Control of the Spin State of a Light Atomby Changing the Density of Surrounding
Conduction Electrons

In fact, S is found to exhibit a universal behavior inaccordance with “the mean-field theory” or inproportion to (rs-rsc) for rs near rsc.

Takada GroupInterests in spintronics are on the rise from bothscientific and technological points of view. Since
devices in spintronics involve active control andmanipulation of spin degrees of freedom in solid-statesystems, it is absolutely necessary to have a deeper
understanding of fundamental interactions between
electron spins and its solid-state environments. Inview of this situation, we are interested in a composite
system of an atom immersed into the otherwise
homogeneous electron gas (EG).
In an isolated atom, the ground state obeys theHund’s multiplicity rule that requires the highest spin
configuration compatible with the Pauli’s exclusion
principle. Physically this rule is interpreted as theconsequence of an effectively larger nuclear charge ina higher spin configuration due essentially to theexchange effect.
Similarly in a uniform EG, the same effect favors
spin polarization, bringing about the spontaneous
spin-symmetry breaking or the spin-density-wave
state which was proven to be the ground state atarbitrary electron densities within the Hartree-Fock(exchange only) approximation. The correlation effect,
however, acts in the opposite direction and this effectis so strong in an EG as to lead eventually to theparamagnetic ground state for the majority of metals.
We have studied the ground state of the composite
system (or pseudoatom) in the spin-density functional
theory [1] and found several intriguing features suchas (i) sharp transition from a spin-neutral state to aspin-polarized one with the decrease of the electron
density of the EG, if the immersed atom is either B, C,N, or O; (ii) smooth evolution from the spin-polarizedstate of the pseudoatom to that of the negative ion of
the corresponding isolated atom with the further
decrease of the density; (iii) formation of the spherical
combined spin density/charge density wave, whichslowly decays with the distance from theimmersed-atom site; and (iv) significant shrinkage ofthe size of the spin-polarized pseudoatom as comparedwith its spin-neutral counterpart.
In order to elaborate the first two points, we show
the calculated total spin S of the ground-state
pseudoatom as a function of rs (the conventionalparameter characterizing the electron density of theenveloping EG) in Fig. 1, which clearly indicates aspontaneous magnetization of the pseudoatom for rs
larger than some threshold value rsc. The net electronic
spin S depends on both rs and the atomic number of
the atom Z. This finds itself in contrast with the result
for the net electronic charge around of the atom,which is uniquely determined by Z due to the fullscreening of a charge in the EG.
The steep fall in S near the critical point in Fig.1 issuggestive of a “phase transition” of the second order.

Fig. 1. Calculated total spin of the pseudoatom versus the EG
density parameter rs. Solid curves are the fittings of the datawith the universal (rs-rsc)0.5 relation.

Generally, the obtained S is not a multiple of 1/2.
This fundamental difference between an isolated atomand this pseudoatom is brought about by thecontribution of an infinite number of delocalized
electrons in the latter, implying a complicatedmany-body nature in this atom-EG composite system.
The trend in S at low densities (large rs) has a clear
qualitative interpretation: Because of the positiveelectron affinity (EA) of the B, C, and O isolated
atoms (0.010, 0.046, and 0.054 a.u., respectively),
each atom immersed into the EG in the limit of zerodensity should be reduced into a negative ion (NI) of
the corresponding atom. According to the Hund’s rule,
the population of the 2p orbitals is with 2 electrons
with spin up (3P), 3 electrons with spin up (4S), and 3
electrons with spin up and 2 electrons with spin down
(2P) for B , C , and O ions, respectively,corresponding to the total spin of 1, 3/2, and 1/2,respectively, which is clearly satisfied in Fig. 1 atlarge rs. On the other hand, the NI of the N atom is
unstable although long living (EA= 0.003 a.u.), andthe slow growth of S of this pseudoatom between 1
and 3/2 at large rs can be understood as thecompetition between the NI 3P and atomic 4S states.
Our model might be too primitive to discuss actualsystems, but because of the sharpness of the transitionin Fig. 1, we may suggest a novel method of spin
manipulation by changing the carrier density in asystem across the threshold. For example, we may
think of an impurity atom in an appropriate
semiconductor host, where the carrier density in thesemiconductor will be altered by either applying thegate voltage in the FET (field-effect transistor)
structure or optical pumping.
References[1] V. U. Nazarov, C. S. Kim, and Y. Takada, Phys.
Rev. B 72, 233205:1-4 (2005).
Authors
V. U. Nazarov,a C. S. Kim,a and Y. Takada
aChonnam National University