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Nuclear quadrupole
resonance studies of an
organic quantum magnet
NiCl2 - [SC(NH2)2]4
Allen R. Majewski
Department of Physics
University of Florida
February 2015
• The value of nuclear
quadrupole resonance
• DTN - motivation
(spin ordering)
• NQR technique
• The superhet and results
• Theory of EFG and quadrupole
coupling constant
• Search for DTN NQR
• DFT analysis - GIPAW
NQR is a chemical fingerprint
• The NQR frequency of a given nucleus is
compound specific => NQR is a chemical
• The NQR frequency has EXTREME temperature
dependence. It is an excellent thermometer.
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 :
Oil well logging by precise measurement of P, T …
Motivation – Bose
Glass in
NiCl2-[SC(NH2)2]4 (DTN)
Phase diagram – DTN @
T < 1.2K
Superheterodyne Spectrometer
Hetero means “other”
Example: A
radio station is
transmitting on
300 kHz and the
receiver was set
to 400 kHz, the
station would
be heard not
only at the
300 kHz, but
also at 100 kHz
and 700 kHz.
Pulse Generator –
- details
Probe section
Impedance matching
Impedance matching – circuit A
isolation – hybrid tee
Isolation – quarter waves
RF amplifier stage – miteq fast
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;
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)
Quadrupole interaction energy
with field.
Laplace’s equation -> EFG is
Nucleus has cylindrical symmetry
–> only one indep.endent nonvanishing 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
Hamiltonian for quadrupole interaction of
nucleus with external field
…matrix elements…
energy levels
NQR transition frequencies
NQR frequencies
Use of density functional
theory in NQR
NiCl2 - [SC(NH2)2]4
Allen R. Majewski
Department of Physics
University of Florida
February 2015
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
• Not really
• Density functional theory is possibility
• WEIN2k, CASTEP, Quantum Espresso
• Frozen core, pseudopotentials
• 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
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/