Chapter 5: Intrinsic Defect Induced Room Temperature
5.9. Origin of ferromagnetism
visible P L intensities in A 50 0 V (2555.2 arb. unit) and precursor TiO 2 powder (28 40 .2 arb.
unit) are comparable. Thus, concentration of defects such as oxygen vacancies alone does not decide the magnitude of magnetic moment. O ur results suggest that the defect environment (i.e., the distribution of point defects and formation of F+ and Ti3+ defects and their interactions) and the surface morphology of the N R bs, in particular the nanopores and nanobrick lik e structures, are critical ingredients for the buildup of measurable ferromagnetic interaction.
N ote that the relatively weak ferromagnetic hysteresis loops for the samples A 50 0 , A 7 0 0 , A 9 0 0 observed at low magnetic field may be due to oxygen vacancies and the linear M -H behavior observed at high field without any saturation magnetic moment up to 12 k O e may be due to the conduction band electrons.50 W hen the oxygen content of the unit cell is decreased, ferromagnetism is dominant. Interestingly, we notice a clear hysteresis loop with enhanced magnetic properties in terms of M s, M r and Hc in the vacuum annealed sample owing to increased oxygen vacancy concentration that may increase the B M P density. This seems to support the percolation model of B M P developed by K aminsk i and D as S arma and Coey et al.56 , 58 O ur systematic study shows that the oxygen vacancy defect constituted B M P is one of the most promising candidates to manifest the R TFM in this system. W ithin the B M P model, the greater density of the oxygen vacancy helps to produce more B M P which yields a greater overall volume occupied by B M P , leading to an overlap of B M P s and enhancing ferromagnetic behavior. This evolution is observed in our case, enhancing the ferromagnetic nature in the post-growth vacuum annealed sample indicating that a large density of defects overcomes the percolation threshold and establishes a long-range magnetic ordering.
For a more quantitative understanding about the suitability of the B M P model and its relationship to the oxygen vacancy concentration as revealed from P L analyses, we attempted to fit the observed M v ers u s H data to the B M P model by following M cCabe et al.59 A ccording to the B M P model, the measured magnetiz ation can be fitted to the relation
*+*,-./ 01 2 (5.5)
where the first term is from B M P contribution and the second term is due to paramagnetic matrix contribution. Here, * + 345, 3 is the number of B M P involved (per gram) and 45 is the effective spontaneous moment per B M P . ,-./ + 6789-./ : ;<. is the Langevin
function with . + 4=>>1 <?@ , where 4=>> is the true spontaneous moment per B M P , and at higher temperature it can be approximated to 45+ 4=>>. W e have analyz ed the M – H curve by using eqn (5.5). The parameters *, 4=>>, and 0 are free variable in the fitting process. The experimental data along with the fitted data are shown in F ig . 5.1 0 for the samples D 9 0 0 and G 50 0 . W e notice that the fitted data closely follows the experimental data and the fitted parameters are tabulated in T a b le 5.1. The total B M P magnetiz ation * values are found to be in the order of 0 .0 48 – 0 .19 emu g-1. The paramagnetic susceptibility 0 is found to be of the order of 10-6 cgs unit and its value marginally changes with different growth conditions. The spontaneous moment per B M P , 4=>> is found to be in the order of 10-17 emu. B y assuming 45 + 4=>>, we have estimated the concentration of B M P , which was found to be in the order of 1016 cm-3 (see T a b le 5.1). N ote that B M P concentration is highest in A 50 0 V , followed by D 9 0 0 , D 50 0 and G 50 0 . Interestingly, we found a strik ingly linear correlation between the B M P concentration and the integrated P L intensity due to oxygen vacancies, as shown in F ig . 5.1 0 ( c ). The symbols are for calculated B M P density from the fitting of experimental data and the solid line is a linear fit to the experimental data.
It implies a one to one correlation of the B M P density with oxygen vacancy concentration.
D espite the fact that quantitative estimation of defects is rarely possible from the P L intensity comparison due to possible presence of nonradiative channels, our observed correlation is remark able. This is the first time such a linear relation has been found between the densities of B M P and oxygen vacancies. This provides a more conclusive evidence that observed R TFM is directly induced by oxygen vacancies.
R ecently, in A g doped Z nO system, He et al.6 0 fitted the experimental M – T curve with the B M P model and the concentration of B M P was found to be of the similar order (~ 1015cm-3). However, the reported TC was relatively higher (9 9 5 K ), though the feature of the M -T curve was identical to our observation. S ince the polarons we have described in this system are bound to oxygen vacancies, the term bound magnetic polaron is justified.
Interestingly, the B M P remains localiz ed over a wide temperature range, presumably due to strong localiz ation provided by the defect site and stability of these defects. N ote that the as- prepared samples have undergone high temperature calcination that indicates high thermal stability of the oxygen vacancies and a large concentration of oxygen vacancies may aid to form even small clusters of vacancies that can provide higher localiz ation of the charges
nvolved in the exchange interaction. However, more studies are required to pinpoint the exact mechanism of high temperature FM . N evertheless, besides the established applications of TiO 2 nanostructures, these results open up the possibility of defect engineered TiO 2
nanostructures as potential platform for future spintronic and magneto-optic devices.
F ig . 5.1 0 .Initial portion of the M – H curve fitted with B M P model (eqn (5.5)) for samples (a) D 9 0 0 and (b) G 50 0 . S ymbols are for experimental data and the solid line is a fit with the B M P model.
E xtracted parameters are listed in T a b le 5.1. (c) Integrated P L intensity versus calculated B M P density showing a nearly linear behavior.