1. Search for nuclear quadrupole resonance in an organic quantum magnet
Allen R. Majewski
Department of Physics, University of Florida
November 11, 2015

2. Theory of the nuclear quadrupole resonance
The electrostatic energy of a charge in fields written in terms of multipole moments.
The last term in the energy is the quadrupole moment’s interaction with the electric field gradient .
The traceless quadrupole moment tensor is the familiar expression.

3. Electric field gradient (EFG) Vij
Quadrupole interaction energy with field.
Laplace’s equation -> EFG is traceless.
Choice of axes permit ordering eigenvalues of EFG by convention
Cylindrical symmetry –> only one non-vanishing quadrupole moment

4. Only two independent parameters
Assymetry parameter
Cq = e2qQ is the “quadrupole coupling constant.” q is a measure of our ignorance.

5. NQR transition frequencies
Hamiltonian for quadrupole interaction of nucleus with external field
…matrix elements…
energy levels

6. NQR transition frequencies
NQR frequencies

7. Spin 1 transition frequencies (14N)
For non-axial field gradients, nitrogen has two principle transition frequencies and a third low frequency transition being the difference

8. Spin 3/2 transition frequencies (35Cl)
For non-axial field gradients, chlorine has two transition frequencies

9. 14N NQR is a chemical fingerprint for explosives and narcotics
The NQR frequency of a given nucleus is compound specific => NQR is a chemical fingerprint with at least 5 digit accuracy
NQR spectra for 14N usually contained 0 < f < 6 MHz
Land Mine Detection - As of 29 July 2014, there were square kilometers (226.7 square miles) of Croatian territory suspected to contain land mines. These areas are located in 11 counties and 82 cities and municipalities.
TSA – obvious reasons
DEA – MDMA, methamphetamine, heroine all have known NQR spectra

10. NQR for interesting solid state physics
NQR is extremely sensitive to electronic environment and atomic positions
NQR can characterize
Structural phase transitions (by the T-dependence of NQR frequencies)
Molecular motions in solids
Internal field geometry, bonding characteristics
Condensed matter: order/disorder properties, ferroelectric properties, affects of doping -> magnonetic transitions of quasiparticles (AFM ordering, BEC, bose glass)

11. Motivation – Bose Glass in NiCl2-[SC(NH2)2]4 (DTN)

12. Superheterodyne Spectrometer

13. Hetero means “other”
Example: A radio station is transmitting on 300 kHz and the oscillating receiver was set to 400 kHz, the station would be heard not only at the original 300 kHz, but also at 100 kHz and 700 kHz.

14. Pulse Generator – overview

15. Pulse generator - details

16. Probe section http://www.phys.ufl.edu/~majewski/superhetdetails.zip

17. Impedance matching

18. Impedance matching – circuit A

19. isolation – hybrid tee

20. Isolation – quarter waves

21. RF amplifier stage – miteq fast recovery

22. Receiver section

23. Generator and receiver – side by side

24. IF (audio) amplifier stage – LM386

25. Labview controller - YB

26. Coil – large L

27. Probe section

28. DAQ – by YB
NaClO3 response to a transient at MHz, pulse width=50us, signal averaging N=1000;
Data:
Plotter scripts:
Fourier transform (left) of discrete FID (above). res =7204 pixels; horizontal_axis=100us/div

29. BEC magnet Phase diagram – DTN @ T < 1.2K

30. Cap and coil selection

31. Use of density functional theory in NQR
NiCl2 - [SC(NH2)2]4
dichloro-tetrakis-thiourea-nickel

32. Original Plan – 35Cl in DTN
Chlorine NQR typically at 25 – 42 MHz
But with cubic symmetry, Cq = 0 -> no NQR
With some symmetry, NQR much lower

33. Only two independent parameters
Assymetry parameter
Cq or quadrupole coupling constant ~ eq

34. Can we calculate the quadrupole coupling constant?
Not really
Density functional theory is possibility
WEIN2k, CASTEP, Quantum Espresso
Frozen core, pseudopotentials

35. Timeline
In summer 2013, Tim Green (Oxford) used CASTEP to calculate EFG in DTN
In fall 2013, I traveled to ETH to use Quantum Espresso to replicate calc
Both predicted chlorine resonance below 10 MHz due to symmetry

36. See Handout for data summary
Evidence for accuracy of DFT simulation:
CASTEP correctly predicted NQR in Sodium Chlorate as a control
CASTEP and QE predicted 14N NQR in DTN similar to that of known values for thiourea!!
CASTEP and QE widely agree, despite being completely independent software packages
with-CASTEP-and-QE-software.pdf

37. External http://www.phys.ufl.edu/~majewski/nqr/equation.pdf
DTN-using-GIPAW-with-CASTEP-and-QE-software.pdf