported a similar increase of resistance in martensite phase,although the field had eliminated the twin boundaries in thesample. On the other hand, it is suggested by Slebarski  et al. , 7 that the resistivity behavior in Heusler alloys is influ-enced by local atomic environment. In view of this, it be-comes important to study the effect of twin boundary mo-tions on electrical transport in these crystals. Also,observation of intermartensitic phases has been made bymany researchers, 8–12 but the understanding of intermarten-sitic transformation temperature with the twin boundary mo-tion is not clear yet.The interesting feature of these crystals is that the twinboundaries can be moved by application of any of the fol-lowing: stress, temperature, or magnetic field. Lengthchanges   strain   by application of magnetic field 13 and met-allographical evidence of rearrangement of twin boundariesby application of magnetic field 14,15 have been shown in re-lated crystals. In the present case, we have applied stress tovary the twin configuration of the crystal. Twin arrangementcan be achieved by application of a shear across the twinboundary. In a rectangular-prism sample cut with austenite  100   faces, the twin planes are at 45° to the cross section of the sample so they can be moved by application of a suitablecompressive stress on two opposing faces. By incrementallycompressing the crystal in a defined way, we move the twinboundaries so as to induce states having increasing volumefraction of variants with  c  axis along the direction of com-pression. Thus, we can control the relative volume of   c   I   and c   I   variants in tetragonal martensitic Ni 49 Mn 29 Ga 22  single-crystal by using external stress.The crystal is martensitic at room temperature and wasinitially cut in a way so as to have  c  axes of variants parallelto the long direction of the crystal   i.e., the direction of cur-rent flow  ; we designate this state as  c   I  ,  e 0 =0. This initialsample length was  L 1 =9.71 mm. Here  e 0  designates the per-centage strain relative to the longitudinally compressed state.External pressure was then applied along the breadth of thecrystal to achieve the maximum length  L 2 =10.25 mm. Fur-ther application of stress along the breadth direction did notchange the length, defining  L 2  as a limit. We call this state c   I  ,  e 0 =5.6. In both these extreme cases, the crystal is as-sumed to be essentially a single variant, i.e., few if any twinboundaries exist in the crystal, with atomic decoration   localcrystal orientation   as defined. In between the two extremecases, we could achieve various intermediate variant distri-butions   and possibly multiple twin boundaries   that are as-sumed to correlate with transverse compression-inducedstrains  e 0 . Thus, the length of the sample in the long, currentdirection is used as a measure of twin structure. Since appli-cation of compression could change the length of the samplereversibly by 5.6%   the maximum strain reported on thecrystal was   6%  , we could assume that the applied com-pression eliminated the twin boundaries completely and theyare expected to be single variants. It is assumed that theeffect is linear. At  e 0 =2.5 it is expected that half the variantshave  c   I   and half have  c   I  .We made electrical resistivity measurements on aNi 49 Mn 29 Ga 22  single crystal for different twin configurationsaround an intermartensitic transition and studied this prob-lem in detail. Based on our previous results, 12 we concentrateour studies in the temperature range of 200 K  T   300 K,where the crystal shows a sharp intermartensitic phase tran-sition   at 273 K  . The specifics of the phase transitions arenot of interest here   results of XRD studies will be published a  Author to whom correspondence should be addressed; electronic mail:rmala@physics.iitd.ac.in APPLIED PHYSICS LETTERS  89 , 222107   2006  0003-6951/2006/89  22   /222107/3/$23.00 © 2006 American Institute of Physics 89 , 222107-1 Downloaded 31 Oct 2007 to Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp  separately  . This particular region is chosen so that the effectof twin boundaries on transition temperatures can be studied.Figure 1 shows the     vs  T   plots for the crystal at allstrain percentages   0  e 0  5.6   in the temperature range of 200 K  T   300 K. All these curves are for data taken dur-ing heating. For the sake of clarity, not all the plots areshown here. As shown in this figure, the features of     - T  curves are qualitatively similar for all strains. The resistivityincreases smoothly up to a certain temperature   T  1   and thena sharp rise   10%–20%   in resistivity is observed. Thisindicates the transformation from one martensitic phase toanother at  T  1  that is complete at  T  2 , beyond which the  d     /  dT  is again small. On closer look, the two main features that canbe observed from this figure are   i   the resistivity decrease asthe sample is changed from  c   I    e 0 =0   to  c   I    e 0 =5.6   and  ii   the intermartensitic transformation temperature  T  1  varieswith changing  e 0 ;  T  1  is minimum for  e 0 =2.5   see inset of Fig. 1  . The data were repeated several times, spaced overseveral months.Resistivity versus strain graphs at different temperatures  barring the transition range of 260 K  T   274 K   areshown in Fig. 2  a  . Figure 2  a   shows the raw data and theinset of the figure shows the same curves averaged over fivepoints. Resistivity decreases monotonically with the increasein variants having  c   I  . The  d     /  dT   below  T  1  