Antiferromagnetic Superconductor Research Articles

Neutron scattering studies of heavy fermion systems (invited) (abstract)

We review our results of neutron scattering experiments on the heavy electron systems UPt3, U2Zn17, and URu2Si2. In the superconductor UPt3 we have established the existence of spin fluctuations on an energy scale of 0.5 meV and correlated in the same structure as the antiferromagnetic order in the Th- and Pd-doped systems. In the antiferromagnet U2Zn17 overdamped antiferromagnetically correlated excitations dominate the excitation spectrum above and below TN. However, in an applied field the resonances are induced in the transverse response. In the antiferromagnetic superconductor URu2Si2 the excitations in the ordered phases are propagating, longitudinal and similar to observations in singlet rare-earth ground-state systems. However, the ordered moment of 0.03μB is anomalously small and the transverse response is overdamped. We discuss a simple model of exchange coupled overdamped responses which gives a consistent description of the diffusive spin-fluctuations in several heavy electron systems.

Cooling of TbMo6S8 by Adiabatic Magnetization

Adiabatic magnetization cooling of the antiferromagnetic superconductor TbMo6S8 has been investigated between 0.2 K and 2 K in magnetic fields up to 2.5 kOe. It was found that the cooling occurs only in the antiferromagnetic phase and is largest (80 mK/kOe) at temperatures which are about a factor of two below the Neél point. The observed dependence of the temperature on the magnetic field is qualitatively reproduced by a combination of spin-wave theory and Ginzburg-Landau theory. The results obtained for TbMo6S8 and those from our previous work for GdMo6S8 are compared.

Spin wave spectrum for an antiferromagnetic superconductor

The Ginzburg-Landau theory has been applied for an antiferromagnetic superconductor in order to calculate the spin-wave spectrum, taking into consideration electromagnetic effects and the long-range spin-spin interaction. It is shown that the superconducting state has a strong influence on the spin-wave spectrum of the antiferromagnetic state.

On the mean field theory of one-dimensional antiferromagnetic superconductors

The mean field theory for antiferromagnetic superconductors introduced by Nass et al. is applied to a strong coupling system. It is possible to show that in such systems the critical value of the staggered molecular field H Q which arises from antiferromagnetism is largely affected by the strong coupling corrections. The critical value found for such systems is now of the order of 10 to 20 K for the one-dimensional system. Moreover the additional pairing state Δ Q does not vanish in strong coupling systems which is in contrast to BCS related theories.

Superconductivity and magnetism of a body-centered tetragonal ErRh4B4 single crystal. I. Metamagnetism under the fourfold magnetic anisotropy.

Magnetization was measured on a single crystal of body-centered tetragonal ${\mathrm{ErRh}}_{4}$${\mathrm{B}}_{4}$, an antiferromagnetic superconductor. It was found that the c axis is the strong hard-magnetization direction. A large fourfold magnetic anisotropy was observed in the tetragonal c plane. The [100] and [010] axes are the easy-magnetization directions and the [110] axis is the hard-magnetization one in the c plane. The magnetization curves below ${T}_{N}$ show two-step jumps in both cases of H\ensuremath{\parallel}[100] and H\ensuremath{\parallel}[010] and show only one-step jumps in the case of H\ensuremath{\parallel}[110]. Furthermore, it is shown that superconductivity coexists with intermediate magnetic states under a magnetic field in the c plane. The magnetization process in the c plane is understood as metamagnetism and can be explained by a four-sublattice model taking account of the fourfold magnetic anisotropy. Based on the fact that Er spins are approximately located on an fcc lattice in bct ${\mathrm{ErRh}}_{4}$${\mathrm{B}}_{4}$, the type of the antiferromagnetic order is discussed. The two-step jump in the magnetization for H\ensuremath{\parallel}[100] indicates that the magnetic structure belongs to the first-kind ordering in the antiferromagnetic fcc lattice. The magnetization process below ${T}_{N}$ is discussed, and the exchange constants between the magnetic spins are determined. The results obtained are consistent with the stability condition of the first-kind ordering.

Superconductivity and magnetism of a body-centered tetragonal ErRh4B4 single crystal. II. Large anisotropy of Hc2.

