Nuclear Magnetic Resonance
Why use NMR to study correlated systems?
The exotic magnetic and charge-ordering properties shown by highly correlated electronic systems are primarily investigated via neutron scattering methods. There are cases, however, where difficulties in growing crystals or the presence of very low energy excitations, make the use of neutrons unsuitable or even impossible.
In these cases the well-established, complementary technique of nuclear magnetic resonance (NMR) comes to help. With its ability to detect low-energy excitations, even in crystals as small as a few millimetres, NMR is our technique of choice when it comes to the study of, e.g., low-dimensional quantum spin systems, correlated materials with orbital order, or spin-density waves.
Complementary techniques
Besides NMR, we employ SQUID magnetometry to investigate macroscopic magnetization and use regularly large-scale facilities to perform complementary (neutron, µSR, and x-ray) measurements.
What really is NMR?
Nuclear Magnetic Resonance (NMR) represents the selective absorption of electromagnetic radiation by nuclei with non-zero spin placed in an external magnetic field.
In an externally applied magnetic field, nuclei endowed with an intrinsic magnetic moment, related with their angular momentum, will precess like tiny magnets about the field direction. The rules of quantum mechanics restrict the possible apertures of the precession cone (spin orientations), giving rise to well defined, differently populated quantum levels. The absorption of an incident radiation will be particularly efficient only when the photon energy equals the energy difference between these levels, hence implying transitions among different quantum states.
For typical laboratory magnetic fields (5-9 T) and for most nuclei, the conditions of resonant absorption are matched by photons belonging to the radio-frequency (RF) region of the electromagnetic spectrum. Classically speaking, the resonance occurs when the natural precession frequency of the nucleus, corresponds to the frequency of the external radio wave striking the material.
The resonance condition may be attained either by tuning the nuclear frequency ν to that of the radio wave (through a change of magnetic field), or by tuning the RF wave frequency to that of the nuclear magnets. Although conceptually simple, both these models of excitation, known as continuous wave (cw), have been almost completely superseded by the more sensitive pulsed Fourier transform (FT) method. Here the magnetic field is kept fixed and the sample is irradiated by a strong RF pulse containing a broad spectrum of frequencies. The sample's response, known as the free-induction decay - FID, is then collected and Fourier transformed to obtain the NMR absorption spectrum.
In the absence of some mechanism enabling the nuclear spins to return to the ground state, the populations of the different energy levels will soon become equal, and no more RF energy will be absorbed. Two important mechanisms, which allow the system to "get rid" of the constantly flowing RF energy, are represented by the longitudinal and transverse relaxation processes.
The first, known also as spin-lattice relaxation, is characterized by a rate constant T1, and describes the loss of energy from excited nuclear spins to the surrounding molecules. The second, known also as spin-spin relaxation, is characterized by a rate constant T2, and involves a transfer of energy from one nucleus to the other.
Even though parameters such as f, T1, T2 (and others, not mentioned here) refer to the same nucleus, they depend strongly on the nucleus surroundings, making it a highly sensitive probe to the immediate environment. From this fact stems the extreme versatility of NMR as a spectroscopic tool of investigation. Its incredibly vast and successful applications in the most disparate fields of science is witnessed among others by the many Nobel prizes in physics, chemistry and medicine, awarded for work related to NMR.