Real Space Visualization of Thermomagnetic Irreversibility within Supercooling and Superheating Spinodals in M n 1.85 C o 0.15 Sb using Scanning Hall Probe Microscopy
Pallavi Kushwaha, Archana Lakhani, R Rawat, A Banerjee, P Chaddah
aa r X i v : . [ c ond - m a t . s t r- e l ] J a n Real Space Visualization of Thermomagnetic Irreversibility within Supercooling andSuperheating Spinodals in
M n . Co . Sb using Scanning Hall Probe Microscopy Pallavi Kushwaha, Archana Lakhani, R Rawat, A Banerjee and P Chaddah
UGC-DAE Consortium for Scientific ResearchUniversity Campus, Khandwa RoadIndore-452001, India. (Dated: November 2, 2018)Phase coexistence across disorder-broadened and magnetic-field-induced first order antiferromag-netic to ferrimagnetic transition in polycrystalline Mn . Co . Sb has been studied mesoscopicallyby Scanning Hall Probe Microscope at 120K and up to 5 Tesla magnetic fields. We have observedhysteresis with varying magnetic field and the evolution of coexisting antiferromagnetic and fer-rimagnetic state on mesoscopic length scale. These studies show that the magnetic state of thesystem at low field depends on the path followed to reach 120 K. The low field magnetic statesare mesoscopically different for virgin and second field increasing cycle when 120 K is reached bywarming from 5K, but are the same within measurement accuracy when the measuring temperatureof 120K is reached from 300K by cooling. PACS numbers: 75.30.Kz, 72.15.Gd
I. INTRODUCTION
First order magnetic transitions have been of extensivescientific interest in recent years. The interest in thesesystems arise due to their technological importance likegiant magnetoresistance, magnetocaloric effect, magneticshape memory effect etc. as well as their fundamentalimportance to understand various interesting phenomenalike phase separation, metastability, glass like magneticstate etc. Quench disorder in a system can lead to spreadof local transition temperature resulting in the broaden-ing of a first order transition . This broadening givesrise to coexistence of competing phases in the transitionregion. The metastability of coexisting phases within(and below) the supercooling and superheating spinodalshas been of wide interest and actively pursued in a widevariety of systems like systems showing metal insulatortransitions , multiferroics , intermetallics etc. Theunderstanding of magnetic first order transition (due toeasy control of magnetic field (H) and temperature (T)) also has implication to wider class of systems wherefirst order transition plays a role (like glass transitionwhere pressure and quenching rate are sometimes diffi-cult to control). It has been argued that the glass likemetastable states resulting from the slow dynamics of thetransition are different from the metastable states whicharise due to supercooling and superheating near the firstorder transition . Both kind of metastable states canshow seemingly similar features in some of their physicalproperties e.g. open hysteresis loop in isothermal R-Hmeasurement. However, it has been shown recently thatsuch open hysteresis loop due to supercooling and super-heating will be observed only for T within these spin-odals and will be observed only during cooling or onlyduring heating, depending on the sign of the slope oftransition band in H-T space. Mesoscopic investigationby Scanning Hall Probe Microscopy (SHPM) has showncoexisting antiferromagnetic (AFM) and ferromagnetic (FM) phase around critical field in doped CeF e and Gd Ge . For the T chosen in these studies, it did notmatter whether the measurement temperature is reachedby cooling or by warming. Here we present real spacemagnetic imaging study by SHPM along with magneti-zation and resistivity measurement of M n . Co . Sb toshow that field induced transition for T (=120 K) lyingbetween supercooling and superheating spinodal dependson the path followed to reach the measurement temper-ature.Doped M n Sb shows first order antiferro (AFM) to fer-rimagnetic (FRI) transition at low temperature . Belowtransition temperature ( T N ) AFM to FRI transition canbe induced with the application of magnetic field. When T N is shifted to lower temperature, these systems showanomalous magnetic behavior . We have addressedsome of these anomalous behavior in our magnetotrans-port studies of Co doped M n Sb . In these studies wehave shown that anomalous thermomagnetic irreversibil-ities at low temperature are a result of critically slowdynamics of the transition and these are different fromthe seemingly similar irreversibility that arise due to su-percooling and superheating. II. EXPERIMENTAL DETAILS
