Nuclear quadrupole resonance studies of an

organic quantum magnet

Allen R. Majewski

Department of Physics

University of Florida

February 2015

NiCl2 - [SC(NH2)2]4

dichloro-tetrakis-thiourea-nickel

Overview

• The value of nuclear quadrupole resonance spectroscopy

• DTN - motivation

(spin ordering)

• Technique NQR

• The superhet and results

• Theory of EFG and quadrupole coupling constant

• Search for DTN NQR

• DFT analysis - GIPAW

Motivation - industrial/civil use of NQR

Explosives (14N) 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.

Flight security :

Detection of explosives, 14N containing narcotics …

Oil industry :

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

Phase diagram – DTN @T < 1.2K

BEC magnet

Superheterodyne Spectrometer

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

Pulse generator - details

Probe section

Impedance matching

Impedance matching – circuit A

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 YBNaClO3 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

Cap and coil selection

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.

Nucleus has cylindrical symmetry –> only one indep.endent non-vanishing quadrupole moment

Choice of axes permit ordering eigenvalues of EFG by convention

Only two independent parameters

Assymetry parameter

Cq or quadrupole coupling constant ~ eq

NQR transition frequencies

NQR transition frequenciescase: (eta === 0) {

if (spin === half-int) {// symmetric & half-int}

else {// symmetric &int}};

case: (eta !== 0) { if (spin === half-int) {

// asymmetric & half-int}else {

// asymmetric & int}};

Use of density functional theory in NQR

Allen R. Majewski

Department of Physics

University of Florida

February 2015

NiCl2 - [SC(NH2)2]4

dichloro-tetrakis-thiourea-nickel

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

See Handout for data summary

• Evidence for accuracy of DFT simulation:1) CASTEP correctly predicted NQR in Sodium

Chlorate as a control2) 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

External

• https://github.com/Altoidnerd/NMR-Tank-Circuits/blob/master/matching-A-min

• https://apps.ufl.edu/Citrix/XenAppEXT/auth/login.aspx

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

• http://www.quantum-espresso.org/

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