**2. Field-induced superconductors**

The discovery of field-induced superconductors is about a decade earlier than the discovery of the high-Tc superconductors (which have been found since 1986), while not many fieldinduced superconductors have been found. Both types of materials, field-induced superconductors and high-Tc superconductors, are highly valuable in science and engineering due to their important physics and wonderful potentials in technical applications.

Here are typical field-induced superconductors found so far, with chemical compositions as shown in the following


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

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, and the theory of anti-proximity effect.

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

4 Superconductors – Materials, Properties and Applications

will be briefly described in Section 3.

condensed matter and materials physics.

**2. Field-induced superconductors** 

shown in the following

etc. [10-13].

help materials scientists in search of new superconductors.

1. EuxSn1-xMo6S8-ySey, EuxLa1-xMo6S8, PbGd0.2Mo6S8, etc.[5, 7].

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

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

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

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

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

The discovery of field-induced superconductors is about a decade earlier than the discovery of the high-Tc superconductors (which have been found since 1986), while not many fieldinduced superconductors have been found. Both types of materials, field-induced superconductors and high-Tc superconductors, are highly valuable in science and engineering

Here are typical field-induced superconductors found so far, with chemical compositions as

3. Al-nanowires (ANWs), Zinc-nanowires (ZNWs), MoGe nanowires, and Nb nanowires,

due to their important physics and wonderful potentials in technical applications.

2. λ–(BETS)2FeCl4, λ–(BETS)2FexGa1-xBryCl4-y, κ–(BETS)2FeBr4, etc.[4, 8, 9].

measurements, and nuclear magnetic resonance (NMR) measurements, etc.

of superconductivity by magnetic field is a counter-intuitive unusual phenomenon.

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 internal magnetic field (*H***J**), *H*J = *J<S>/g*μB, created by the magnetic moments [proportional to 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 magnetic field *H*. This picture is sketched as that shown in Fig. 1.

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

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

field in total that the conduction electron spins experience becomes zero (also a complete suppression of the Zeeman effect), and thus the superconductivity is induced in this case.

Field-Induced Superconductors: NMR Studies of λ–(BETS)2FeCl4 7

But it has been observed that the application of a small magnetic field *H* can decrease the resistance in even simple narrow superconducting wires (i.e., negative magnetoresistance) [12, 13], while larger applied magnetic field *H* can increase the critical current (*I*C) significantly [14]. These indicate an enhancement of superconductivity in nanowires by the application of magnetic field. But to understand the enhancement of superconductivity by magnetic field in nanoscale systems is very challenging currently in the science community.

On the other hand, when a superconducting nanowire is connected to two normal metal electrodes, generally a fraction of the wire is expected to be resistive, especially when the wire diameter is smaller than the superconducting coherence length. This is called the

Similarly, when a superconducting nanowire is connected to two bulk superconducting (BS) electrodes, the combined sandwiched system is expected to be superconducting (below the *TC* of the superconducting nanowire and the BS electrodes), and the superconductivity of the nanowire is then expected to be more supportive and more robust through its coupling with the superconducting reservoirs. This is also actually what is theoretically expected [15].

Contrary to the proximity effect, it has been found in 2005 [11, 16] that, in a system

electrodes (Sn or In), superconductivity of Zinc nanowires is completely suppressed (or partially suppressed) by the BS electrodes when the BS electrodes are in the superconducting state under zero applied magnetic field. However, when the BS electrodes are driven normal by an applied magnetic field (*H*), the Zinc nanowires re-enter their

superconducting state at ~ 0.8 K, unexpectedly. This is called ''anti-proximity effect''.

**Figure 3.** Schematic of the Zinc nanowires sandwiched between two BS electrodes [11].

This is also a counterintuitive unusual phenomenon, never reported before 2005.

The schematic of the electrical transport measurement system exhibiting the anti-proximity effect with the Zinc nanowires sandwiched between two BS electrodes is shown in Fig. 3.

long, 40 nm diameter Zinc nanowires sandwiched between two BS

*3.3.2. Proximity effect* 

proximity effect [10].

*3.3.3. Anti-proximity effect* 

μ

BS – bulk superconducting electrode; ZNWs – Zinc nanowires;

PM – porous membranes; I – current; V – voltage.

consisting of 2

Certainly, superconductivity could also be possible in this case (as a stable phase), even if without the external field *H* (i.e. *H* = 0). This is because the magnetic moments point to random directions (without *H*) and cancel each other, i.e., *H***J** = 0, and thus the conduction electron spins also feel zero in total field.
