The Defect Mediated Desorption Model

In the DMe model, localized surface defects are created from sputtering and desorption of surface atoms facilitated by the creation of self-trapped excitons (STEs) or self-trapped holes (STHs) in response to valence band electronic excitation [126128, 150]. STEs are electron-hole pairs bound by the coulomb

eld within their own lattice distortion eld. Electronic excitation of valence band electrons leading to sputtering has been observed mainly in insulators such as SiO2 and Alkali halides and can be induced by dierent means includ-ing high energy electron irradiation in which case the mechanism is known as electron stimulated desorption, ESD, by ultraviolet photons i.e. photon stimulated desorption, PSD [151153] and also by ion irradiation [129].

The interaction of HCIs with surfaces produces intense electronic excitation from above the surface and depending on the ion energy and surface properties also several monolayers beneath surface (see introduction to section 3.2.1). The electron emission associated with the transfer of potential energy upon SHCI impacts implies that corresponding holes are created in the valence band at or close to the Fermi edge (cold holes) and also deep in the valence band (hot holes) which subsequently trap electrons from the decaying HA and surround-ing atoms leadsurround-ing to the formation of electron-hole pairs (see Fig. 3.6). Defect creation is enhanced by collisional damage emerging the kinetic energy of the HCIs. In addition, high energy Auger electrons produced from decay of inner-shells can produce defects in the lattice in a similar manner to the case of ESD [129]. Therefore in contrast to ESD by energetic electrons, defects cre-ated in insulating materials by HCI impacts are more spatially conned and are of number density. STEs and STHs decay into dierent colour centres.

For alkali halides, decay of STEs and STHs results in the production of H (an interstitial molecular halide ion) and F (an electron at an anion site) cen-tres. Both centres diuse independently towards the surface and subsequently

Figure 3.6: Electronic transitions between surface and projectile HCI leading to formation of holes (via resonant neutralization) as well as electron-hole pairs (via Auger neutralization [103]

recombine with the surface. Recombination of an H centre with the surface results in the creation of a loosely bound halogen ad-atom which is desorbed via thermal evaporation. On the other hand, an F centre can recombine with the surface by neutralizing an alkali ion leading to its desorption. However, it has been shown [154] that the desorption process of a neutral alkali atom is energetically more feasible by recombination of 2p-excited F^∗ centre with the surface than with the F centre with low coordinated surface site e.g. terraces and edges being the preferential point for the desorption process.

In the case of HCIs, desorption and surface defect (pits) creation in KBr has been shown to be a consequence of a dense agglomeration of numerous F /F^∗

centres within a localized region of several nm³ which is proportional to the ion charged state and the ion uence [129]. However, in addition to the insulating property materials, within the DMe model, the enhancement of sputter yields with increasing charge state of the projectile HCI is only possible for materials with strong electron-phonon coupling which promotes localization of electronic excitation i.e. self-trapping and formation of STEs and/or STHs [103].

Magnetism and Magnetic Materials

The phenomenon of magnetism has been observed mainly in naturally occur-ring solid state materials for a few thousand years. However, it was only until the formulation and development of quantum mechanics that magnetism could be adequately described and understood particularly for temperatures above 0 K for which classical mechanical descriptions are inadequate. The behaviour of electrons, atoms, ions, molecules and their interactions gives fundamental insights into the theory of magnetism. Magnetism is in general a vast eld and for this reason, the present discussion is limited to topics relevant to the current investigation.

4.1 Atomic Magnetism

Consider an electron in orbit at radial distance r and angular velocity ω around an atomic nucleus of charge Z, e.g. as in the hydrogen atom. In Bohr's quantum theory, the orbital angular momentum Pl, is quantized in units of

¯

h (which is related to Planck's constant h by ¯h = h/2π) and is described

using the orbital angular momentum quantum number l such that Pl = ¯hl.

Therefore, the magnetic moment of the electron by orbital motion µl is given by [155]

where e, me are the charge and mass of the electron respectively. The Bohr magneton µB ≈ 9.274 × 10⁻²⁴ [J·T⁻¹]. In addition to the orbital angular momentum, the spin angular momentum contributes to the magnetic moment of an electron in orbit around an atomic nucleus and is described using the spin angular momentum quantum number s

µ_s= − µ₀e m_e



¯

hs = −2µBs (4.2)

where s= ±1/2. Therefore, the total magnetic moment by an electron in orbit around an atomic nucleus is given by [155]:

µ = µ_l+ µs = − (l + 2s) µB = −gjµB (4.3) where the total angular momentum j =l+s and the g is the g-factor where g=2 for l=0. In the case of hydrogen, the nuclear charge is Ze and in this case, the non-relativistic Hamiltonian operator H of an electron in orbit around the nucleus in the absence of external elds is given by:

H₀ = p²

2m_e − Ze²

r (4.4)

where the rst and second terms are the kinetic and potential energy terms respectively. The eigen states are labelled with the integer quantum numbers n, l and m such that

ψ_nlm(r, ϑ, ϕ) = R_nl(r) Y_l^m(ϑ, ϕ) (4.5) of the spherical symmetry of the system, it follows that ψnlm are eigenstates of the orbital angular momentum and its z-component:

L²ψ_nlm= l (l + 1) ¯h²ψ_nlm and L^zψ_nlm= m¯hψ_nlm (4.7)

(L is often dened to be dimensionless; then L²ψ_nlm = l (l + 1) ψ_nlm and L^zψ_nlm= mψ_nlm). The corresponding angular dependence is described by the spherical harmonics Y_l^m(ϑ, ϕ).

Most of the magnetic phenomena observed in solid state materials are strongly related to the magnetic behaviour of their constituent entities such as atoms, molecules, vacancies, crystal structure etc. For an atom with Z electrons, the Hamiltonian of the system is given by [155]

H₀ = with A being the magnetic vector potential which is chosen such that the magnetic eld is homogenous within the atom and the Coulomb gauge ∇·A = 0 is valid. In this situation, the magnetic vector potential can be written as A(r) = (A × r) /2. The corresponding kinetic energy amounts to:

E_kin = 1

2m(p + eA(r))² = 1

2m p²+ e (p · A + A · p) + e²A · A
(4.9) Due to the Coulomb gauge one obtains: p · A = A · p and as result, the Hamiltonian, Hⁱ of the i^th electron is given by [155]

Hⁱ = p²_i

2m + V_i+ e

mA · p + e²

2mA · A (4.10)

The last term can be written can be written as a function of the external magnetic eld The third term of the Hamiltonian can be written as

A · p = 1

2(B × r) · p = 1

2(r × p) · B = 1

2¯hL · B (4.12) where ¯hL is the quantized orbital angular momentum. Therefore the Hamil-tonian Hⁱ of the i^th electron can be expressed as

Hⁱ = p²_i

2m + V_i+ µ_BL · B + e²

8m(B × ri)² (4.13) where the term µBL·B gives rise to the Zeeman eect. The consideration of the electron spin angular momentum S results in an additional term µBgS · B with g ≈ 2 being the g-factor of an electron as before. Therefore the complete Hamiltonian is given by [155]

The part H1 represents the modication of the electronic system due to the external magnetic eld B and amounts to

H1 = µB(L + gS) · B + e²

The rst term H1^para is known as the paramagnetic term and the second term H1^dia is known as the diamagnetic term.