Resonant enhancements for atomic specificity

Further to providing information about the dimensionality, the photon energy dependent spectral weight can provide information about the atomic character of the underlying states, through resonant enhancements of spec- tral weight. Conventional ultraviolet photoemission spectroscopy (UPS) ex- cites a system from a ground state (fig. 4.12ai) into a final state with a va- lence hole and a photoexcited valence electron (fig.4.12aii). If an electron is

84 Chapter 4. Spin-orbital texture of the giant Rashba system BiTeI 0.2 -0.2 k || (Å -1 ) 0.0 32 30 28 26 24 22

Photon energy (eV)

E_F

Min Max

Intensity (arb. units)

0(EF) 50 100 150 230 270 F E-E (meV): a c 30 28 26 24 Ground

state Intermediatestate

RPES final state UPS final state Excitation of core electron Excitation of valence electron Auger-like emission b i iii ii iv

FIGURE 4.12: a) Schematic of two paths (ai-aii or ai-aiii- aiv) to the same final state via conventional UPS or reso- nant enhancements through Auger-like processes. b) Photon energy dependent measurements of an MDC at the Fermi

level (±15meV) of BiTeI in the rangehv = 22−32eV us-

ing p-polarised light along theΓ¯-M¯-direction showing pro-

nounced spectral weight variation. c) Intensity of the peak indicated by the box as a function of photon energy (cor- responding to the outer band). The multiple traces show the binding energy dependent peaks in the spectral weight enhanced at the bismuth O-edge indicating a resonant en- hancement. The two peaks correspond to the splitting of the

Bi5dspin-orbit doublet. Cartoon adapted from [95].

photoemitted from the Fermi level, EB = 0, then the equation for the con-

servation of energy in the photoemission process (eq. 3.15) can be written asEk =hv−φ. Therefore the photoemitted electron at the Fermi level has

a continuously tuneable energy, providedhv > φ.

The photon energy can be tuned such that it coincides with the energy of a so-called absorption edge in the material, with an absorption threshold energy,E0. This is defined as the energy at which core holes can be created

within a particular electron shell (and so is closely related to the binding energy of that core shell). If the photon energy is tuned such that it coincides with the absorption threshold energy of a deeper lying core electron shell, a core electron can be excited to an unoccupied valence state, with energyEm

near the Fermi level (fig. 4.12aiii). In this case, the photon must supply an energyhv=E0+Em.

4.2. Giant Rashba splitting in the bulk 85

larger energy than states near the Fermi level). The system will then relax back to the ground state which it can do in a vast number ways involving inelastic scattering of the electron, or emission of a photon or electron. The relaxation process which is relevant for resonant photoemission is that in which the excited electron can decay back into the core hole directly, simul- taneously ejecting a valence electron in an Auger-like process (fig. 4.12aiii) [96]. This process leaves the system in a one-hole final state with an ejected valence electron, which is the same final state as with conventional UPS. The simultaneously emitted valence electron in this process receives the full energy of the excited electron in the relaxation back to the core hole. It there- fore has an energyEk=Em+E0−φ=hv−φ, identical to the direct photoe-

mission case. This process can result in a resonant enhancement of the pho- toemission intensity, through interference of these two final states (through direct and Auger-assisted photoemission). In particular, since this process involves bringing the photon energy into resonance with a core shell ab- sorption energy, this resonant enhancement depends on the atomic species, providing element specific resonant enhancements. We exploit this in our measurements to gain atomic specificity. First we will approach how this occurs.

Including the resonance process, the photoemission intensity can be writ- ten as a sum of the direct photoemission pathway, with additional terms corresponding to the resonant pathway [96]:

I(E) = 2πX f hΨf|Vr|Ψii+ X m hΨf|VA|ΨmihΨm|Vr|Ψii Ei−Em+iΓm/2 2 δ(Ef−Ei) (4.4)

where |Ψii, |Ψmi,|Ψfi are the initial, intermediate and final states respec-

tively with energiesEi,m,f.Vr denotes the radiative interaction, andVAde-

notes the Auger decay interaction strength. The lifetime of the core-excited state|Ψmiprovides a linewidthΓm.

