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

2. Nuclear Quadrupole Resonance (NQR) as an emerging technique

3. NATO – interest in NQR NATO Science for Peace and Security Series publishes annual “Magnetic Resonance Detection of Explosives and Illicit Materials” bulletin “Magnetic Resonance Detection of Explosives and Illicit Materials” bulletin NQR employs non-invasive radio frequency methods Can penetrate luggage Is chemically specific Challenge: low sensitivity – signal to noise ratio limits practical application 2014 edition: 14 studies, 168 pages … excerpt 1excerpt 1

4. 14N NQR is a chemical fingerprint for explosives and narcotics The NQR signal unambiguously identifies a molecular structure Land Mine Detection - As of 29 July 2014, there were 587.2 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 – airport scanner DEA – MDMA, methamphetamine, heroine all have known NQR spectra

5. NQR for interesting solid state physics (non-terrorist related) 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)

6. my objectives

7. NQR – the technique Increase the SNR for NQR in general, especially in the low frequency regime (< 5 MHz where 14N NQR is typically found) Improve the feasibility of locating an unknown NQR in a new material Catalog undiscovered NQR frequencies in to reveal new physics in certain organometallic systems with quantum behavior Further existing, perhaps incomplete NQR studies using techniques developed (there are many) Investigate 35Cl/14N cross polarization as a means of explosives detection (uncharted territory)

8. first things first …

9. Theory of the nuclear quadrupole resonance

10. 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.

11. Electric field gradient (EFG) V ij 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

12. Only two independent parameters Assymetry parameter Cq = e 2 qQ is the “quadrupole coupling constant.” q is a measure of our ignorance.

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

14. NQR transition frequencies NQR frequencies http://www.phys.ufl.edu/~majewski/ nqr/equation.pdf

15. 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

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

17. Motivation – Bose Glass in NiCl 2 -[SC(NH 2 ) 2 ] 4 (DTN)

18. Superheterodyne Spectrometer http://www.phys.ufl.edu/ ~majewski/nqr/nqr- combined.pdf

19. 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.

20. Pulse Generator – overview http://www.phys.ufl.edu/~majewski/ nqr/superhetdetails.zip

21. Pulse generat or - details http://www.phys.ufl. edu/~majewski/nqr/ superhetdetails.zip

22. Probe section http://www.phys.ufl.edu/~majewski/superhetdetails.zip http://www.phys.ufl.edu/~majewski/nqr/nqr-combined.pdf http://www.github.com/Altoidnerd/nmr-tank-circuits

23. Impedance matching

24. Impedance matching – circuit A http://www.phys.ufl.edu/~majewski/nqr/nqr-combined.pdf http://www.github.com/Altoidnerd/nmr-tank-circuits

25. isolation – hybrid tee

26. Isolation – quarter waves

27. RF amplifier stage – miteq fast recovery

28. Receiver section

29. Generator and receiver – side by side

30. IF (audio) amplifier stage – LM386

31. Labview controller - YB

32. Coil – large L

33. Probe section

34. DAQ – by YB NaClO3 response to a transient at 29.963 MHz, pulse width=50us, signal averaging N=1000; Fourier transform (left) of discrete FID (above). res =7204 pixels; horizontal_axis=100us/div Data: http://www.phys.ufl.edu/~majewski/ nqr/tek http://www.phys.ufl.edu/~majewski/ nqr/tek Plotter scripts: http://www.phys.ufl.edu/~majewski/ nqr/scripts

35. Phase diagram – DTN @ T < 1.2K BEC magnet http://www.nature.com/nature/ journal/v489/n7416/pdf/nature 11406.pdf

36. Cap and coil selection

37. Use of density functional theory in NQR NiCl 2 - [SC(NH 2 ) 2 ] 4 dichloro-tetrakis-thiourea-nickel http://www.phys.ufl.edu/~majewski/nqr/Calculations-of-the-EFG-tensor-in-DTN-using-GIPAW-with-CASTEP-and-QE- software.pdf

38. 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

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

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

41. 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 http://www.phys.ufl.edu/~majewski/nqr/Calculations-of-the-EFG-tensor-in-DTN-using-GIPAW-with- CASTEP-and-QE-software.pdf

42. See Handout for data summary Evidence for accuracy of DFT simulation: 1)CASTEP correctly predicted NQR in Sodium Chlorate as a control 2)CASTEP and QE predicted 14N NQR in DTN similar to that of known values for thiourea!! 3)CASTEP and QE widely agree, despite being completely independent software packages http://www.phys.ufl.edu/nqr/dft-data-summary-short.pdf http://www.phys.ufl.edu/nqr/dft-data-summary-long.pdf http://www.phys.ufl.edu/~majewski/nqr/Calculations-of-the-EFG-tensor-in-DTN-using-GIPAW- with-CASTEP-and-QE-software.pdf

43. External http://www.phys.ufl.edu/~majewski/nqr/equation.pdf http://www.phys.ufl.edu/~majewski/nqr/nqr-combined.pdf http://www.phys.ufl.edu/~majewski/nqr/Calculations-of-the-EFG-tensor-in- DTN-using-GIPAW-with-CASTEP-and-QE-software.pdf http://www.phys.ufl.edu/~majewski/nqr/Calculations-of-the-EFG-tensor-in- DTN-using-GIPAW-with-CASTEP-and-QE-software.pdf http://www.phys.ufl.edu/~majewski/nqr/tek http://www.phys.ufl.edu/~majewski/nqr/dft.pdf http://www.phys/ufl.edu/~majewski https://apps.ufl.edu/Citrix/XenAppEXT/auth/login.aspx http://www.nature.com/nature/journal/v489/n7416/pdf/nature11406.pdf https://www.github.com/Altoidnerd/nmr-tank-circuits http://www.phys.ufl.edu/~majewski/nqr/scripts