M n . Co . Sb sample used in the present studyis taken from same ingot which has been used forearlier resistivity/magnetoresistance studies . Resistiv-ity/magnetoresistance measurement were performed us-ing home made resistivity setup inside Oxford magnetsystem. Magnetization measurement were performed us-ing VSM option of PPMS. Magnetic imaging was carriedout using Scanning Hall Probe Microscope from Nano-Magnetics Instruments, U.K. The microscope incorpo-rates a chip sensor, which consists of a 1-micron sizesquare Hall sensor integrated adjacent to a tunneling tip.The tunneling tip is used for bringing the Hall sensor inclose proximity to sample surface. The sensor chip isaligned with a small angle ( ≈ ) to keep tunneling tipcloser to sample surface than Hall sensor. Magnetic imag-ing is carried out by scanning the Hall sensor over thesample surface while simultaneously measuring the Hallvoltage, which is proportional to perpendicular compo-nent of the magnetic field at the surface. In the presentstudy we have carried out magnetic imaging in lift offmode. In this mode sample surface is reached by find-ing tunneling current. After finding the sample surfacetip is retracted few hundred nanometers, called lift off,and scanning is performed at this constant height. Forlow temperature and high field measurements this insertis placed inside 9-Tesla superconducting magnet (Amer-ican Magnetics) system supported on a two-stage vibra-tion isolation stage. Approximately 6mm diameter and 2mm thick sample is polished to mirror finished surface forSHPM imaging. All the images in the present study areof 27 µm × µm scan area and pixel size 128 × . µm lift off and 5 µm/sec scan speed.All the measurements were carried out as a function ofMagnetic field at 120 K for two protocols; (i) Sampleis cooled from 300 K to 120K (i.e reached by cooling)in zero field and (ii) sample is cooled to 5 K and thenheated back to 120 K (i.e. reached by warming)in zerofield. III. RESULTS AND DISCUSSION
Figure 1 [a]and [b] show the temperature dependenceof resistivity ( ρ ) in zero magnetic field and magnetiza-tion (M) in 0.1 Tesla magnetic field respectively for cool-ing and then warming cycle. AFM (higher resistivity andlower magnetization) to FRI (lower resistivity and highermagnetization) transition is visible as a sharp decreasein resistivity (increase in magnetization) with increasingtemperature and shows a hysteresis of 10K between heat-ing and cooling cycle. The slightly lower transition tem-peratures obtained from magnetization measurement arein accordance with magnetic field dependence of T N . Be-side the 10 K hysteresis, transition is broad for both cy-cles during cooling as well as warming. This is expectedfor substitutional alloys where inherent chemical disordercan result in distribution of local transition temperatureon the length scale of correlation length . The spread inlocal transition temperature result in a band of transitionin H-T space and two phases (here FRI and AFM) can co-exist within this band. Therefore, this broadening of firstorder transition makes this compound suitable to studythe coexistence of phases and their evolution with mag-netic field. The schematic of ( H ∗ , T ∗ ) and ( H ∗∗ , T ∗∗ ) forAFM to FRI transition is shown in the inset of figure 1 [a].For the sake of simplicity ( H ∗ , T ∗ ) and ( H ∗∗ , T ∗∗ ) spin-odals are shown well separated in contrast to overlappingbands actually observed in the present system. Here,isothermal measurement were carried out along path QS S R Q P
T * *T N T * H T [a] Mn Co Sb ( m c m ) Temperature (K) [b] Mn Co Sb M ( B /f. u . ) Temperature (K)
FIG. 1: [a]
Resistivity in zero field and [b]