Upper critical field ${H}_{c2}$ and magnetization are measured on a single crystal of body-centered tetragonal (bct) ${\mathrm{ErRh}}_{4}$${\mathrm{B}}_{4}$ which is an antiferromagnetic superconductor and behaves metamagnetically in the c plane under a magnetic field below ${T}_{N}$. The temperature dependences of ${H}_{c2}$ along the [001] and [100] axes are roughly similar to each other in that both ${H}_{c2}$(T) take maxima with decreasing temperature but the magnitude of ${H}_{c2}$ along the [001] axis is quite large compared to that along the [100] axis. Furthermore, the angular dependence of ${H}_{c2}$ in the c plane shows the fourfold anisotropy above ${T}_{N}$ and the complex twofold anisotropy below ${T}_{N}$. The anisotropy of ${H}_{c2}$ is closely related with that of the magnetization. From the analysis in which the spin polarization due to the s-f exchange interaction and the electromagnetic interaction are taken into account it is made clear that the spin polarization plays a very important role in determining ${H}_{c2}$. The s-f exchange constant and the spin-orbit scattering parameter are also determined. It is indicated that the s-f exchange interaction is ferromagnetic and the spin-orbit scattering is very strong in the bct ${\mathrm{ErRh}}_{4}$${\mathrm{B}}_{4}$ crystal. Finally temperature dependence of ${H}_{c2}$ in the c plane below ${T}_{N}$ is qualitatively discussed, being connected with metamagnetism.

Theory of the magnetic scattering of neutrons in the antiferromagnetic superconductors

The influence of the superconducting state on the antiferromagnetic ordering in an antiferromagnetic superconductor is analysed. The integrated neutron cross section and the spin waves spectrum have been calculated.

The critical point in an antiferromagnetic superconductor

We study the stability criterion for the critical point of a transition of the second kind in the T-H Q plane of an antiferromagnetic superconductor AFS (T is temperature and H Q is the staggered molecular field). The AFS is described by using the mean-field model given by Nass, Levin and Grest and we assume a one dimensional electron band. Some properties of the system near the critical point are also investigated.

Hc2 and magnetization process bct (RE)Rh 4B 4, RE = Ho, Er

The H c2 and magnetization of both bct ErRh 4B 4 and bct HoRh 4B 4 have been measured. Both compounds are antiferromagnetic superconductors. The magnetization process below T N is metamagnetic in both compounds. The H c2 of bct HoRh 4B 4 shows a hysteresis between increasing and decreasing fields below T N, while in bct ErRh 4B 4 such a hysteresis is not observed. Whether H c2 shows the hysteresis or not is closely related with the coexistence between superconductivity and any magnetic structure in a magnetic field. It is concluded that the hysteresis of H c2 in HoRh 4B 4 originates from the fact that superconductivity is quenched by a matamagnetic transition because the Ho spin has a larger magnetic moment than the Er spin.

Theory of Antiferromagnetic Superconductors in the Presence of Nonmagnetic Impurities: One-Dimensional Model

Theory of Antiferromagnetic Superconductors in the Presence of Nonmagnetic Impurities: One-Dimensional Model

Magneto-caloric effect in antiferromagnetic superconductors

We have investigated adiabatic magnetization cooling in the antiferromagnetic superconductors GdMo 6S 8 and TbMo 6S 8 in their antiferromagnetic states. At 0.5 K the temperature decreased by 0.04 K for GdMo 6S 8 and by 0.13 K for TbMo 6S 8 when a magnetic field of 2.5 kOe was applied. In the superconducting state the magnetization cooling is partly masked by a heating effect, possibly resulting from flux flow. In the spin canted and in the paramagnetic states, increasing the field produced a temperature rise.

