Ferromagnetic Superconductor Research Articles

Quasiclassical theory for interfaces with spin-orbit coupling

In recent years, substantial progress has been made regarding the application of quasiclassical theory on superconducting hybrid structures. This theoretical framework is reliant on a proper set of boundary conditions in order to describe multilayered systems. With the advent of the field of superconducting spintronics, systems which combine heavy metal layers, in which there is large spin--orbit coupling, with ferromagnets have received a great deal of attention, due to their potential for generating long range triplet superconductivity. In contrast to interfaces of strongly spin polarized materials, which are well understood, a quasiclassical theory for interfaces in systems where there is significant spin--orbit coupling does not yet exist. After reviewing the quasiclassical theory for interfaces, we here solve this problem by deriving a new set of boundary conditions which take spin--orbit coupling explicitly into account. We then go on to apply these boundary conditions to a superconductor-ferromagnet (SF) bilayer and an SFS Josephson weak link, demonstrating the emergence of long range triplet superconductivity in these systems.

Current assisted memory effect in superconductor–ferromagnet bilayers: a potential candidate for memristors

AbstrsctSuperconductivity and ferromagnetism are two very useful phenomena, hoewever they rarely coexist in bulk materials. Bringing them together in an artificial hybrid bilayer produces some unusual results. We designed and studied a system of superconductor-ferromagnet bilayer with a thin insulating buffer layer between them. Such a superconductor-ferromagnet bilayer with magnetostatic coupling is proposed for use as a multibit superconductor memory device and a potential candidate as a memristor. Numerical simulations were performed by using Ginzburg–Landau and Landau–Lifshitz-Gilbert models for superconductor and ferromagnet materials, which highlighted some interesting resistive memory effects in the superconducting layer in the bilayer system. A vortex pattern in the superconductor was observed to be strongly coupled with the ferromagnet domain structure, while their dynamics were controlled by the current flowing through the superconductor. Carrier concentration, energy components and magnetization in the superconducting layer were studied as a function of applied current pulses in the superconductor layer, indicating the information storage of the current pulses. Multiple resistive states were observed, pointing towards the possibility that such a device could be used as a multibit data storage device.

Spin-triplet superconductivity in the paramagnetic UCoGe under pressure studied by Co59 NMR

A $^{59}$Co nuclear magnetic resonance (NMR) measurement was performed on the single-crystalline ferromagnetic (FM) superconductor UCoGe under a pressure of 1.09 GPa, where the FM state is suppressed and superconductivity occurs in the paramagnetic (PM) state, to study the superconducting (SC) state in the PMstate. $^{59}$Co-NMR spectra became broader but hardly shifted across the SC transition temperature. The Knight-shift change determined from fitting the spectral peak with a Gaussian was much smaller than the spin part of the Knight shift; this is in good agreement with the spin-triplet pairing suggested from the large upper critical field. The spectrum broadening in the SC state cannot be attributed to the SC diamagnetic effect but is related to the properties of spin-triplet superconductivity. The origins of the broadening are discussed herein.

Spin polarization and orbital effects in superconductor-ferromagnet structures

We study theoretically spontaneous currents and magnetic field induced in a superconductor-ferromagnet (S-F) bilayer due to direct and inverse proximity effects. The induced currents {are Meissner currents that appear even in the absence of an external magnetic field due to the magnetic moment in the ferromagnet }and {to the magnetization } in the superconductor . The latter is induced by the inverse proximity effect over a distance of the order of the superconducting correlation length $\xi _{S}$. On the other hand the magnetic induction $B$, caused by Meissner currents, penetrates the S film over the London length $\lambda _{S}$. Even though $\lambda _{S}$ usually exceeds considerably the correlation length, the amplitude and sign of $B$ at distances much larger than $\xi _{S}$ depends crucially on the strength of the exchange energy in the ferromagnet and on the magnetic moment induced in the in the S layer.

The 0–π Phase Transition in Epitaxial NbN/Ni60Cu40/NbN Josephson Junctions**Supported by the Strategic Priority Research Program (A) of Chinese Academy of Sciences under Grant No XDA18000000.

