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
The other is the orbital effect , 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 (
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.
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 , 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 ) found in the nanowires recently . 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 –(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.
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 field-induced 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
This theory was proposed by Jaccarino, V. and Peter, M. in 1962 . 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
In some cases, this
Certainly, superconductivity could also be possible in this case (as a stable phase), even if without the external field
3.2. Theory of spin fluctuation effect
This theory was mainly reported by Maekawa, S. and Tachiki, M.  in 1970s, with the discovery of field-induced superconductors EuxSn1-xMo6S8-ySey. These types of materials have rare-earth 4f-ions and paired conduction electrons from the 4d-Mo-ions. The rare-earth 4f-ions have large fluctuating magnetic moments, while the conduction electrons from the 4d-Mo-ions have strong electron–electron interactions and they form Cooper pairs.
Without externally applied magnetic field (
However, when external magnetic field is applied (
3.3. Theory of anti-proximity effect
3.3.1. Superconductivity in nanowires enhanced by applied magnetic field
Unlike the bulk superconductors, a nanoscale system can have externally applied magnetic field
But it has been observed that the application of a small magnetic field
3.3.2. Proximity effect
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 proximity effect .
Similarly, when a superconducting nanowire is connected to two bulk superconducting (BS) electrodes, the combined sandwiched system is expected to be superconducting (below the T
3.3.3. Anti-proximity effect
Contrary to the proximity effect, it has been found in 2005 [11, 16] that, in a system consisting of 2
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.
3.3.4. Theory of anti-proximity effect
There are several theoretical models that could be used for the theoretical explanation of the magnetic field-induced or -enhanced superconductivity in nanowires, while some of which were proposed long before the anti-proximity effect was reported. Thus they are not generally accepted.
a. Phase fluctuation model
This model proposes that there is an interplay between the superconducting phase fluctuations and dissipative quasiparticle channels .
When the bulk electrodes are superconducting, there is a supercurrent flowing between the nanowire and BS electrodes, and the contact resistances (R) vanish (R = 0). Thus the circuit frequency becomes low, and the quantum wire is shunted by the capacitor (C) if the energy (frequency
When the bulk electrodes are driven normal by the applied magnetic field (H 30 mT), the contact resistances R ≠ 0. Similarly, if the electrodes are normal but the nanowire is superconducting (or vice versa), there will be a resistance due to charge conversion processes . This results in a high circuit frequency
In order words, when the magnetic field is applied (
b. Interference model
The interference model proposes that there is an interference between junctions of two superconducting grains, with random Josephson couplings J and J' associated with disorder, as sketched shown in Fig. 5. It produces a configuration-averaged critical current <
This is a periodic function of [cos2(2/0)] with a period of half flux quantum (0/2 = hc/4e), where is the magnetic flux through each hole due to the existence of disorder in the sample (note, the sample has an array of holes through each of which there has a flux ).
Thus when is small, <IC> increases as increases, and this corresponds to a negative magnetoresistance, i.e., when applied magnetic field
c. Charge imbalance length model
This model proposes that there is a charge-imbalance length (or relaxation time) associated with the normal metal - superconductor boundaries of phase-slip centers . Applying magnetic field reduces the charge-imbalance length (or relaxation time), resulting in a negative magnetoresistance at high currents and near
d. Impurity model
The impurity model deals with the superconductivity for nanoscale systems that have impurity magnetic moments with localized spins as magnetic superconductors , in which there is a strong Zeeman effect. According to this model, superconductivity is enhanced with the quenching of pair-breaking magnetic spin fluctuations by the applied magnetic field.
These are major theoretical models for the explanation of the anti-proximity effect in nanoscale systems. Their validity needs more experimental evidence.
4. Field-induced superconductor –(BETS)2FeCl4
The field-induced superconductor –(BETS)2FeCl4 is a quasi-two dimensional (2D) triclinic salt (space group P ) incorporating large magnetic 3d-Fe3+ ions (spin Sd = 5/2) with the BETS-molecules inside which have highly correlated conduction electrons (-electrons, spin S = 1/2) from the Se-ions, where BETS is bis(ethylenedithio)tetraselenafulvalene (C10S4Se4H8). It was first synthesized in 1993 by Kobayashi
–(BETS)2FeCl4 is one of the most attractive materials in the last two decades for the observation of interplay of superconductivity and magnetism and for the synthesis of magnetic conductors and superconductors.
We expect it to show strong competition between the antiferromagnetic (AF) order of the Fe3+ magnetic moments and the superconductivity of the material, where the properties of the conduction electrons are significantly tunable by the external magnetic field, together with the internal magnetic field generated by the local magnetic moments from the Fe3+ ions as well. Thus it has been of considerable interest in condensed matter and materials physics.
This interplay originates from the role of the magnetic 3d-Fe3+ ions moments including the effect of their strong interaction with the conduction -electrons. Because of this interplay, –(BETS)2FeCl4 has an unusual phase diagram [Fig. 5 (c)], including an antiferromagnetic insulating (AFI) phase, a paramagnetic metallic (PM) phase, and a field-induced superconducting (FISC) phase [4, 8].
