SUPPLEMENTARY INFORMATION ABOUT OUR MAGNETO-OPTICAL IMAGING SET UP USED IN OUR EXPERIMENTS Magneto Optic Imaging (MOI) technique 1 is based on Faraday rotation, consisting of a reflecting polarization microscope (Carl Zeiss, model: Axio Tech Vario) and a Peltier cooled charge coupled device (CCD) camera (Andor, ixon, 512x512 pixels, 16 bit). The setup is shown schematically in fig.1. We work at 550nm wavelength where the quantum efficiency of the CCD is maximum (85%). Incident and reflected linearly polarized light rays are shown by dotted blue and solid red lines respectively. Linearly polarized light is reflected off the sample (superconductor, in our case) on which a Faraday active material (ferrite garnet film (FGF) marked as V in fig.1) with high Verdet constant (V) and thickness (d) is placed. The reflected light undergoes Faraday rotation by an angle θ =VB z 2d, where B z is the z Figure 1. Schematic of MOI setup component of local magnetic field at the location of the sample consisting of ordinary unpolarized light underneath the FGF where light is reflected off. The intensity of the source (S), linear polarizer (P), beam splitter (B), objective (O), FGF film (V), faraday rotated light follows the relation, I(x,y) sin 2 (V2dB z (x,y)), sample (T), and analyzer (A). Also indicated is the local magnetic field using which we map the z component of local field distribution across direction (B z ). The blowup shows the state of linear polarization in the incident the sample viz., B z (x,y). (blue, dotted line) and reflected beam (red, solid line). We have modified the above conventional MOI setup by replacing the polarizer (P) by a home made Compact Faraday Rotator (CFR) shown in fig. 2(a). The CFR consists of a linear polarizer placed behind a transparent FGF film (without the reflecting mirror layer) with high V and a coil wound around it (see fig.2(b)). The design in very compact and provides high sensitivity 2 for detecting B z (x,y). Sending a current through the coil (cf., C in fig.2(a)), we rotate (by α) the polarization of the linearly polarized light passing through the CFR (typically, 0.4 Amp current through C gives α = 0.3º rotation). Using the CFR we obtain an average differential image δ ( x, y) = ( I I ) +, where I + and (a) (b) (a) (b) I are intensities obtained with ± α, and.. signifies averaging over a number of images. Figure 2. (a) Modified MOI setup (schematic) showing the CFR which consists of a film polarizer (P), transparent FGF film (F), and a coil wound around it (C). Modulation by ±α of the incoming linearly polarized light is shown in the blowup. The modulation is in a plane perpendicular to the plane of the page. (b) A picture of the CFR.
Following the scheme proposed in ref.3, δ ( x, y) provides information about B z (x,y) distributed across the sample 2. Using the above technique, we obtain at least an order of magnitude improvement in signal to noise ratio over a conventional MOI setup while measuring B z (x,y). Unlike other differential MOI imaging procedures 4 which require modulation of external temperature or field, the present procedure discussed above does not have this requirement, as a result it can be applied to measure the field distribution even in the hysteretic magnetization regime of materials (superconductor in our case). 1 J. Sinha et al., Phys. Rev. E 77, 046118 (2008). 2 Pabitra Mandal et al., (MS under preperation) 3 Rinke J. Wijngaarden et al., Review of Scientific Instruments 72, 6 (2001) 4 Alex Soibel et al., NATURE, 406, 20 (2000)