Of these two pathways (the direct ionising pathway and the resonant Auger-assisted autoionising pathway), the direct pathway changes more slowly with photon energy than the resonant channel, which changes rapidly

86 Chapter 4. Spin-orbital texture of the giant Rashba system BiTeI

a b

FIGURE4.13: a) The Fano lineshape for various values of the

asymmetry parameter,q. b) Early photoemission measure-

ments showing a Fano resonance in nickel. (a) Reproduced

from [97], (b) reproduced from [98].

as the photon energy is tuned through the resonance. The contributions to the photoemission intensity from the amplitudes of the transition matrix el- ements (eq. 4.4) for the different pathways interfere with different phases above and below the resonant energy. This constructive and destructive interference gives a characteristic asymmetric lineshape for the resonant enhancement in intensity. Asymmetric lineshapes of this nature were de- scribed by Fano in 1961, having the form [97]:

I = (q+ε) 2

1 +ε2 (4.5)

where εis a reduced energy which is zero at the resonance energy, and q

is a factor governing the asymmetry, proportional to the ratio of transition probabilities resulting from the two pathways [96]. The largerq value, the greater the effect of the resonance, and the sign ofq indicates the phase of the resonance (i.e. being constructive or destructive, above or below the resonance energy) [99–101].

Figure4.13ashows calculated Fano lineshapes for various strength asym- metries given by the value ofq. Fano interference or resonant enhancements in intensity were first observed in photoemission for the metallic Ni(001)

4.2. Giant Rashba splitting in the bulk 87

6 4 2 0

Intensity (arb. units)

32 30 28 26 24 22

Photon energy (eV)

Intensity profile at: EF - 270 meV Total fit 5d (3/2) Peak 5d (5/2) Peak

FIGURE4.14: Example Fano fit to our resonant photoemis- sion measurements on BiTeI. The trace shown is the lowest binding energy intensity profile over the range given in fig-

ure4.12, for the negative k|| outer band. The two compo-

nents arise from the spin-orbit doublet from the Bi5dcore

level.

surface for a satellite peak in the photoemission spectra [98]. The intensity of this satellite feature as a function of photon energy was found to follow a Fano lineshape (fig. 4.13b) at photon energies corresponding to transitions from deeper lying3pstates to unoccupied near-Fermi level3dstates. In the case of the nickel surface, the two interfering pathways are:

3p63d94s+hv→3p53d104s (4.6)

3p53d104s↔3p63d84s+e− (4.7)

and

3p63d94s+hv→3p63d84s+e− (4.8)

where the first expression describes absorption of a photon producing the given intermediate state (eq. 4.6), and the second expression shows the Auger-assisted autoionisation process of an electron decaying back into the

3plevel and ejecting a3delectron (eq.4.7). The final state given by equation 4.7 can be produced also through direct UPS, given in the third expression (eq.4.8).

88 Chapter 4. Spin-orbital texture of the giant Rashba system BiTeI

asymmetric peaks in intensity as a function of photon energy. These features occur around energies corresponding to the bismuth O-edge, comparable with the binding energy of the Bi5dcore level. We can then attribute these features to be a resonant enhancement of the bismuth derived states at this energy. Considering only the bismuth states, the two relevant interfering pathways are arising from:

5d106p3+hv→5d96p4 (4.9)

5d96p4 ↔5d106p2+e− (4.10)

and

5d106p3+hv →5d106p2+e−. (4.11)

Further evidence for this is given by the fact that this effect increases approaching the band bottom, which is known to be more bismuth domi- nated, since there is less mixing of tellurium atomic character at the band bottom [70]. The extracted intensity profile has two peaks which are asso- ciated with the spin-orbit splitting of the 5dcore level, so themj = 5₂ peak

is less deeply bound than the mj = 3₂ peak. We can fit the two peaks to

Fano lineshapes and extract asymmetry parameters (shown for the deepest binding energy trace in figure4.14) and in the region corresponding to the resonant enhancement this reproduces the measured intensity profile rea- sonably well. The total fit is a summation of the two Fano lineshapes with a global intensity scaling factor (a constant scaling factor used for both peaks). The dip in intensity is potentially then a result of the destructive interference from the Fano-like resonance.

4.3. Probing the orbital texture 89