Significant enhancement of magnetoresistance with the reduction of particle size in nanometer scale

The Physics of materials with large magnetoresistance (MR), defined as the percentage change of electrical resistance with the application of external magnetic field, has been an active field of research for quite some times. In addition to the fundamental interest, large MR has widespread application that includes the field of magnetic field sensor technology. New materials with large MR is interesting. However it is more appealing to vast scientific community if a method describe to achieve many fold enhancement of MR of already known materials. Our study on several manganite samples [La1−xCaxMnO3 (x = 0.52, 0.54, 0.55)] illustrates the method of significant enhancement of MR with the reduction of the particle size in nanometer scale. Our experimentally observed results are explained by considering model consisted of a charge ordered antiferromagnetic core and a shell having short range ferromagnetic correlation between the uncompensated surface spins in nanoscale regime. The ferromagnetic fractions obtained theoretically in the nanoparticles has been shown to be in the good agreement with the experimental results. The method of several orders of magnitude improvement of the magnetoresistive property will have enormous potential for magnetic field sensor technology.

1 Supplementary information 1.1 Section-1 According to the Scherrer's formula, the average particle size (d ) of nanocystalline compound is given by Here K ∼ 0.9 (constant) and λ = 1.54Å(wave length of x-ray). Effective full width at half maxima (FWHM), β is calculated using the relation Where 'B ' and 'b' are FWHM of a peak of the nanocrystalline sample at a particular angle of diffraction and FWHM of the corresponding peak of the bulk form of that sample (measured in the same instrument)

Section-2
According to the theoretical report on the phase separated (PS) chargeordered nanoparticle (Appl. Phys. Lett., 2007, 90, 082508), when a chargeordered core is wrapped by a FM shell, the energy (E P Snano ) can be expressed by the equation 3.
Where E CO and E F M represent the energy per unit volume of the CO and the FM part respectively. The total and core radii of the nanoparticle are represented by r and r c respectively. The parameter, J AF is the super exchange interaction. However the energy (E COnano ) of a spherical nanoparticle of pure chrageordered state can be represented by equation 4 The energy difference between the pure charge-ordered and phase-separated state is For a stable phase-separated state in nanoscale regime δE > 0. From the equation 6, for a stable FM shell requires Where A = J AF /(E F M -E CO ) is the variable parameter which is connected with the nearest neighbor super exchange interaction of Mn-ions (J AF ). The ferromagnetic volume fraction is calculated by the expression

Section-3
In our present study it was observed that the enhancement of the magnetoresistance is appears even at low magnetic field region with the reduction of the particle sizes in nanometer scale. The enlarged view of the external magnetic field dependent magnetoresistance in the lower magnetic field range for all the nanoparticles are given in Figure

Section-4
To determined the average particle sizes, the Transmission Electron Microscopy (TEM)study have been carried out. In addition to that, we have also done the Scanning Electron Microscopy (SEM) study for the nanocrystalline compounds. As a demonstrative representation the average particle size determination of the nanoparticle having average particle size 70 nm (LCMO-3 series) from the different studies is given below.
The TEM picture of the nanocrystalline compound (LCMO-3 series) along with the histogram of the particle size distribution is given in the Figure-2. From the particle size distribution histogram the average particle size found to 70 nm. Similar as TEM study, we have estimated the average particle size from the Scanning Electron Microscopy (SEM)study. The SEM image along with the particle size distribution curve of the same nanocrystalline compound is given in Figure- In addition to that, as mentioned in the Section-1 of the supplementary information part, the calculated average particle size from the x-ray diffraction data of the LCMO-3 series is found to ∼ 60 nm.
The crystallinity in nanoparticles may also influence the magneto-transport properties. In our present case, the High Resolution Transmission Electron Microscopy (HRTEM) image of nanoparticle (average particle size 70 nm) indicate the well crystalline nature. One representative HRTEM image is given in Figure-

Section-5
It is emphasized in different earlier studies that oxygen non-stoicheometry can influence the physical properties of the manganites. The electron conduction and magnetic interaction can be significantly modified due to the presence of oxygen vacancies. Such changes are usually manifested in transitions. In some cases, one characteristic transition can even be hindered due to this oxygen non-stoicheometry (J. Phys.: Condens. Matter, 24, 366004(2012)). In the present study, there is no significant change in charge ordering transition temperatures of nanoparticles in comparison with bulk. We have also performed the x-ray photoelectron spectroscopy (XPS) measurements on bulk and nanocrystalline compounds. As a representative example, we have included the XPS data of La 0.48 Ca 0.52 MnO 3 compound (bulk and one nanoparticle (∼ 65 nm))in  According to the chemical composition of the La 0.48 Ca 0.52 MnO 3 compound, the ratio of the Mn 4+ and Mn 3+ ion is 1.0833 (52/48 = 1.0833). Our experimental results of XPS measurements indicate that the ratio of Mn 4+ and Mn 3+ for bulk is 1.084 and for nanoparticle, it is 1.089. The experimental observed values are very close to above mentioned value (1.0833) for the La 0.48 Ca 0.52 MnO 3 compound. In this context it can be mentioned that the bulk and the nanoparticles were prepared using the same powder of LCMO, just by heating at different temperature and time duration as discussed in the manuscript. Hence it may assume that the variation of the particle size played the vital role behind the phenomena addressed in the manuscript.