Energy Dispersive X-ray (EDX) and Electron Probe Micro Analysis (EPMA) analysis of CaFe 1.94 Co 0.06 As 2 (a) Count (a.u) (b) 6 5 4 3 2 1 Fe Co As 0 0 2 4 6 8 10 12 3 Ca 1 E (kev) 4 Fe Co (a) Local Energy Dispersive X-ray (EDX) spectra (with beam diameter of 50 nm) shown in normalized scale (the peak corresponding to Fe occurred at 6.4 kev is normalized to unity) on four different locations on the sample. (b) The locations of local EDX spectra are marked as 1, 2, 3 and 4 in the MO image taken form fig. 3(c). Fe 2 1 2 3 4 As I. Energy Dispersive X-ray (EDX) analysis across different regions of single crystal of CaFe 1.94 Co 0.06 As 2 : We have captured four local Energy Dispersive X-ray (EDX) spectra (spot size ~ 50 nm) on four different locations. In the adjoining figure (b) locations for EDX analysis are marked as 1, 2, 3 and 4 on the Magneto-optical (MO) image of fig. 3(c) of the sample. The peaks in the spectra identify different elements, viz., Ca, Fe, Co & As. Note that at all the four locations, the peaks occurs at the same location in energy (E) and the variation in the ratio of peak heights is less than five percent across all the four locations. These results indicate that the relative concentrations of elements locally are nearly identical across different regions in the sample. The sample is therefore chemically homogenous not only on the macroscopic but also on the microscopic scale. Therefore, even though, we observe variations in the MO contrast (compare regions 3 and 4, 1 and 2 in fig.(b)), locally all the regions are chemically homogenous. Below we show an optical image of our sample (c). It was cleaved (c) 3 4 1 2 (c) Optical image of the sample mounted on a copper block with conducting silver paint.
with a sharp blade to get a new fresh surface for EDX measurement and mounted on a copper block with conducting silver paint which is necessary to avoid charging effects during EDX. The locations where spot EDX has been done are marked by 1, 2, 3 and 4, like in the MO image in fig. (b). 0.00164 (very close to 3%, making the sample composition CaFe 1.94 Co 0.06 As 2 ). The above suggests the homogeneity of Co concentration all across the sample. Therefore, our investigation using two different methods, EDX and EPMA, suggests that there is indeed no chemical inhomogeneity in our sample. ***** II. Electron Probe Micro Analysis (EPMA) of CaFe 1.94 Co 0.06 As 2 : Electron Probe Micro Analysis (EPMA) was performed on a commercially available Cameca Sx100 Electron Probe Micro Analyzer. A small piece of the sample was first cleaved using a sharp blade and the sample with cleaved surface facing down was molded into a stub using a commercially available conducting S.No Concentrati -on (x) S.No Concentrati -on (x) S.No Concentrati -on (x) 1 0.0610 6 0.0650 11 0.0625 2 0.0620 7 0.0625 12 0.0605 3 0.0630 8 0.0600 13 0.0590 4 0.0620 9 0.0640 14 0.0625 5 0.0615 10 0.0595 15 0.0610 Table 1: Measured Co concentration (x) in CaFe 2-x Co x As 2 at 15 different points across a 100 100 µm 2 area of the sample. powder in a hot press. The stub was polished using various grade of sand paper and alumina powder. Final polishing was done using 0.05 µm alumina powder to give a mirror finish polishing. Measurements were performed at 15 different points spreading across a 100 100 µm 2 area. The Co concentration (see table 1) obtained by this method is 0.06173 ±
The light gray straight line like features running diagonally across the image in fig. 1(h) are present not only inside the sample but also outside it. These line like features are linear defects which appear in the magneto-optical garnet indicator films which are placed on top of the sample during MO imaging. Therefore these linear defects appear not only in the sample but also outside the sample. Below we present some results similar to those discussed in fig.1 in the paper on another sample from the same batch of crystal, by using a magneto optical garnet indicator film which has lesser number of linear defects. Magneto - optical imaging (MOI) of a different CaFe 1.94 Co 0.06 As 2 sample from the same batch as the crystal reported in our paper We show some recent MO images in figure a and b captured on a same batch of sample of CaFe 1.94 Co 0.06 As 2 (370µm 160 µm 50 µm) at 14K, with a different, relatively cleaner magneto-optical garnet indicator film placed on the sample for magneto-optical imaging. Figure (a) is obtained at 211 Oe while increasing the field from zero in virgin (a) (b) 95 µm 200 (c) virgin run 211 Oe (d) reverse run 208 Oe B z (G) 150 100 50 0 1 Oe 50 100 150 200 250 300 350 400 x (μm) 50 100 150 200 250 300 350 400 x (μm) 0 Oe Figure (a) MO image at H = 211 Oe in the virgin run, (b) at H = 0 Oe in reverse run after coming back from 211 Oe at 14K. (c) B z (x) profile for virgin run and (d) for reverse run. The B z (x) profiles show exactly similar behavior as in fig. 2 (a & b) in our MS. Note that there is no straight line like features on the images. run and figure (b) is at 0 Oe when the field is decreased to zero (reverse run) from 211 Oe. In the MO images in fig. (a) & (b), it is clear that there are no light gray parallel lines