Sputtered films of superconductingSmRh4B4

Films of the coexistent antiferromagnetic superconductor ${\mathrm{SmRh}}_{4}$${\mathrm{B}}_{4}$ have been made by sputtering. These films have been characterized by x-rays and superconducting critical temperatures ${T}_{c}$, fields, and currents. Our best films have residual resistance ratios, ${r}_{R}$, as high as or higher than for films of ${\mathrm{ErRh}}_{4}$${\mathrm{B}}_{4}$ reported in the literature, and the highest ${T}_{c}$ is 2.36 K. We find an anomalous dependence of ${T}_{c}$ on ${r}_{R}$, and offer two possible explanations (proximity-effect and disorder-enhanced spin-flip scattering), as well as propose a radiation-damage experiment to distinguish between these. The antiferromagnetic ordering temperature is shown to decrease with film disorder as does the ferromagnetic ordering temperature in radiation-damaged ${\mathrm{ErRh}}_{4}$${\mathrm{B}}_{4}$. We find an approximately 1000-\AA{}-thick RhAl impurity phase at the sapphire-substrate/film interface which seems to result from a reaction with the substrate. The potential importance of RhAl and trace impurity phases on present measurements and planned tunneling experiments are discussed in detail. Finally, the full critical-field curves are presented along with an explanation of why the low-temperature values are independent of ${T}_{c}$.

Effect of radiation damage on the coexistent antiferromagnetic superconductorSmRh4B4

Radiation-damaged films of coexistent antiferromagnetic superconductor SmRh/sub 4/B/sub 4/ have been studied. The upper critical field, superconducting and magnetic transition temperature, and resistivity ratio were determined as a function of dose. The anomalous dependence of the superconducting transition temperature on resistivity ratio found previously for ''as-made'' films was also found in the damaged films, indicating the anomaly is intrinsic to SmRh/sub 4/B/sub 4/. A disorder-enhanced-spin-flip model is proposed to explain this effect.

Theory of magnetic superconductors in an external magnetic field

The theory of Abrikosov and Gor'kov has been extended to study superconducting systems containing a lattice of magnetic ions. Differential equations have been set up for the Green's-function matrices which describe a magnetic superconductor in the presence of local-spin-conduction-electron exchange and external magnetic field. The self-consistent gap equation for the system has been formulated in terms of normal-state Green's functions. The solutions for the normal-state Green's functions ${?}^{0}$ have been obtained including the effects of magnetic order and spin fluctuations. The gap equation has been solved to obtain an analytical expression for the upper critical field ${H}_{c2}(T)$ of a magnetic superconductor. With the use of the results for the normal-state Green's functions ${?}^{0}$, the upper critical field has been calculated for a ferromagnetic superconductor in paramagnetic phase and a few antiferromagnetic superconductors in both paramagnetic and antiferromagnetic phases. The anomalous temperature dependence of the upper critical field ${H}_{c2}(T)$ has been analyzed in terms of contributions from magnetic order, spin fluctuation, and an indirect interaction of the conduction electron with staggered magnetization ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{M}}}_{Q}$ via magnetic induction field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}$.

Possibility of two-stage flux penetration in antiferromagnetic superconductors

An induced ferromagnetism in antiferromagnetic superconductors is possible, caused by a magnetic structure of vortex lines appearing in an external magnetic field strong enough to “flip over” the spins in the vortex core from their antiferromagnetic configuration. If the magnetic field is less than the “flip over” field the vortex line is entirely in the antiferromagnetic phase. Therefore the vortex interaction with the surface of a sample is altered when an applied magnetic field exceeds the “flip over” field. This mechanism makes the appearance of a new energy barrier that strongly influences the flux penetration possible. An estimation of the second critical entry field is made for DyMo 6S 8.

NMR Study of 59Co and 11B in RECo4B4 (RE=Gd, Tb, Dy, Ho, Er and Tm)

Pulsed NMR studies of 59 Co and 11 B have been performed in a series of antiferromagnetic RECo 4 B 4 compounds (RE=Gd, Tb, Ho, Er, Tm) in both paramagnetic and magnetically ordered states. In the paramagnetic state, NMR signals of both 59 Co and 11 B were observed only in GdCo 4 B 4 in the temperature range of 77–300 K. From the isotropic Knight shift measurement, we obtained the conduction electron spin polarization at both Co and B sites generated by the d - f exchange interaction on the rare earth site. The electron spin polarization estimated in RECo 4 B 4 is about twice as large as that in RERh 4 B 4 system. In the antiferromagnetic state, zero-field resonances of 59 Co and 11 B were observed for GdCo 4 B 4 , TbCo 4 B 4 and DyCo 4 B 4 at 1.3 K. From the hyperfine fields and NMR spectra, the spin structure is shown to be the same type as in the antiferromagnetic superconductor Ho(Rh 0.3 Ir 0.7 ) 4 B 4 .

