We construct a mean-field theory for itinerant ferromagnetism coexisting with a non-unitary superconducting state, where only the majority-spin band is gapped and contains line nodes, while the minority-spin band is gapless at the Fermi level. Our study is motivated by recent experimental results indicating that this may be the physical situation realized in the heavy-fermion compound UGe$_2$. We investigate the stability of the mean-field solution of the magnetic and superconducting order parameters. Also, we provide theoretical predictions for experimentally measurable properties of such a non-unitary superconductor: the specific heat capacity, the Knight shift, and the tunneling conductance spectra. Our study should be useful for direct comparison with experimental results and also for further predictions of the physics that may be expected in ferromagnetic superconductors.
For the UGe$_2$ ferromagnetic superconductor the forms of the order parameter admitted by the crystal symmetry within the strong spin-orbit coupling scheme are written down. For each of the two possible phases existence of gap nodes required by symmetry is discussed and the nodes are found. Some consequences of presence of the nodes, which may be useful for experimental identification of the phases are discussed as well.
Recently co-existence of the ferromagnetism and superconductivity was reported in the high-pressure region (1.0-1.6 GPa) in UGe$_2$. We performed the heat capacity measurement on UGe$_2$ under high pressure. At 1.13 GPa, we found a peak corresponding to the superconducting transition. The superconducting temperature $T_{SC}$ and ${\itΔ} C/(γT_{SC})$ are 0.6 K and 0.25, respectively. The superconducting transition was also confirmed by the appearance of the Meissner effect in the {\it ac} susceptibility. From these results, we confirm a bulk nature of the superconductivity in UGe$_2$. The value…
It is assumed that U atoms in $UGe_2$ have a number of $f$ electrons appropriate to give them each a spin $s=1$ as well as one extra itinerant electron which may equally well be on one or other U atom. The dynamical degrees of freedom are spin-s operators of localized spins and spin-1/2 fermi operators of itinerant electrons. Applying hydrostatic pressure changes the bandwidths of spin-up and spin-down itinerant electrons in different way, which leads to decreasing of the contribution of the fermions to the magnetization keeping the spin-fermion interaction unchanged. In turn the local spin-fe…
The present paper discusses magnon-mediated superconductivity in ferromagnetic metals. The mechanism explains in a natural way the fact that the superconductivity in UGe_2, ZrZn_2 and URhGe is apparently confined to the ferromagnetic phase.The order parameter is a spin anti-parallel component ofa spin-1 triplet with zero spin projection. The transverse spinfluctuations are pair forming and the longitudinal ones are pair breaking.The competition between magnons and paramagnons explains the existence of two successive quantum phase transitions in UGe_2, from ferromagnetism to ferromagnetic super…
We present a unified theory of magnetism and superconductivity of $UGe_2$. To this end, we consider part of $5f$ uranium electrons as mostly itinerant and other ones as mostly localized. The main feature that distinguishes the localized from the itinerant electrons is the effect of the pressure on them. The pressure strongly screens the itinerant electrons while the localized ones are almost unaffected. The screening of itinerant electrons leads to decreasing of their Coulomb repulsion, therefore to formation of doubly occupied and empty states. These states are spin-singlet and the effective …
We report on the itinerant ferromagnetic superconductor UGe_2 through ^73Ge-NQR measurements under pressure (P). The P dependence of the NQR spectrum signals a first-order transition from the low-temperature (T) and low-P ferromagnetic phase (FM2) to high-T and high-P one (FM1) around a critical pressure of P_x ~ 1.2 GPa. The superconductivity exhibiting a maximum value of T_sc=0.7 K at P_x ~ 1.2 GPa, was found to take place in connection with the P-induced first-order transition. The nuclear spin-lattice relaxation rate 1/T_1 has probed the ferromagnetic transition, exhibiting a peak at the C…
Inelastic neutron scattering was used to study the low energy magnetic excitations of the ferromagnetic superconductor UGe$_{2}$. The ferromagnetic fluctuations are of Ising nature with a non-conserved magnetization and have an intermediate behavior between localized and itinerant magnetism.
The coexistence of a homogeneous (Meissner-like) phase of spin-triplet superconductivity and ferromagnetism is investigated within the framework of a phenomenological model of spin-triplet ferromagnetic superconductors. The results are discussed in view of application to metallic ferromagnets as UGe$_2$, ZrZn$_2$, URhGe, and Fe.
