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

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.

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

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

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

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

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

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

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 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 – obvious reasons DEA – MDMA, methamphetamine, heroine all have known NQR spectra

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)

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

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

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.

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

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

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

Impedance matching

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

isolation – hybrid tee

Isolation – quarter waves

RF amplifier stage – miteq fast recovery

Receiver section

Generator and receiver – side by side

IF (audio) amplifier stage – LM386

Labview controller - YB

Coil – large L

Probe section

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

BEC magnet Phase diagram – DTN @ T < 1.2K http://www.nature.com/nature/journal/v489/n7416/pdf/nature11406.pdf

Cap and coil selection

Use of density functional theory in NQR NiCl2 - [SC(NH2)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

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

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

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

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

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 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

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/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