We fabricate high quality superconductor/ferromagnet/superconductor (SFS) Josephson junctions using epitaxial NbN/Ni60Cu40/NbN trilayer heterostructures. Both experimental measurements and theoretical calculations of the ferromagnet layer thickness dependence of the Josephson critical current are performed. We observe the damped oscillation behavior of the critical current as a function of the ferromagnetic layer thickness at 4.2 K, which shows a 0–π phase transition in this type of magnetic Josephson junction. Clear 0–π and reverse π–0 phase transitions occur around the Ni60Cu40 thicknesses of 3.2 and 6.7 nm. Numerical calculations based on the quasi-classical Usadel equation and the Green function fit well with the experimental results. Compared with the dirty limit, the intermediate regime without the dead layer gives better fit for our SFS Josephson junctions because of the epitaxial structure. Both of the 0- and π-phase junctions show the ideal magnetic field dependence with a Fraunhofer-like pattern at 4.2 K.

Direct Observation of Vortex and Meissner Domains in a Ferromagnetic Superconductor EuFe2(As0.79P0.21)2 Single Crystal

A spontaneous vortex structure in magnetic domains (vortex domains) has been visualized by the decoration technique near the ferromagnetic transition temperature (TC = 18 K) in a ferromagnetic superconductor EuFe2(As0.79P0.21)2 single crystal with the superconducting transition temperature (TSC = 22 K). Meissner domains previously observed by magnetic force microscopy have also been observed in a narrow temperature range (ΔT ∼ 1 K) near TC. A domain structure with the alternating direction of the magnetic flux has been observed upon cooling below TC. Experimental results are in reasonable agreement with a theoretical estimate of the periods of domain structures and the temperature interval below TC in which they are observed.

Novel critical behavior of magnetization in URhSi: Similarities to the uranium ferromagnetic superconductors UGe2 and URhGe

We study the critical behavior of dc magnetization in the uranium ferromagnet URhSi around the paramagnetic to ferromagnetic phase transition at ${T}_{\mathrm{C}}\ensuremath{\sim}10$ K with a modified Arrott plot, a Kouvel-Fisher plot, the critical isotherm analysis, and the scaling analysis. URhSi is isostructural to uranium ferromagnetic superconductors URhGe and UCoGe. The critical exponent $\ensuremath{\beta}$ for the temperature dependence of the spontaneous magnetization below ${T}_{\mathrm{C}}$, $\ensuremath{\gamma}$ for the magnetic susceptibility, and $\ensuremath{\delta}$ for the magnetic isotherm at ${T}_{\mathrm{C}}$ in URhSi have been determined as $\ensuremath{\beta}=0.300\ifmmode\pm\else\textpm\fi{}0.002$, $\ensuremath{\gamma}=1.00\ifmmode\pm\else\textpm\fi{}0.02$, and $\ensuremath{\delta}=4.38\ifmmode\pm\else\textpm\fi{}0.04$ by the scaling analysis and the critical isotherm analysis. These critical exponents fulfill the Widom scaling law $\ensuremath{\delta}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}1+\phantom{\rule{0.16em}{0ex}}\ensuremath{\gamma}/\ensuremath{\beta}$. Magnetization has strong uniaxial magnetic anisotropy in the ferromagnetic state of URhSi. However, the universality class of the ferromagnetic transition does not belong to the three-dimensional Ising system with short-range exchange interactions between magnetic moments ($\ensuremath{\beta}=0.325$, $\ensuremath{\gamma}=1.241$, and $\ensuremath{\delta}=4.82$). The obtained exponents in URhSi are similar to those in the uranium ferromagnetic superconductors ${\mathrm{UGe}}_{2}$ and URhGe, and uranium ferromagnets UIr and $\mathrm{U}({\mathrm{Co}}_{0.98}{\mathrm{Os}}_{0.02}$)Al. We have previously reported the unconventional critical behavior of magnetization in the uranium ferromagnetic superconductors [N. Tateiwa et al., Phys. Rev. B 89, 064420 (2014)]. The universality class of the ferromagnetic transition in URhSi may belong to the same one in the uranium ferromagnetic superconductors and the uranium ferromagnets. The unconventional critical behavior of the magnetization in the uranium compounds cannot be understood with previous theoretical interpretations of critical phenomena. The absence of the superconductivity in URhSi is discussed from several viewpoints. The improvement of the sample quality in URhSi could provide a good opportunity to gain a deeper understanding of the ferromagnetic superconductivity in the uranium ferromagnets.

