Abstract

The aim of this project is to observe Nuclear Magnetic Resonance (NMR) in bulk metallic samples in low

magnetic fields using SQUID detectors using pulsed magnetic fields.

Platinum is a good metal to study as it is magnetically active, Platinum-195 atoms are spin half particles

with a reasonably high natural abundance of 33.7%.

Nuclear Magnetic Resonance on Bulk Metal Samples

Cameron Dilley Supervisor: Dr C. Lusher

Theory of NMR

Nuclear Magnetic Resonance is a process where magnetic moments of nuclei in a sample are excited using an external magnetic field. Much

like a gyroscope in a gravitational field, the magnetic moments begin to rotate about the direction of the magnetic field, due to the energy

difference between the spin states. This is known as Larmor precession, and is characterised by ω0 = γB0 where ω0 is the angular frequency

precession (known as the Larmor frequency), B0 is the strength of the applied magnetic field, and γ is gyromagnetic ratio. Generally the

direction of B0 is taken to be the z direction.

The magnetisation can be treated as an exponentially decaying sinusoidal wave with the equation Mx = M0 cos(ω0t) exp(-t/T2), where T2 is the

transverse relaxation time, this is known as the Free Induction Decay (FID) (right). Both the gyromagnetic ratio and transverse relaxation time

are material specific constants.

A frame of reference rotating at the Larmor frequency can be defined, such that the moments at the Larmor frequency are stationary in the

absence of other magnetic fields, This is known as the rotating frame. Although in principle there will always be a distribution of frequencies in

the sample.

Pulsed NMR

In pulsed NMR a magnetic field is applied in the x axis in the

rotating frame in order to cause the moments to rotate away

from the z-axis. In this experiment the pulse rotates the spins

by 90o in order to maximise the magnetisation in the x-y plane.

The duration of this pulse is given by t = π/2γB, where B is the

strength of the applied field in the rotating frame.

After the pulse is applied the x-magnetisation then decays as

the moments realign with the magnetic field following an FID.

Samples

The two avaialble samples are a sample of powdered platinum and a sample of a single thin

plate of platinum (left).

For NMR these two samples act differently due to an effect known as the skin effect. This

means that the applied pulses can only penetrate a certain distance into the metal, so not all

the moments will be active in the sample. The skin depth of platinum in this experiment is

22.9 μm at a frequency of 410kHz to be used in this experiment.

This affects the plate sample, not the powder. This is because the particles of the powdered

sample are small enough to allow the rf fields to penetrate fully, where the plate is not. This

means it is easier to detect an NMR signal from the powder than the plate. Figure to show the samples, the single platinum plate sample plate on

the left and the platinum powder sample on the right.

Figure to show the characteristic shape of the free induction decay of the magnetisation in a

sample, for instance the x magnetisation.

Expected Results

The main advantage of using low fields for platinum is that power dissipation due to eddy currents in the metal is lower in low frequencies. The

power dissipation would heat a sample at low temperatures. So there are less eddy current heating at low frequencies and a larger skin depth,

giving rise to a bigger signal. Other effects such as the broadening of peaks (left) with increasing B0 are less important in the platinum sample as

the value of T2* is not strongly frequency dependent.

The signal to noise ratios (SNR’s) have been calculated for 4 different samples to get an idea of how easy each is to detect with the apparatus

for a single measurement using a measurement field of 47mT. The platinum samples are held at 4.2K in a Dewar of liquid helium, where the

sample of YbRh2Si2 would be held close to the superconducting transition of approximately 1mK to probe the superconducting transition.

—The cylindrical sample of platinum powder with a diameter of 5mm and a height of 5mm, gave an SNR of 56.6.

— The single cuboid plate sample of dimensions 4 x 4 x 0.25mm gives an expected SNR of 0.7077.

— Twelve plates of platinum, the predicted SNR is 8.49.

— A 1 x 1 0.1mm sample of superconductive YbRh2Si2 results in a value of 0.00304. Figure to show how the magnetic field. Part A being measured at 1.8mT and part B

measured at 1.8μT. [1]

References:

[1] Robert McDermot, Andreas H. Trabesinger, Michael Muck, Erwin L, Hahn, Alexander Pines and John Clarke, Liquid-State NMR and Scalar Couplings in Microtesla Magnetic Fields, Science, New Series Vol. 29, 2247—2249 (2002)

For further Reading consider the following:

[1] B. P. Cowan, Nuclear Magnetic Resonance and Relaxation, Cambridge University Press, 1st Edition 1997 or second Edition 2005

[2] Ya. S. Greenberg, Application of Superconducting quantum interference devices to nuclear magnetic resonance, Reviews of Modern Physics Vol. 70, 175—222 (1998)

Current Progress

My current progress in this project is as follows:

—Removing the previous shielding and insulation to allow access to the wiring for the required maintenance and mapping of connections before re-insulating and shielding.

—Altering the existing sample holder (right) to accommodate the available samples and to allow the adjustment of the position of the sample within the magnet.

—Rewiring of required connectors to meet the requirements of the probe and rewiring the transmitter box for the probe,

—Cooling the probe and testing the SQUID to ensure that the SQUID had been wire correctly and was functioning properly. Figure showing the Platinum Powder Sample in the

altered sample Holder

Picture showing the NMR probe used in this experiment