also decreasesmonotonically   not shown in figure   with the increase invariants having  c   I  . At every temperature   200 K  T   300 K  , the observed resistivity values were maximumwhen the sample was single variant with  c  axis parallel to thecurrent direction   e 0 =0   and minimum when the sample wascomprised mainly of a single variant but with  c  axis perpen-dicular to the current direction   e 0 =5.6  . Figure 2  b   showsthe plots at the temperatures near the transition range, alongwith the plots taken at 280 and 300 K. As can be seen, all theplots in this range   260 K  T   274 K   have a general ten-dency to show  lower   resistivity as one goes from  I   c  axis to  I   c  axis and they show a distinct peak at  e 0 =2.5. The rea-son for this anomalous behavior at  e 0 =2.5 are discussed inthe following paragraphs. The overall changes in resistivityare   10%–20%, as we go from one extreme variant state tothe other in both Figs. 2  a   and 2  b  .Monotonic variations of resistivity as  c  axes are variedwith respect to  I    variation in resistivity with  e 0   implies thatas opposed to previous reports 4,9 the number of twin bound-aries does not play major role in electrical resistivity of thesample and also suggests that the resistivity of the martensi-tic phase is dominated by the direction of current with re-spect to the  c  axis of the crystal. Thus, as indicated by Sle-barski  et al. , 7 our results clearly show that it is the localenvironment of the atoms   c   long direction or  c   long di-rection   rather than the number of twin boundaries, whichinfluence the electrical transport properties of this Ni–Mn–Ga Heusler alloy single crystal. Assuming free-electrontheory     RT = m *  /  ne 2     and      10 −14 s   from our measuredresistivity values, we estimated the  m * . The effective mass of this Heusler alloy off-stoichiometric crystal is   50 times thefree-electron mass and thus Ni 49 Mn 29 Ga 22  alloy falls in thecategory of Heusler alloys in which the local environment isknown to influence 6 the magnetic and electrical resistivitybehaviors.The larger resistance in the  c   I    long direction   configu-ration suggests that the bonding in the crystal is strongeralong the  c  axis; it is characterized by a more localized bond-ing charge distribution along the lines joining the nearestneighbor atoms. On the other hand, in the  c   I   direction, thecharge density in the current direction is more antibonding ordelocalized in nature, leading to lower resistance.The other interesting feature that can be noticed fromFig. 1 is that  T  1  varies slightly   3.7%   with changing vari-ant distribution   corresponding also with changing strain  .The lowest value of   T  1   263 K   is for 2.5% strain and highest  273 K   for both extremal states, i.e.,  e 0 =0 and  e 0 =5.6  single variants with few if any twin boundaries  . On closerlook, the slope of the resistivity   d     /  dT    at the intermarten- FIG. 1.     vs  T   plots in the temperature range of 200 K  T   300 K, for allstrain percentages   0%  e 0  5.5%  . Strain percentages are indicated byarrows. Inset shows  T  1  vs strain percentage   e 0  . At 2.5% when twin bound-ary is maximum,  T  1  is found to be minimum.FIG. 2.   Color online   a      vs strain percentage   raw data   at differenttemperatures   barring the temperatures near  T  1 , i.e., 260 K  T   274 K  .Inset shows the smoothed   over five points   graphs for the same data.   b     vs strain percentage   raw data   in the transition range   260 K  T   274 K  along with the data at 280 and 300 K shown for comparison. Inset shows    vs  T   plots in the temperature range of 200 K  T   300 K for 2%, 2.5%, and3% strains separately. 222107-2 Srivastava, Chatterjee, and O’Handley Appl. Phys. Lett.  89 , 222107   2006  Downloaded 31 Oct 2007 to Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp  sitic transformation also varies with  e 0 , the smallest variationbeing for  e 0 =2.5.The data for 2%, 2.5%, and 3% strains shown in theinset of Fig. 2  b   allow the anomalous behavior of Fig. 2  b  to be better understood. Although the resistivity values at alltemperatures change as expected   decreasing with increasingstrain  , in the temperature range 260 K  T   274 K, due tosuppression of the intermartensitic transition temperature  T  1 for the twinned state, the resistivity values for 2.5% arelarger than the 2% curve, giving rise to this anomaly.This important observation   the lower-temperature mar-tensitic phase is stabilized in the highly twinned   e 0 =2.5  state   is difficult to interpret without more knowledge of thestructures of the two martensites. However, it is likely that inthe highly twinned state when both variants are present, thecrystal has a large internal elastic energy due to variant in-compatibility. Stress is known to stabilize martensite, makingit possible for the phase transition to occur at the cost of lesser energy. The presence of twin boundaries in the  e 0 =2.5 configuration eases the accommodation of internalstress from whatever source, leading to lower transitiontemperatures.In conclusion, our measurements indicate that the elec-trical resistivity of the crystal is not related to the number of twin boundaries   as previously reported   but instead dependson whether the variants are oriented in a way such that the  c axes are parallel to the direction of current or they are per-pendicular to the current flow. The crystallographic aniso-tropy of the resistivity is appreciable:    c   I     c   I  . 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