Nuclear quadrupole resonance studies of an organic quantum magnet Allen R. Majewski Department of Physics University of Florida February 2015 NiCl 2 - [SC(NH 2 ) 2 ] 4 dichloro-tetrakis-thiourea-nickel

Overview The value of nuclear quadrupole resonance spectroscopy 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 fingerprint 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 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 NiCl 2 -[SC(NH 2 ) 2 ] 4 (DTN)

Phase diagram – 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 generat or - 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 YB NaClO3 response to a transient at 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) V ij 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 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 Allen R. Majewski Department of Physics University of Florida February 2015 NiCl 2 - [SC(NH 2 ) 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 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

External Circuits/blob/master/matching-A-min Circuits/blob/master/matching-A-min tensor-in-DTN-using-GIPAW-with-CASTEP-and-QE-software.pdf tensor-in-DTN-using-GIPAW-with-CASTEP-and-QE-software.pdf