Magnetization in0.1 Tesla magnetic field as a function of temperature measuredduring cooling and subsequent warming for Mn . Co . Sb .Inset shows the schematic of supercooling ( H ∗ , T ∗ ) and super-heating ( H ∗∗ , T ∗∗ ) spinodal in H-T space. Isothermal mea-surements presented in Figure 2 (Figure 3) were carried outalong path QS when point Q is reached by cooling (warming)following path PQ (RQ). for two conditions, viz when the point Q is reached (i)by following path PQ (cooling from T > T ∗∗ ) and (ii) byfollowing path RQ (heating from T < T ∗ ).Figure 2 shows some of the representative SHPM im-ages as a function of magnetic field with increasing andthen subsequent decreasing field at 120K when reachedfrom 300 K (i.e. reached by cooling). All the images,shown in figure 2, are plotted on same scale after sub-tracting the applied magnetic field. The labels on theseimages are marked on corresponding ρ − H and M − H curves (plotted in the middle row of figure 2) to corre-late these results. Image (a) of figure 2, taken at 0.5Tesla shows inhomogeneous magnetic state where bothFRI (blue) and AFM (red) phases co-exists. The imagecontrast remains almost same with further increase inmagnetic field to 1 Tesla, image (b), which is consistentwith almost constant ρ and M between these field values.At 2 Tesla image (c) shows increased FRI fraction andmuch smaller AFM fraction indicating a field inducedAFM to FRI transition. Further increase in magneticfield to 4 Tesla results in homogeneous FRI state (im-age (d)). On reducing magnetic field from 5 Tesla to 2Tesla image (e) shows almost homogeneous FRI phase incontrast to field increasing cycle where we observed coex-isting FRI and AFM phase image (c). However image (f)taken at 1 Tesla during field decreasing cycle, shows inho-mogeneous magnetic state which is similar to image (c)observed during field increasing cycle at 2 Tesla. This ir-reversibility is consistent with the first order nature of thefield induced magnetic transition. Both resistivity valueas well as magnetization value are identical for point ‘c’and point ‘f’ as shown in bottom graphs. As the magneticfield reaches 0.5 Tesla the image (g) resembles image (a)taken during field increasing cycle for same field valuei.e. the magnetic state of the system is same before andafter the application of magnetic field at low field. This [a] [b] [c] AFMFRI [d][e][f][g]
25 50 75 100 [e][c]
25 50 75 [f][b]
Normalized Magnetic Induction (%)
25 50 75 C oun t s [g][a] g f e da b ( m c m ) c (ii)(i) H (Tesla) (ii)(i)b ceg dfa M ( B / f. u . ) H (Tesla)
FIG. 2: [a]-[g]
SHPM Images of Mn . Co . Sb as a functionof magnetic field at 120 K (reached by cooling from 300 K)along with corresponding resistivity and magnetization curve.Scan area is 27 µm × µm and image label corresponds torespective point in resistivity and magnetization curves. Bot-tom row shows the histograms of magnetic images at labeledfield values for increasing and decreasing field cycle. Inhomo-geneous magnetic state and similar magnetic state after fieldcycling at low field is highlighted along with characteristichysteresis associated with magnetic field induced first ordertransition is consistent with the ρ − H and M − H curves, wherezero field resistivity is found to be same before and afterthe application of magnetic field and virgin curve (curvetaken during first field increasing cycle) overlaps with theenvelope curve (taken during second field increasing cy-cle).The weak contrast in the images arises due to bulksample (thickness 2mm), whereas the observed phase sep-aration is on the length scale of few µm . To demonstratemagnetic inhomogeneity more clearly, histograms of mag-netic field distribution are plotted in the bottom row cor-responding to magnetic images shown in same figure. Forthe sake of comparison, field window for histogram cal-culation as well as vertical scale are kept same in all theplots. For 0.5 Tesla both the curves (curve ‘a’ and ‘g’)are almost identical with slightly higher FRI phase forcurve ‘g’. The magnetization at point ‘g’ is only slightlyhigher than in point ‘a’. At 1 Tesla, curve ‘b’ and curve‘f’, indicate entirely different magnetic field distribution on sample surface during field increasing and decreasingcycle. Similar to 1 Tesla, we observe entirely different his-tograms corresponding to image (c) and image (e) takenat 2 tesla.We repeated similar measurement under identical con-dition at 120K, when reached by warming from 5K underzero field condition. This experiment also shows a fieldinduced AFM to FRI transition with varying field andassociated irreversibility. However, our main interest isto study the state of the system at zero field before andafter field cycling i.e. across virgin and envelope curve.Therefore in Figure 3, we show resistivity and magne-tization data along with only two sets of images; onetaken at 0.1 Tesla and other taken at 1 