Thesis High-Resolution Photoemission Study of Kondo Insulators ...

42 Chapter 3. Photoemission Study of YbB12 with Variable Photon Energies
Appendix: Calculation of Magnetic Susceptibility
Here, we present the AIM calculation [3.26, 27] of magnetic susceptibility for the de-
generacy of Nf = 8, which corresponds to the 4f7/2 level in Yb compounds. First we
reproduced both the Kondo-peak position of ∼ 23 meV and the 4f-hole occupancy
of ∼ 0.86 by varying the bare f (f 13 → f 14 ) level (ε0 f ) measured from EF and the
hybridization strength ∆ as shown in Fig. 3.7 (a). Then we calculated the magnetic
susceptibility using the same parameters that were used for the calculation of the photoemission
spectrum in Fig. 3.7 (a). We have found that a maximum of the magnetic
susceptibility appears around ∼ 80 K in Fig. 3.7 (b). Therefore, we have reproduced
the peak position in the photoemission spectrum, the 4f-hole occupancy, and the maximum
in the magnetic susceptibility using a single set of parameters, confirming the
validity of the single-site Anderson model for YbB12.
Intensity (arb. units)
T = 10 K
PES
BIS
-0.15 -0.10 -0.05 0 0.05
Energy relative to E F (eV)
χ (T) / χ (0)
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
(a) (b)
4 6
10
2 4 6
100
T (K)
2 4 6
1000
Figure 3.7: Photoemission (PES) spectrum and inverse-photoemission (BIS) spectrum
(a) and magnetic susceptibility (b) calculated with the bare f level (ε0 f ) = 0.90 eV and
the hybridization strength ∆ = ρV 2 = 0.023 eV. A conduction band of 10 eV width
with a constant DOS was considered and thus the magnetic susceptibility holds an
enhanced Pauli paramagnetism at low temperature. Since the error increases at very
low temperature, we have calculated the photoemission spectra at 10 K to deal with
the Kondo-peak position.