• Journal of Magnetics
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• 제16권2호
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• pp.108-113
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• 2011

The electron spin resonance lineshape (ESRLS) function for the electron spin resonance linewidth (ESRLW) of $Cr^{3+}$ (S = 3/2) in ferroelectric lithium niobate single crystals doped with 0.05 wt% of Cr, is obtained by using the projection operator technique (POT), developed by Argyres and Sigel. The ESRLS function is calculated to be axially symmetric about the c - axis and analyzed by using the spin Hamiltonian $H_{SP}={\mu}_B(B{\cdot}{^\leftrightarrow_{g}}{\cdot}S)+S{\cdot}{^\leftrightarrow_{D}}{\cdot}S$ with the parameters g = 1.972 and D = $0.395\;cm^{-1}$. In the ca plane, the linewidths show a strong angular dependence, whereas in the ab plane, they are independent of the angle. This result implies that the resonance center has an axial symmetry along the c - axis. Further, from the temperature dependence of the linewidths that is shown, it can be seen that the linewidths increase as the temperature increases, at a frequency of v = 9.27GHz. This result implies that the scattering effect increases with increasing temperature. Thus, the POT is considered to be more convenient to explain the scattering mechanism as in the case of other optical resonant systems.

• 한국자기공명학회논문지
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• 제19권1호
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• pp.11-17
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• 2015

The Kubo formalism and utilizing the projection operator technique (POT) introduced by Kawabata, the electron spin resonance (ESR) line-shape formula for carbon nanotubes through the hyperfine interaction introduced earlier in terms of POT. We can see that the line-width decreases exponentially as the temperature increases. The spin relaxation time show gradual decrease as magnetic field becomes larger. The analysis reveals the peculiarities in spin relaxation inherent to one dimensional system at low temperature and weak magnetic fields. Thus, the present technique is considered to be more convenient to explain the carbon nanotubes as in the case of other optical transitions.

• 한국자기공명학회논문지
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• 제16권1호
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• pp.11-21
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• 2012

The line-width of carbon nanotubes (CNTs) was studied as a function of the temperature at a frequency of 9.49 GHz in the presence of external electromagnetic radiation. The relative frequency dependence of the absorption power is obtained with the projection operator technique (POT) proposed by Kawabata. The line-width increased as the temperature increased in the high-temperature region (T>200 K). The scattering is little affected in the low-temperature region (T<200 K) because there is no correlation between the resonance field and the Fermi-Dirac distribution function. Thus, the present technique is considered to be more convenient to explain the resonant system as in the case of other optical transition problems.