**1. Introduction**

It has been widely known in condensed matter and materials physics that the application of magnetic field to a superconductor will generally destroy the superconductivity as a usual scenario. There are two reasons responsible for this.

One is the Zeeman effect [1-2], where the alignment of the electron spins by the applied magnetic field can break apart the electron pairs for a spin-singlet (but not a spin-triplet) state. In this case, the electron spin pairs have opposite spins (such as the *s*-wave spins typical in type I superconductors). The applied magnetic field attempts to align the spins of both electrons along the field, thus breaking them apart if strong enough. In terms of energy, one electron gains energy while the other (as a pair) loses energy. If the energy difference is larger than the amount of energy holding the electrons together, then they fly apart and thus the superconductivity disappears. But this does not apply to the spin triplet superconductivity (*p*-wave superconductors) where the electron pairs already have their spins aligned (along the field) in a *p*-wave state.

The other is the orbital effect [3], which is a manifestation of the Lorentz force from the applied magnetic field since the electrons (as a pair) have opposite linear momenta, one electron rotating around the other in their orbitals. The Lorentz force on them acts in opposite directions and is perpendicular to the applied magnetic field, thus always pulling the pair apart. This does not matter with their spin pairing symmetries (*s*-wave, *p*-wave or *d*wave). In type-II superconductors, the Meissner screening currents associated with the vortex penetration in the applied magnetic field can also increase the electron kinetic energy (and momentum). Once this energy becomes greater than the energy that unites the two electrons, the electron pairs break apart and thus superconductivity is suppressed. Therefore, the orbital effect could be even more important in type-II superconductors.

© 2012 Wu and Clark, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Wu and Clark, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

However, in certain complex compounds, especially in some low-dimensional materials, superconductivity can be enhanced [4 - 5] by the application of magnetic field. The enhancement of superconductivity by magnetic field is a counter-intuitive unusual phenomenon.

Field-Induced Superconductors: NMR Studies of λ–(BETS)2FeCl4 5

B, created by the magnetic moments [proportional to

**3. Theory for field-induced superconductors** 

and the theory of anti-proximity effect.

**3.1. Theory of Jaccarino-Peter effect** 

internal magnetic field (*H***J**), *H*J = *J<S>/g*

**Figure 1.** Schematic of Jaccarino-Peter effect [8]

In this section, we will briefly describe the theoretical aspects for the field-induced superconductors regarding their mechanisms of the field-induced superconductivity. We will mainly discuss the theory of Jaccarino-Peter effect, the theory of spin fluctuation effect,

This theory was proposed by Jaccarino, V. and Peter, M. in 1962 [6]. It means that if there is an existence of localized magnetic moments at a state and conduction electrons as well at the same state in a material, then it could lead to a negative exchange interaction *J* between the conduction electrons and the magnetic moments when an external magnetic field (*H*) is applied. This negative exchange interaction *J* is formed due to the easy alignment of the localized magnetic moments (along the external magnetic field direction) while the external magnetic field *H* is applied. Thus the spins of the conduction electrons will experience an

the average spins (<S>) of the moments]. Here the internal magnetic field *H***J** is called the exchange field and the direction of the exchange field *H***J** is opposite to the externally applied

In some cases, this *H*J could be very strong. Therefore, if the exchange field *H***J** is strong enough to cancel the externally applied magnetic field *H*, i.e., *H***J** = − *H,* then the resultant

μ

magnetic field *H*. This picture is sketched as that shown in Fig. 1.

In order to understand this interesting phenomenon, different theoretical mechanisms have been proposed, while there are still debates and experimental evidence is needed. The first theory is the Jaccarino-Peter compensation effect [6], the second theory is the suppression effect of the spin fluctuations [7-9], and the third theory is the anti-proximity effect (in contrary to the proximity effect [10]) found in the nanowires recently [11]. These theories will be briefly described in Section 3.

Experimentally, there are several effective techniques that can be used to the study of the superconductivity of the materials with magnetic field applications. They include electrical resistivity measurements, Nernst effect measurements, SQUID magnetic susceptibility measurements, and nuclear magnetic resonance (NMR) measurements, etc.

Among these experimental techniques, NMR is one of the most powerful ones and it is a versatile local probe capable of directly measuring the electron spin dynamics and distribution of internal magnetic field including their changes on the atomic scale. It has been widely used as a tool to investigate the charge and spin static and dynamic properties (including those of the nano particles). It is able to address a remarkably wide range of questions as well as testing the validity of existing and/or any proposed theories in condensed matter and materials physics.

The authors have extensive experience using the NMR and various other techniques for the study of the novel condensed matter materials. This chapter focuses on the NMR studies of the quasi-two dimensional field-induced superconductor λ–(BETS)2FeCl4. This is a chance to put some of the work together, with which it will help the science community for the understanding of the material as well as for the mechanism of superconductivity. It will also help materials scientists in search of new superconductors.
