Search for Nuclear Quadrupole Resonance in an Organic Quantum Magnet
Allen Majewski
Department of Physics, University of Florida
2001 Museum Rd.
Gainesville, FL 32611
Contents:
1. Dichloro-tetrakis Thiourea Nickel (DTN)
2. Nuclear Quadrupole Resonance (NQR) Spectroscopy
3. The initial plan: locate 35Cl NQR in DTN
4. Conclusion: search space for unknown 35Cl NQR too large, experimentally infeasible
5. Reduction of Search Space Size
6. The GIPAW calculation
7. Outlook, road to graduation
Dichloro-tetrakis Thiourea Nickel (DTN)
• DTN is an organic metal complex and a quantum magnet
FIG: DTN Structure (xcrysden)
FIG: BE/BG phase space
• Magnonetic BE condensation at low T, high field, with bose glass state observed in disordered (Br-doped) DTN
• Detailed phase diagram for DTN across a wide temperature range and details of the nature of spin fluid phase transitions to be determined
Nuclear Quadrupole Resonance (NQR) Spectroscopy
NQR is like NMR, except
• No static B is applied
• NQR is only possible with quadrupolar nuclei (nuclear spin >= 1)
• Effect vanishes in fluids, and solids with high crystal symmetry
• Has poorer S/N (one cannot crank up frequency like in NMR)
• The experimenter cannot control or otherwise choose the resonance frequency, in contrast to NMR where
ω=γB
• NQR is a result of the interaction of
• the nuclear electric quadrupole moment of a nucleus with
• its electronic environment (a second order tensor)
• The NQR spectrum of a solid is a chemical fingerprint, unique to a sample
• NQR research is accelerating due to its proposed applications to explosives and narcotics detection (because a a single NQR line can identify a molecular structure exactly)
NQR details
• An NQR experiment is a direct observation of the electric field gradient (EFG) tensor at a nuclear site
• NQR results from the interaction of the nucleus with its electronic environment in a very precise manner (the electric quadrupole moment of the nucleus' interaction with the EFG
FIG: some equations
• An NQR experiment is a direct observation of the electric field gradient (EFG) tensor at a nuclear site
• NQR is extremely sensitive to atomic positions
• NQR is indicative of the nature of phase transitions in solids
FIG: Cq vs T in methyl ammonium manganese chloride, and pure thiourea, showing kinks
• NQR would be sensitive to the details of DTN's quantum critical behavior
The initial plan (2012-2013): try to find 35Cl NQR in DTN
• Standard samples: NaClO3, p-dichlorobenzene, having ~ 30 MHz, 34 MHz NQR frequency
• Signal in p-dichlorobenzene found at 34 MHz
• Signal in NaClO3 was heavily optimized, S/N improvement x 5 by:
• filters for transmit/receive (mostly crossed diodes!)
• GOOD amplifiers
• RF amplifiers → miteq
• IF amplifiers home built band-pass amplifiers
• quarter wave bridge
• reduction in lead length, fewer transmission lines/RF interconnects
• Tried to find NQR in DTN (REU student reported 30.18 MHz): No NQR found 28-33 MHz
• This took way too long
FIGS: Apparatus, tanks, amplifiers, NaClO3 data S/N improvements etc
Conclusion (late 2013): search space for unknown 35Cl NQR too large, experimentally infeasible
The point-to-point method
1) choose test frequency f
2) tune and match the probe to f
3) adjust any spectrometer parameters to accommodate f and program pulse sequence
4) signal average over N cycles
5) if there is any signal at all, try to increase S/N iteratively
This takes too long
1) Assume NQR signal has 10 KHz line width
2) 35Cl resonance typically in range 15-42 MHz (Lucken E.A.)
→ 27 MHz search space → at 10 KHz per test, 2700 probe configurations
... and for each of these, must at least[1] optimize C1, C2 by hand for tuning/matching each 10KHz → must tune the probe 2700 times
→ 90 degree pulse width T90 unknown: 10-60 us typical → incrementing by 10 us → ~ 6 pulse sequence configurations → 2700 x 6 = 16200 configurations due to spectrometer frequency and pulse duration along
→ estimate the time required for each configuration (here's a lower bound):
→ N=500 signal averaging with pulse separation Tout = .1 sec → ~1 min collection
→ 3-4 min processing (with suboptimal labview code)
→ minimum 5-7 min each, even if completely autonomous
→ assuming one conclusive test of a 10 KHz band every 30 minutes[2]→ working 40 hours/week doing only perfect runs → 202 weeks ~ 4 years to search this space
Reduction of search space
Method 1: infer from similar compounds
(1) Thiourea
For 14N, NQR frequencies in pure thiourea is known (Smith, Cotts 1964)
• Cq = 3.1216 MHz, 3.0996 MHz (inequivalent sites)
• η = .3954, .3930
• It is natural to ask whether 14N's Cq would deviate significantly in DTN, which contains thiourea 4x per unit cell
FIG: “spectrum” of thiourea from only Cq and η
(2) Methyl ammonium manganese chloride
For 35Cl, we might compare DTN to MnCl_4-(CH_3NH_3)_2 (Kind 1976)
Results:
• Cq unknown exactly
• 35 Cl NQR confirmed two inequivalent sites
• resonance frequencies located with super-regenerative detector at 4.456, 7.71 MHz at room T (T-dependence • asymmetry parameter Vzz/(Vyy-Vxx) → η = 0 for lower line, η thought to be ~.7 for higher nqr line but still not known (lack of sensitivity)
ToDo:
• calculate efg tensors in QE
• locate NQR lines with superhet and measure asymmetry parameter exactly for higher freq transition in MnCl_4-(CH_3NH_3)_2
Is the NQR spectrum confined to < 5 MHz?