Tesla. For eachset, images were taken during first field increasing cy-cle i.e. virgin curve , field decreasing cycle and secondfield increasing cycle. These curves are labeled as (i), (ii)and (iii) in ρ − H and M − H plots along with markersat which magnetic images were taken. To compare theSHPM images at constant field, magnetic scale is keptsame for each set of images separately but varied for dif-ferent magnetic field. As can be seen in top row (0.1Tesla); image (a) is distinctly different from other twoimages (d) and (e) which are identical. Image (a) showsalmost homogeneous AFM state whereas other two im-ages shows coexisting FRI and AFM states. This is con-sistent with the ρ − H curve where point ‘d’ and ‘e’ havealmost same resistivity but much smaller compared topoint ‘a’. In case of M − H also, M is same for point ‘e’ . T e s l a [a] [d] [e] . T e s l a [b] [c] [f] (iii)(ii)(i) fed cba ( m c m ) H (Tesla)
T= 120 K reached by warming (iii)(ii) (i)fed cba M ( B / f . u . ) H (Tesla)
T= 120 K reached by warming
FIG. 3: [a]-[f]
SHPM Images of Mn . Co . Sb at 0.1 and1.0 Tesla taken at 120 K (reached from 5 K) along with cor-responding resistivity and magnetization curve. Scan area is27 µm × µm and magnetic scale is same for each row sepa-rately. and ‘d’ and smaller for point ‘a’. This is in contrast tofigure 2 (measured during cooling) where magnetic stateof the system at low field is identical before and after theapplication of magnetic field. Images for 1 Tesla (bot-tom row) show that magnetic state of the system aremore similar during curve (i) and curve (iii) (image (b)and image (f)) compared to that measured during curve(ii) (image (c)). Image (c), taken during field reducingcycle, has much larger FRI phase fraction compared toimage (f) taken during field increasing cycle at same fieldvalue. This is consistent with ρ − H curve where point ‘b’and point ‘f’ have similar resistivity values compared topoint ‘c’. A closer inspection of these images show higherFRI fraction in image (f) compared to image (b). C oun t s EDCBAEDCBA
Normalized Magnetic Induction (%) [c] 25 50 75 1001.0 Tesla [f] [a] 0.1 Tesla [b] 1.0 Tesla
FIG. 4: Histograms of SHPM Images of Mn . Co . Sb at0.1 Tesla and 1.0 Tesla for virgin curve, field decreasing cy-cle and second field increasing cycle at 120 K (reached bywarming from 5 K). These curves highlight that the histogramcorresponding to second field increasig cycle are distincly dif-ferent from first cycle. Histograms of magnetic images at low field are shownin figure 4 for 0.1 and 1.0 Tesla magnetic field for all thethree cycles. Similar to figure 2, field window chosen forhistogram calculation and vertical scale are kept same forall the figures. At 0.1 Tesla, histogram corresponding toimage (a) has sharp peak and has distinctly different fielddistribution compared to curve (e).In case of histogram(a) about 87% of scanned region have magetic induc-tion in the range AB where magnetic induction is less than 25% of the total scale, indicating almost homoge-nous AFM state for image (a). Whereas for histogram(d) and (e) more than 90% region has magnetic induc-tion in the range BD (25 −
75% of total scale). Even at 1Tesla there is a difference in magnetic field distributionfor curve (b) and (f) though less drastic compared to thatobserved in 0.1 Tesla. Here also, more than 81% regionfor histogram (b) have magnetic induction in the rangeAB (0-25 % of total scale) comapared to only ≈ ρ − H and virgin curve lying outside envelope curve in M − H as well as ρ − H measurements. IV. CONCLUSIONS
The SHPM images of
M n . Co . Sb at 120 K showalmost homogenous AFM state at low field when 120 Kis reached by warming in contrast to coexisting AFMand FRI state when reached by cooling i.e. the mag-netic state of the system on mesoscopic length scale de-pends on the path followed to reach the measuerementtemperature. Almost homogenous low field AFM stateduring warming is converted to coexisting AFM and FRIstate on mesoscopic length scale after isothermal fieldcycling. These studies provide the origin of open hys-teresis loop observed in ρ − H and virgin curve lyingoutside the envelope curve in ρ − H and M − H measure-ments observed during warming only. Similar studies onfrozen glassy magnetic states will provide further insighton phase seperation and metastability. V. ACKNOWLEDGMENTS
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