running across the images as was observed in fig. 1(h) in the manuscript both outside and inside the sample. The present study confirms the light gray lines running across the image correspond to defects in the magneto-optical indicator film. The behavior seen in fig. (b) is identical to that shown in fig.1(h) of our manuscript, viz., within the Meissner region of the sample the contrast enhances as the field is reduced to zero (see the region encircled by dashed orange circle in fig. (b)). The B z (x) profiles for virgin and reverse run are shown in fig. (c) and fig. (d) respectively. The profile is calculated along the orange lines shown on the images which goes through the Meissner like region marked by dashed orange circle in fig. (b). The profiles show exactly similar qualitative behavior as shown in fig. 2(a & b) in our manuscript, viz., we can clearly identify an anomalous Meissner region of ~35µm width (marked by downward arrows in fig. (c) and (d)). In fig. (c), we find that the local B increases up to 92 G without prior appearance of any gradient while the external field is being increased to 211 Oe in virgin run. Upon reducing the field to zero, that particular Meissner like region gives a remanence of 32 G. Note, we find, larger the field from where the magnetization is reversed, the larger is the remnant field. Differential magneto-optical (DMO) imaging of the Meissner like region of the sample Here we present evidence in support of our claim that there is no channel of conventional flux penetration inside the so called Meissner like region in our sample. Had there been flux penetration into the Meissner like region of the sample, then in response to an external field modulation, there should be a change in the contrast inside the Meissner like region of the sample. In figure below, we show a differential magneto-optical image δi (captured at 90 Oe), which is obtained by modulating the applied magnetic field by 1 Oe, viz., we obtain the differential image δi shown below by capturing a magneto-optical image at 91 Oe and subtracting from it another one taken at 90 Oe, viz., δi = I (91 Oe) I(90 Oe) at 14 K. Note in the region of the sample outside the yellow encircle where magnetic flux has penetrated the sample, the differential intensity changes in response to the external field modulation = 1 Oe. Infact the change in gray scale intensity inside the sample where the magnetic flux has penetrated is comparable to the gray scale intensity change occurring outside the sample in the magneto-optical indicator film due to the 1 Oe modulation in the applied magnetic field. However, note that the contrast inside the Meissner region of the sample, viz., region of the sample inside the yellow dashed circle, there is no change in contrast in response to the external magnetic field modulation. Therefore this region is a Meissner like region of the sample which strongly shields the magnetic field, and there is no conventional flux penetration in this region. We have confirmed this behavior across different field and temperature regimes. Infact we have also now confirmed this in other batches of our samples with the same doping concentration.
14 K 90 Oe Differential MO image at 14K, 90 Oe ( 90 Oe is the maximum field we went upto in the virgin run in fig. 1 in our MS). No contrast variation is observed in response to 1 Oe external field modulation inside the Meissner like region (encircled by yellow dashed circle).