Review of U-based Ferromagnetic Superconductors: Comparison between UGe2, URhGe, and UCoGe

The discovery in 2000 that the ferromagnetic (FM) compound UGe2 (T_Curie = 52 K at ambient pressure) becomes superconducting under a pressure of P = 1.1 GPa until it enters the paramagnetic (PM) phase above Pc = 1.6 GPa was a surprise. Successive searches for new materials (URhGe and UCoGe) led to the discovery of the coexistence of superconductivity (SC) and ferromagnetism at ambient pressure. Furthermore in UCoGe, it was found that SC survives in the PM regime from P_c = 1.1 to 4 GPa. Focus has been on low-temperature experiments under extreme conditions of magnetic field (H), pressure, and uniaxial stress. In UGe2, strong interplay exists between Fermi surface (FS) reconstructions in the cascade of different FM and PM ground states and their magnetic fluctuations. Similar phenomena occur in URhGe and UCoGe but, at first glance, the SC seems to be driven by the FM fluctuations. In UCoGe, a longitudinal field scan leads to a drastic decrease in the FM fluctuations, while a transverse field scan leads to suppression of the Curie temperature, T_Curie; the consequence is a boost in FM fluctuations, leading to a reinforcement of SC. The singularity in URhGe is the weakness of the anisotropy between c- and b-axes; the most noteworthy feature is the detection of reentrant SC near H_R. All the experimental results give evidence that the SC in these three materials originates from the FM fluctuations, which are amplitude modes of magnetic excitations in the FM state. Spin-triplet pairing has been anticipated in the FM superconductors and was actually observed by Knight-shift measurements in the SC state of UCoGe. Their fascinating (p, T, H) phase diagrams are now well established. Discussion is presented on how different theoretical approaches can describe the various phenomena discovered by experimentalists.

Ground-State Phase Diagram of theS= 1 One-Dimensional Kondo Lattice Model with a Uniaxial Anisotropy under Transverse Fields

We study the effects of transverse magnetic fields on the $S=1$ one-dimensional Kondo lattice model with a uniaxial anisotropy using the density matrix renormalization group. The model can be regarded as a simplified one for analyzing the Ising ferromagnetic superconductor URhGe. We find various phases such as ferromagnetic and antiferromagnetic phases, Kondo plateau (KP) phases, Tomonaga-Luttinger liquids, and fully polarized phases. In the KP phase, a pseudoplateau emerges in the magnetization due to strongly bound pairs between the local and the conduction electron spins. This is why we call this phase the Kondo plateau. At the critical field between the ferromagnetic and KP phases, we find metamagnetic behavior in the magnetization curve. We discuss various correlation functions and the Friedel oscillations in detail, and the experimental data under transverse magnetic fields in URhGe are discussed on the basis of the present results.

Triplet superconductivity in ferromagnets due to magnon exchange

We consider the superconducting pairing induced by spin waves exchange in a ferromagnet with both conduction and localized electrons, the latter being described as spins. We use the microscopic Eliashberg theory to describe the pairing of conducting electrons and the RPA approach to treat the localized spins assuming an exchange coupling between the conducting electrons and spins. In the framework of non relativistic Hamiltonian twe found that he spin wave exchange results in equal spin electron pairing described by the two components of the order parameter, $\Delta^{\uparrow}$ (both spins up) and $\Delta^{\downarrow}$ (both spins down). Due to the conservation of total spin projection on the axis of the spontaneous ferromagnetic moment, the spin wave exchange at low temperatures includes an emission of magnons and an absorption of thermal magnons by the conduction electrons. The absorption and emission processes depend differently on the temperature, with the absorption being progressively suppressed as the temperature drops. As a result, the superconducting pairing exists only if the electron-spin wave exchange parameter $g$ exceeds some critical value $g_c$. At $g>g_c$ pairing vanishes if the temperature drops below the lowest point $T_{cl}$ or increases above the upper critical point $T_{ch} \approx T_m$ (the Curie temperature) where the spin waves cease to exist. This behavior inherent to the spin carrying glue is in an obvious disagreement with the results of conventional BCS approach which assumes that the effective electron-electron attraction is simply proportional to the static magnetic susceptibility.