Relaxation of ferromagnetic ordering in pseudoternary superconductors

The low-temperature phase diagrams of the superconducting and magnetic pseudoternary systems ${\mathrm{Ho}}_{1.2\ensuremath{-}x}{R}_{x}{\mathrm{Mo}}_{6}{\mathrm{S}}_{8}$ with $R=\mathrm{Tb}$ and Er have been determined by means of low-frequency ac magnetic susceptibility and neutron-diffraction measurements and are qualitatively described with a molecular-field model. A very slow transition from a ferromagnetic to a superconducting state was observed at 100 mK in Ho-rich ${\mathrm{Ho}}_{1.2\ensuremath{-}x}{\mathrm{Er}}_{x}{\mathrm{Mo}}_{6}{\mathrm{S}}_{8}$ compounds with $x$ values between 0.2 and 0.4. This unusual behavior can be interpreted in terms of the similarity of the free energies of the antiferromagnetic superconducting and normal ferromagnetic states at very low temperatures. Neutron-diffraction measurements on a ${\mathrm{Ho}}_{1.0}$${\mathrm{Tb}}_{0.2}$${\mathrm{Mo}}_{6}$${\mathrm{S}}_{8}$ sample revealed the presence of a long-wavelength oscillatory magnetic phase which coexists with superconductivity, similar to the one that occurs in pure ${\mathrm{Ho}}_{1.2}$${\mathrm{Mo}}_{6}$${\mathrm{S}}_{8}$.

Coexistence of superconductivity and magnetic order

The microscopic theory of simple antiferromagnetic superconductors is extended to structures where the magnetic order is described by a spin-density wave. For the case where the magnetic system is inherently ferromagnetic, the free energy of the combined system is minimized with respect to the amplitude and the wave vector of the spin-density wave. It is found that the wave vector depends very weakly on temperature. We apply the theory to the coexistence region in ErRh 4B 4, finding a first-order re-entry transition.

Theory of the upper critical field in antiferromagnetic superconductors

We compute the temperature $T$ dependence of the upper critical field ${H}_{c2}(T)$ in antiferromagnetic (AF) superconductors. Using a strong-coupling formalism we explicitly treat the effects of the molecular field ${H}_{Q}$, inelastic and elastic spin-fluctuation scattering and magnetic as well as nonmagnetic impurities. A sum rule is used to relate the $T$ dependence of ${H}_{Q}$ to that of the spin-fluctuation scattering. The decreased pair breaking observed below the N\'eel temperature in Sm${\mathrm{Rh}}_{4}$${\mathrm{B}}_{4}$ and the increased pair breaking seen in the AF Chevrel compounds will both occur in our theory for a reasonable choice of parameters. For larger values of the dimensionless spin-exchange coupling constant $N(0){J}^{\mathrm{cf}}$, spin-fluctuation-scattering effects dominate over those of ${H}_{Q}$ and decreased pair breaking is observed below ${T}_{N}$. For smaller values of the coupling constant, the converse is true. Impurity scattering is treated in a self-consistent fashion. As a consequence, the molecular field ${H}_{Q}$ is altered by nonmagnetic impurities. This leads to important pair-breaking effects in ${H}_{c2}$. A physical manifestation of this pair breaking is a qualitative change in the shape of the ${H}_{c2}$ versus $T$ curve, as nonmagnetic impurities are added. We give detailed predictions for the expected effects of these impurities on ${H}_{c2}$ which can be tested experimentally.

Theory of upper critical field of antiferromagnetic supercocductors

An analytical expression for the upper critical field H c2( T) of an antiferromagnetic superconductor is derived using normal state Green functions. The anomalous temperature dependence of H c2( T) is analysed in terms of contributions from the conduction-electron-local-spin exchange interaction and the electrodynamic effect. The theoretical results show excellent agreement with experimental results.