1. STUDY OF THE ZEEMAN EFFECT IN THE [17. 6]7. 5-X18
STUDY OF THE ZEEMAN EFFECT IN THE [17.6]7.5-X18.5 TRANSITION OF HOLMIUM MONOXIDE (HoO)
Colan Linton
University of New Brunswick, Canada
Hailing Wang and Timothy C. Steimle
Arizona State University, USA
Funding: DOE-BES and NSERC

2. Goals Determine magnetic g-factors of lanthanide monoxides
Use results to examine configurations, coupling cases and to test theory (Ligand Field Theory = LFT)
LFT model successfully predicts properties of LnO & LnX(X=F,Cl,Br).
LnO ground states predominantly Ln2+[4fNσ(6s6p)]O2-
Changed spelling for Lanthanide above periodic table
HoO →Ho2+(4f106s)O2- → Ω = 8.5

3. LFT Coupling in the Ω=8.5 Ground State
For f10s configuration: f10 ground state is 5I8
where Lf=6, Sf=2 and Jf=8
The s electron has l=0, s=0.5, j=0.5
Combining gives 2 states separated by exchange interaction
Total atomic Angular momentum Ja=7.5 or 8.5 Sf j
The ground state has Ja=8.5 Jf Ja Lf
Projection on axis gives Ω=8.5 Ground State Ω

4. Hyperfine Structure F = 5 - 12 Lowest level J=8.5
Ho has nuclear spin I = 7/2
Each rotational level has 8 hyperfine components
Ground state Ω = 8.5.
Lowest level J=8.5
F =

5. R Branch
8-7
7-6

6. F=6-5 Perpendicular Parallel ΔM = -1 +1 22 Transitions 11 Transitions-6 +6 -5 +5
ΔM =
22 Transitions
11 Transitions

7. M” = -2 +5
ΔM=+1
M” = -5 +2
ΔM=-1

8. Zeeman Analysis Results for R(8.5)
The Zeeman shifts (first-order perturbation theory H=-mB):
Results for R(8.5)
State J geff Correlation Matrix Std. dev.(MHz)
X (2)
[17.6] (3) MHz
Spelling for correlation and matrix. Don’t know what picture in middle represents. Also erased the geff= after the equation. Not sure what was meant there

9. Calc
Obs

10. Calc
M” = -6 +5
ΔM=-1
M” = -5 +6
ΔM=+1
Obs

11. P Branch

12. 75MHz

13. Calc(1st order) M’ M” +4 -4 +4 -4 +3 -5 +5 -3
Obs

14. Including terms off diagonal in F introduces asymmetry in Zeeman shifts
(Brown and Carrington p )
J′=7.5 F M -4 5 +4 -4 4 +4

15. Zeeman Analysis Final Results X18.5 8.5 11.04(2) 1.00
State J geff Correlation Matrix Std. dev.(MHz)
X (2)
[17.6] (2)
[17.6] (2)

16. Calc
Obs

17. For f10(5I8)s configuration
Magnetic g-factors of ground state (Jj coupling scheme):
For f10(5I8)s configuration
B = 3Jf(Jf+1)+Sf(Sf+1)-Lf(Lf+1) = 3x8x9+2x3-6x7 = 180
D=3j(j+1)+s(s+1)-l(l+1) = 3x0.5x x1.5-0 = 3.0
g(Lf,Sf,Jf: l,s,j: Ja,Ω) = g (6,2,8: 0,0.5,0.5: 8.5,8.5) = 11.00

18. Lowest f10 state, 5I8 (Lf=6,Sf=2,Jf=8)
Magnetic g-factors of ground state (LS coupling scheme):
Lowest f10 state, 5I8 (Lf=6,Sf=2,Jf=8) LS
Ho2+(4f106s)O2-
6I8.5 ground state +
s, (l=0,s=0.5,j=0.5)
Hund’s Case c
g(6,2.5,8.5,8.5)=11.00
Hund’s Case a
g(Λ,Σ,Ω) = (Λ Σ)
g(6,2.5,8.5)=11.01
Same result in LS or Jj scheme and same for case a and case c
Experiment
g = 11.04(2)

19. Upper State Ω=7.5 Possibly f10p configuration 4,6H, I, J States State
(LS)
Possibly f10p configuration
4,6H, I, J States
State
Case(a)
Case(c)
6H7.5
10.00
4I7.5
9.00
6I7.5
9.25
6I8.5
9.71
Observed g: 9.86 at J = 7.5, at J = 9.5

20. Conclusions Zeeman Effect has shown
1. The ground, X1(Ω=8.5) state of HoO originates from a single Ho2+(f10s)O2-(6I8.5) configuration as predicted by LFT.
2.The excited [17.6]7.5 state at J=9.5 appears to originate from a single 6H7.5 state whereas the J=7.5 level appears to show some configurational mixing.