Pf-hybridization and magnetic phase transitions in ferromagnetic superconductors

Abstract In the framework of the Anderson pf-model, magnetic phase transitions in 5f-ferromagnetic superconductors with hybridization of localized (f-) and delocalized (p-) electrons are discussed. We consider a free-energy functional containing a contribution due to the mode-mode coupling spin fluctuations. The calculated p-T-diagram of magnetic states describes transitions of the first and second order and the region of the ferromagnetic short-range order too. It is shown that when the temperature and pressure change, a shift of the chemical potential to the pseudogap region is possible, with a jump-like increase in the occupation of the spin-symmetrized electronic states and an increase in the screening of the local magnetic moments.

Enhancement of superconductivity by pressure-induced critical ferromagnetic fluctuations in UCoGe

A $^{59}$Co nuclear quadrupole resonance (NQR) was performed on a single-crystalline ferromagnetic (FM) superconductor UCoGe under pressure. The FM phase vanished at a critical pressure $P_c$, and the NQR spectrum just below $P_c$ showed phase separation of the FM and paramagnetic (PM) phases below Curie temperature $T_{\textrm{Curie}}$, suggesting first-order FM quantum phase transition (QPT). We found that the internal field was absent above $P_c$, but the superconductivity is almost unchanged. This result suggests the existence of the nonunitary to unitary transition of the superconductivity around $P_c$. Nuclear spin-lattice relaxation rate $1/T_1$ showed the FM critical fluctuations around $P_c$, which persist above $P_c$ and are clearly related to superconductivity in the PM phase. This FM QPT is understood to be a weak first order with critical fluctuations. $1/T_1$ sharply decreased in the superconducting (SC) state above $P_c$ with a single component, in contrast to the two-component $1/T_1$ in the FM SC state, indicating that the inhomogeneous SC state is a characteristic feature of the FM SC state in UCoGe.

Unconventional superconductivity in 3d rocksalt transition metal carbides

Through calculation and analysis of the dynamic and electronic properties of 3d rocksalt transition metal carbides, we identify MnC as a novel material displaying ferromagnetic superconductivity mediated by minority-spin-triplet Cooper pairs.

Strong Correlation between Ferromagnetic Superconductivity and Pressure-enhanced Ferromagnetic Fluctuations in UGe_{2}.

We have measured magnetization at high pressure in the uranium ferromagnetic superconductor UGe_{2} and analyzed the magnetic data using Takahashi's spin fluctuation theory. There is a peak in the pressure dependence of the width of the spin fluctuation spectrum in the energy space T_{0} at P_{x}, the phase boundary of FM1 and FM2 where the superconducting transition temperature T_{sc} is highest. This suggests a clear correlation between the superconductivity and pressure-enhanced magnetic fluctuations developed at P_{x}. The pressure effect on T_{Curie}/T_{0}, where T_{Curie} is the Curie temperature, suggests that the less itinerant ferromagnetic state FM2 is changed to a more itinerant one FM1 across P_{x}. Peculiar features in relations between T_{0} and T_{sc} in uranium ferromagnetic superconductors UGe_{2}, URhGe, and UCoGe are discussed in comparison with those in high-T_{c} cuprate and heavy fermion superconductors.

Magnetism induced by nonlocal spin-entangled electrons in a superconducting spin-valve

In the traditional view, the magnetic moment appearing in the superconducting region is induced by equal-spin triplet superconducting correlations in superconductor (S) ferromagnet (F) heterostructure with noncollinear magnetization. In this paper, we represent that in (N-normal-metal) spin-valve structure the induced magnetic moment emerging in both the S and N regions can also be generated by Cooper pair splitting: one electron coherently tunnels from the S layer into the F1 layer, and the other one stays in the S layer or tunnels into the N layer. Two electrons are spatially separated from each other but their total spin ground state is entangled in this process. In contrast, the magnetic moment induced by the equal-spin triplet correlations hardly penetrates from the S layer into the N layer. In particular, by tuning the size of the exchange field and the thickness of the F1 layer, one may control the direction of the induced magnetic moment in the N layer. This interesting phenomenon can be attributed to the phase-shift obtained by the spin-entangled electrons. Our theoretical proposal will offer an effective way to control the entanglement of the nonlocal electrons, and also may provide possible explanations for previous and recent experimental observations (Stamopoulos et al 2005 Phys. Rev. B 72 212514; Ovsyannikov et al 2016 J. Exp. Theor. Phys. 122 738; Flokstra et al 2016 Nat. Phys. 12 57).