The crystal structure of –(BETS)2FeCl4 in a unit cell is shown in Fig. 6 (a) . In each unit cell, there are four BETS molecules and two Fe3+ ions. The BETS molecules are stacked along the
Noticeably, the conducting layers comprised of BETS are sandwiched along the
At the room temperature (298 K), the lattice constants are:
5. NMR studies of –(BETS)2FeCl4
In order to study the mechanism of the superconductivity in –(BETS)2FeCl4 and to test the validity of the Jaccarino-Peter effect, as well as to understand the multi-phase properties of the material as show in the unusual phase diagram [Fig. 6 (c)], we successfully conducted a series of nuclear magnetic resonance (NMR) experiments.
5.1. 77Se-NMR measurements in –(BETS)2FeCl4
5.1.1. 77Se-NMR spectrum
The 77Se-NMR spectra of –(BETS)2FeCl4 at various temperatures are shown in Fig. 7. The spectrum has a dominant single-peak feature which is reasonable as a spin I = 1/2 nucleus for the 77Se, while it broadens inhomogeneously and significantly upon cooling (the linewidth increases from 90 kHz to 200 kHz as temperature is lowered from 30 K to 5 K). What the77Se-NMR spectrum measures is the local field distribution in total at the Se sites. Apparently, these spectrum data indicate that all the Se sites in the unit cell are essentially identical.
The sample used for the 77Se-NMR measurements was grown using a standard method  without 77Se enrichment (the natural abundance of 77Se is 7.5%). The sample dimension is
Due to the small number of spins, a small microcoil with a filling factor ~ 0.4 was used. For most acquisitions, 104–105 averages were used on a time scale of ~ 5 min for 104 averages. The sample and coil were rotated on a goniometer (rotation angle
5.1.2. Temperature dependence of the 77Se-NMR resonance frequency
The temperature (
The resonance frequency is counted from the center of the 77Se-NMR spectrum peak (maximum). What it measures is the average of the local field in magnitude in total, including the direct hyperfine field from the conduction electrons and the indirect hyperfine field that coupled to the Fe3+ ions at the Lamar frequency of the 77Se nuclei (see details in Section 5.1.4).
Figure 8 indicates that in the PM state above ~ 7 K at the applied field
where the fit parameters
This result is a strong indication that the temperature T dependence of the77Se-NMR resonance frequency is dominated by the hyperfine field from the Fe3+ ion magnetization M
It is important to notice that the sign of the contribution from M
Now, to verify to validity of the Jaccarino-Peter mechanism, we need to find the field from the 3d Fe3+ ions at the Se -electrons is (i.e., the -d exchange field
According to the
5.1.3. Angular dependence of the 77Se-NMR resonance frequency
The angular dependence of the 77Se-NMR resonance frequency from our experiments is shown in Fig. 9, which is plotted as a function of angle at several temperatures. The angle
To understand the complexity of these sets of data, we need clarify the angle first as there are many other directions involved here as well. First, the crystal lattice has its a, b and c axes which have their own fixed directions. Second, the z component of the BETS molecule -electron orbital moment,
To distinguish each of these directions, we used the Cartesian xyz reference system and choose the reference
Thus during a sample rotation the direction of
Therefore, an angle
Based on these data shown in Figs. 8 - 9, we can determine the magnitude of the -d exchange field
5.1.4. Determination of the -d exchange field (between the Se- and Fe3+-d electrons)
From the theory of NMR , we can express the contributions to the Hamiltonian (HI) of the 77Se nuclear spins as
The -d exchange field Hd comes from, and the term produces dipolar field
From Eq. (3) the corresponding 77Se NMR resonance frequency
The dashed lines in Fig. 8 are the fit to Eqs. (4) – (5). The gyromagnetic ratio of Se nucleus is 77 = 8.131 MHz/T. The value of
Alternatively, for better accuracy we obtained the following expression for the -d exchange field Hd from Eqs. (4) – (5) to be,
Thus from the data
If the applied field is
This large value of negative -d exchange field felt by the Se conduction electrons obtained from our NMR measurements verifies the effectiveness of the Jaccarino-Peter compensation mechanism responsible for the magnetic-field-induced superconductivity in the quasi-2D superconductor –(BETS)2FeCl4.
We have presented briefly the information about the field-induced-superconductors including the theories explaining the mechanisms for the field-induced superconductivity. We also summarized our 77Se-NMR studies in a single crystal of the field-induced superconductor –(BETS)2FeCl4, while most of our detailed research NMR work including both proton NMR and 77Se-NMR were reported in refs.[20, 23, 24].
Our 77Se-NMR experiments revealed large value of negative -d exchange field (
Future high field NMR experiments (
We are grateful to Prof. S. E. Brown at UCLA for helpful discussions and help with the NMR experiments. We also thank other coauthors J. S. Brooks, A. Kobayashi, and H. Kobayashi for our detailed 77Se-NMR work published in ref. .