• note that 3-5 MHz is well outside of original search space
• experimental technicalities are even more difficult at these frequencies because
• massive capacitances are needed (poor dynamic range of caps for sweeping) or
• massive inductance is needed (this usually comes with a large value of r, meaning lower Q)
• Q = f/df is naturally lower when f is lower
Search space reduction, method 2: do a quantum chemistry calculation of the EFG tensors in the crystal
• Is it possible for such a large unit cell?
• DTN has a lot of electrons, so all-electron models are out, but pseudopotential models are OK
• Luckily, the EFG is due to valence electrons only
• Recently, there is much success interest in predicting solid state NMR parameters (chemical shielding, quadrupole splittings)
• ab-initio calculations of the entire EFG tensor are done with ever increasing frequency using the Gauge Including Projector Augmented Wave method (GIPAW)
• GIPAW is completely implemeted in …
• CASTEP (closed source, expensive)
• Quantum Espresso (QE) (open source, free)
• Method is used along with spectroscopy to assist analysis of NMR data
Timeline of events:
• Summer 2013 - reddit user /u/flangeball (Tim Green, oxford UK) calculates the EFG in NaClO3 and DTN using CASTEP
• October 2013 – I attend QE training at ETH
• October 2013 - calculation for DTN is repeated on ETH computers with input file by Ari. P. Seitsonen
• August 31, 2015 – I complete the calculation on hydra12 using UF computers; aggreement with QE calculation
FIG: Data summary, results of calculations, low Cq for 35Cl in DTN vs. knowns in McCl4, calculated 14N nqr in DTN vs known thiourea
The calculation took 2 years
Still faster than blind point to point search
what happened in between?
Obviously, many late nights of parallel computing. Additionally,
• preparation of spectrometer for < 5 MHz
• fabrication of new probes for low frequency NQR (many problems arise due to low frequency)
• measurement of HMT standard sample confirmed at 3.3 MHz
• developed a python library satisfying experimental needs for speedup, including
• rapid calculation of probe design parameters given known params (a big issue at low frequency)
• conversion of structure files for solids to QE-compatible input
• parsing large QE output data
• processing NQR data from superhet
• Samples grown of pure thiourea
• No NQR found at room T (expected in 2-3 MHz, not sure why: S/N, or torsional motions?)
Outlook, road to graduation
Todo:
FIG: the algorithm below in a flow chart
The following algorithm, in pseudocode, illustrates a decision-tree leading to graduation.
get methyl ammonium manganese chloride sample
while not graduated:
do GIPAW on Thiourea, MnCl4-(CH3 NH3)2
compare with experiments and knowns
try more GIPAW
// η is not known for one of the two transitions reported in the 1975 publication
if NQR in MnCl4-(CH3 NH3)2 is found:
if asymmetry parameter can be measured
publish
else:
can you do the experiment somewhere else? (WURST pulse? other broadband techniques?)
did you find any NQR in DTN?
return to florida and measure Cq vs. T
else:
can you get another interesting sample to try (NaNO3? Anything else)
does it have a known Cq?
No search required. Exploit another feature (phase transition, assymetry, etc)
graduate?
else:
can you do GIPAW on it?
Compare GIPAW vs Experiment
do that again, and again
graduate?
if graduated:
sys.exit()
else:
switch to simulation?
[1] Additionally, as frequency decreases, the capacitances necessary for matching grow outside of the dynamic range of real air gap capacitors, leaving the choice to either 1) solider in additional fixed capacitances, reducing the dynamic range of the probe each time until tuning is no longer possible, or 2) replacing the sample coil for one with a larger inductance and reasonable Q (this becomes difficult as frequency decreases). In practice, it is best to use a new coil for each 2-3 MHz band. For the search space presented, one would require 10 or more different sample coils.
[2] This is still impossible. There no chance of maintaining this rate for long, since
1) 30 minutes exactly, if nothing goes wrong, and there is no need for adjustments (there are often adjustments).
2) It takes at least 1 month to produce a probe enclosure, in practice a new probe enclosure was needed for each ~ 5 MHz band due to the sizes of components → 4-6 more configurations, each with about a month of downtime.
3) There are always bugs.