Temperature dependent MOI at 100 Oe (H c-axis of CaFe 1.94 Co 0.06 As 2 single crystal) peak positive Bz H In the movie (see the movie link, also the movie can be downloaded from http://home.iitk.ac.in/~satyajit/cafecoas2/movie/movie.pdf), notice color will appear at the location, marked by a blue rectangle shown in the above picture of the sample. Prior to the appearance of color, this region has a diamagnetic ( Bz < H ) magnetization response which decreases with increasing temperature due to flux penetration. Appearance of color in the above region corresponds to magnetization response becoming paramagnetic ( Bz > H ). The color variation in the movie from yellow to red corresponds to different positive magnetization values as shown in the above Bz H ( T) graph (cf. text for details).
Section V Zero field specific heat measurement of CaFe 1.94 Co 0.06 As 2 In specific heat measurements, in order to identify features associated with ordering in the electronic state or magnetic ordering, it is important to be able to subtract out the phonon contribution to the specific heat. To identify the phonon contribution to specific heat at different T, one needs to apply magnetic fields which are larger than the upper critical field (H c2 ) of the superconductor so as to suppress the superconducting order parameter. In pnictides due to their large H c2, it is difficult to apply large magnetic fields > H c2. However we have investigated the phonon contribution to the specific heat in the following way. In our zero field specific heat (C) measurement above 20 K, we find a linear behavior in C/T vs T 2 plot, implying phonon contribution to the specific heat. We fit the C/T vs. T 2 data above 20 K to a form C/T = βt 2, where β = 0.28 ± 0.02 mj/k 3 -mole. We determine the phononoic contribution to specific heat down to 2K using the above expression C ph = βt 3 and the parameter β determined from fitting. We subtract C ph from C which has been experimentally determined to obtain (C-C ph )/T vs. T 2 which is shown in fig. (a). Note that below 20K (i.e., below the superconducting T c of the sample) the specific heat behavior deviates from T 3 nature. Below 20 K the variation in the specific heat behavior is slower than T 3. In fig. (b), to investigate the behavior of C well below T c we plot log C vs. T -1 and C vs. T on log-log scale respectively. Recent studies on pnictide compounds have shown the absence of a jump in specific heat [1,2] at the bulk superconducting transition, especially away from the optimally doped regime. (C- C ph ) /T (mj/k 2 -mole) 0-50 -100 20K 0 300 600 900 1200 T 2 (K 2 ) phonon dominated (a) 1.6 ± 0.2 However, the fig.(b) shows that the specific heat in this compound measured below 8 K down to 2 K has a C α exp(- /K B T) behavior, where Δ is the bulk superconducting gap suggesting evidence for bulk superconductivity in our sample. On approaching T c from below it, fig.(a) shows the deviation of the behavior of C(T) from the phonon dominated behavior. To show that C(T) varies slower than T 3, we plot log C vs. log T in fig.(c). It is interesting to note that in fig.(c) for T > 8 K (which is the regime where we have reported
our magneto - optical imaging results in the present paper), the specific heat behavior in the vicinity of T c fits to an unusual form C T α where α = 1.6 ± 0.2 instead of 3 which is observed above 20 K (fig.(a). In recent times there is emerging evidence that strong interband scattering (possibly mediated by magnetic correlations) in pnictides may lead to a sublinear temperature dependence of the superfluid density [3]. In our magnetooptical measurements, we have suggested the presence of enhanced magnetic correlations at T close to T c. We speculate that the presence of magnetic correlations near T c may produce the observed changes in the behavior of C above 10 K, and these may also be responsible for suppressing the jump in C near T c [1,2]. [1] Neeraj Kumar et al., Phys. Rev. B, 79 (2009) 012504; Marcin Matsiak, Zbigniew Bukowski and Janusz Karpinski, Phys. Rev. B, 81 (2010) 020510(R). [2] Bud ko Sergey L., Ni Ni, and Canfield Paul C. Phys. Rev. B 79 (2009) 220516(R); Hafiez M. Abdel et al. (2011) arxiv:1109.3135v1. [3] Vorontsov A. B., Vavilov M. G., and Chubukov A. V., Phys. Rev. B, 79 (2009) 140507(R).