On the Ruderman-Kittel-Kasuya-Yosida interaction in graphene

The two dimensionality plus the linear band structure of graphene leads to new behavior of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which is the interaction between two magnetic moments mediated by the electrons of the host crystal. We study this interaction from linear response theory. There are two equivalent methods both of which may be used for the calculation of the susceptibility, one involving the integral over a product of two Green's functions and the second that involves the excitations between occupied and unoccupied states, which was followed in the original work of Ruderman and Kittel. Unlike the $J \propto (2k_FR)^{-2} \sin (2k_FR)$ behavior of an ordinary two-dimensional (2D) metal, $J$ in graphene falls off as $1/R^3$, shows the $1 + \cos ((\bm{K}-\bm{K'}).\bm{R})$-type of behavior, which contains an interference term between the two Dirac cones, and it oscillates for certain directions and not for others. Quite interestingly, irrespective of any oscillations, the RKKY interaction in graphene is always ferromagnetic for moments located on the same sublattice and antiferromagnetic for moments on the opposite sublattices, a result that follows from particle-hole symmetry.Comment: 12 pages, 5 figures, submitted to AIP Conference Proceeding

RKKY Interaction in Graphene from Lattice Green's Function

We study the exchange interaction $J$ between two magnetic impurities in graphene (the RKKY interaction) by directly computing the lattice Green's function for the tight-binding band structure for the honeycomb lattice. The method allows us to compute $J$ numerically for much larger distances than can be handled by finite-lattice calculations as well as for small distances. % avoids the use of a cutoff function often invoked in the literature to curtail the diverging contributions from the linear bands and yields results that are valid for all distances. In addition, we rederive the analytical long-distance behavior of $J$ for linearly dispersive bands and find corrections to the oscillatory factor that were previously missed in the literature. The main features of the RKKY interaction in graphene are that unlike the $J \propto (2k_FR)^{-2} \sin (2k_FR)$ behavior of an ordinary 2D metal in the long-distance limit, $J$ in graphene falls off as $1/R^3$, shows the $1 + \cos ((K-K').R)$-type oscillations with additional phase factors depending on the direction, and exhibits a ferromagnetic interaction for moments on the same sublattice and an antiferromagnetic interaction for moments on the opposite sublattices as required by particle-hole symmetry. The computed $J$ with the full band structure agrees with our analytical results in the long-distance limit including the oscillatory factors with the additional phases.Comment: 8 pages, 11 figure

Analytical Expression for the RKKY Interaction in Doped Graphene

We obtain an analytical expression for the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction $J$ in electron or hole doped graphene for linear Dirac bands. The results agree very well with the numerical calculations for the full tight-binding band structure in the regime where the linear band structure is valid. The analytical result, expressed in terms of the Meijer G-function, consists of a product of two oscillatory terms, one coming from the interference between the two Dirac cones and the second coming from the finite size of the Fermi surface. For large distances, the Meijer G-function behaves as a sinusoidal term, leading to the result $J \sim R^{-2} k_F \sin (2 k_F R) {1 + \cos[(K-K').R]}$ for moments located on the same sublattice. The $R^{-2}$ dependence, which is the same for the standard two-dimensional electron gas, is universal irrespective of the sublattice location and the distance direction of the two moments except when $k_F =0$ (undoped case), where it reverts to the $R^{-3}$ dependence. These results correct several inconsistencies found in the literature.Comment: 5 pages, 5 figure

Anatomy of neck configuration in fission decay

The anatomy of neck configuration in the fission decay of Uranium and Thorium isotopes is investigated in a microscopic study using Relativistic mean field theory. The study includes $^{236}U$ and $^{232}Th$ in the valley of stability and exotic neutron rich isotopes $^{250}U$, $^{256}U$, $^{260}U$, $^{240}Th$, $^{250}Th$, $^{256}Th$ likely to play important role in the r-process nucleosynthesis in stellar evolution. Following the static fission path, the neck configurations are generated and their composition in terms of the number of neutrons and protons are obtained showing the progressive rise in the neutron component with the increase of mass number. Strong correlation between the neutron multiplicity in the fission decay and the number of neutrons in the neck is seen. The maximum neutron-proton ratio is about 5 for $^{260}$U and $^{256}$Th suggestive of the break down of liquid-drop picture and inhibition of the fission decay in still heavier isotopes. Neck as precursor of a new mode of fission decay like multi-fragmentation fission may also be inferred from this study.Comment: 16 pages, 5 figures (Accepted

Saturation properties and incompressibility of nuclear matter: A consistent determination from nuclear masses

Starting with a two-body effective nucleon-nucleon interaction, it is shown that the infinite nuclear matter model of atomic nuclei is more appropriate than the conventional Bethe-Weizsacker like mass formulae to extract saturation properties of nuclear matter from nuclear masses. In particular, the saturation density thus obtained agrees with that of electron scattering data and the Hartree-Fock calculations. For the first time using nuclear mass formula, the radius constant $r_0$=1.138 fm and binding energy per nucleon $a_v$ = -16.11 MeV, corresponding to the infinite nuclear matter, are consistently obtained from the same source. An important offshoot of this study is the determination of nuclear matter incompressibility $K_{\infty}$ to be 288$\pm$ 28 MeV using the same source of nuclear masses as input.Comment: 14 latex pages, five figures available on request ( to appear in Phy. Rev. C

Photoinduced magnetism in the ferromagnetic semiconductors

We study the enhancement of the magnetic transition temperature $T_c$ due to incident light in ferromagnetic semiconductors such as EuS. The photoexcited carriers mediate an extra ferromagnetic interaction due to the coupling with the localized magnetic moments. The Hamiltonian consists of a Heisenberg model for the localized moments and an interaction term between the photoexcited carriers and the localized moments. The model predicts a small enhancement of the transition temperature in semi-quantitative agreement with the experiments.Comment: 5 pages, 5 figure