Local Magnetic States of the Weakly Ferromagnetic Iron-Based Superconductor Sr2VFeAsO3−δ Studied by X-ray Magnetic Circular Dichroism

We have performed X-ray magnetic circular dichroism (XMCD) measurements on the iron-based superconductor Sr2VFeAsO3−δ to study the origin of weak ferromagnetism (WFM) reported for this compound. While Fe 3d electrons show a magnetic response similar to the other iron pnictides, signals from V 3d electrons remain finite at zero magnetic field and may be responsible for the WFM.

Topological superconductivity in the Kondo-Kitaev model

We investigate possible topological superconductivity in the Kondo-Kitaev model on the honeycomb lattice, where the Kitaev spin liquid is coupled to conduction electrons via the Kondo coupling. We use the self-consistent Abrikosov-fermion mean-field theory to map out the phase diagram. Upon increasing the Kondo coupling, a first order transition occurs from the decoupled phase of spin liquid and conduction electrons to a ferromagnetic topological superconductor of Class D with a single chiral Majorana edge mode. This is followed by a second order transition into a paramagnetic topological superconductor of Class DIII with a single helical Majorana edge mode. These findings offer a novel route to topological superconductivity in the Kondo lattice system. We discuss the connection between topological nature of the Kitaev spin liquid and topological superconductors obtained in this model.

Effects of Lifshitz Transitions in Ferromagnetic Superconductors: The Case of URhGe.

In ferromagnetic superconductors, like URhGe, superconductivity coexists with magnetism near zero field, but then reappears in a finite field range, where the system also displays mass enhancement in the normal state. We present the theoretical understanding of this nonmonotonic behavior. We explore the multiband nature of URhGe and associate reentrant superconductivity and mass enhancement with the topological transition (Lifshitz) in one of the bands in a finite magnetic field. We find excellent agreement between our theory and a number of experimental results for URhGe, such as weakly first-order reentrant transition, the dependence of superconducting T_{c} on a magnetic field, and the field dependence of the effective mass, the specific heat, and the resistivity in the normal state. Our theory can be applied to other ferromagnetic multiband superconductors.

Vortex liquid phase in the p -wave ferromagnetic superconductor UCoGe

The upper critical field for field along the b-axis of the p-wave ferromagnetic superconductor UCoGe has a particular S-shape, akin to the re-entrant superconducting phase of URhGe. To explore the evolution of the superconducting phase under this transverse magnetic field, we report the thermal conductivity and resistivity measurements, revealing a possible field-induced vortex liquid phase, and supporting a field-induced change of the superconducting order parameter.

Domain Meissner state and spontaneous vortex-antivortex generation in the ferromagnetic superconductor EuFe2(As0.79P0.21)2.

The interplay between superconductivity and magnetism is one of the oldest enigmas in physics. Usually, the strong exchange field of ferromagnet suppresses singlet superconductivity via the paramagnetic effect. In EuFe2(As0.79P0.21)2, a material that becomes not only superconducting at 24.2 K but also ferromagnetic below 19 K, the coexistence of the two antagonistic phenomena becomes possible because of the unusually weak exchange field produced by the Eu subsystem. We demonstrate experimentally and theoretically that when the ferromagnetism adds to superconductivity, the Meissner state becomes spontaneously inhomogeneous, characterized by a nanometer-scale striped domain structure. At yet lower temperature and without any externally applied magnetic field, the system locally generates quantum vortex-antivortex pairs and undergoes a phase transition into a domain vortex-antivortex state characterized by much larger domains and peculiar Turing-like patterns. We develop a quantitative theory of this phenomenon and put forth a new way to realize superconducting superlattices and control the vortex motion in ferromagnetic superconductors by tuning magnetic domains-unprecedented opportunity to consider for advanced superconducting hybrids.