The recent discovery that superconductivity occurs in several clean itinerant ferromagnets close to low temperature magnetic instabilities naturally invites an interpretation based on a proximity to quantum criticality. Here we report measurements of the pressure dependence of the low temperature magnetisation in one of these materials, UGe_2. Our results show that both of the magnetic transitions observed in this material as a function of pressure are first order transitions and do not therefore correspond to quantum critical points. Further we find that the known pressure dependence of the s…
We discuss the possibility of coexistence of spin-singlet superconductivity and ferromagnetism in a model where the same electrons are assumed responsible for both of them. Our calculations include both zero and finite momentum pairing states with both s-wave and d-wave pairing symmetry. Under the mean-field approximation, the thermodynamic potential of the non-magnetic superconducting (SC) state is shown to be always lower than that of the superconducting ferromagnetic (SF) state. It follows that the spin-singlet SF state is energetically unfavorable, and a spin-triplet SF state is more likel…
A model for coexistence of p-wave spin-triplet superconductivity (SC) and itinerant ferromagnetism (FM) is presented. The Hamiltonian can be diagonalized by using the so(5) algebraic coherent state. We obtain the coupling equations of the magnetic exchange energy and superconducting gaps through the double-time Green function. It is found that the ferromagnetisation gives rise to the phase transitions of p-wave superconducting states or superfluid of $^{3}He$.
A consistent picture on the mean-field level of the magnetic properties and electronic structure of the superconducting itinerant ferromagnet UGe$_2$ is shown to require inclusion of correlation effects beyond the local density approximation (LDA). The "LDA+U" approach reproduces both the magnitude of the observed moment, composed of strongly opposing spin and orbital parts, and the magnetocrystalline anisotropy. The largest Fermi surface sheet is comprised primarily of spin majority states with orbital projection $m_{\ell}$=0, suggesting a much simpler picture of the pairing than is possible …
We have carried out detailed magnetic and transport studies of the new Sr0.5Ce0.5FBiS2-xSex (x = 0.5, 1) superconductors derived by doping Se in Sr0.5Ce0.5FBiS2. Se-doping produces several effects: it suppresses semiconducting like behavior observed in the undoped Sr0.5Ce0.5FBiS2, ferromagnetic ordering temperature, TFM, decreases considerably from 7.5 K (in Sr0.5Ce0.5FBiS2) to 3.5 K and superconducting transition temperature, Tc, gets enhanced slightly to 2.9 - 3.3 K. Thus in these Se-doped materials, TFM is just marginally higher than Tc. Magnetization studies provide an evidence of bulk sup…
Heterostructures made of itinerant ferromagnets and superconductors are studied. In contrast to most previous models, ferromagnetism is not enforced as an external Zeeman field but induced in a correlated single-band model (CSBM) that displays itinerant ferromagnetism as a mean-field ground state. This allows us to investigate the influence of an adjacent superconducting layer on the properties of the ferromagnet in a self-consistent Bogoliubov-de Gennes approach. The CSBM displays a variety features not present in the Zeeman exchange model that influence the behavior of order parameters close…
The triplet superconductivity in $UGe_2$ and $URhGe$ coexists with itinerant ferromagnetism such that in the pressure-temperature phase diagram the whole region occupied by the superconducting state is situated inside a more vast ferromagnetic region. In the same family metal UCoGe the pressure dependent critical lines T_{Curie}(P) and T_{sc}(P) of the ferromagnet and the superconducting phase transitions intersect each other. The two-band multidomain superconducting ferromagnet state arises at temperatures below both of these lines. Here I describe the symmetry and the order parameters of the…
We study the electronic instabilities of doped bilayer silicene using the random phase approximation. In contrast to the singlet $d+id'$ superconductivity at the low doping region, we find that the system is an itinerant ferromagnet in the narrow doping regions around the Van Hove singularities, and a triplet $p+ip'$ superconductor in the vicinity of these regions. Adding a weak Kane-Mele spin-orbit coupling to the system further singles out the time-reversal invariant equal-spin helical $p+ip'$ pairing as the leading instability. The triplet pairing identified here is driven by the ferromagne…
In this paper we study the ground state phase diagram of a one-dimensional $t-U-J$ model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin-1/2 XY model takes place.
Magnetization, nuclear magnetic resonance, high-resolution x-ray diffraction and magnetic field-dependent neutron diffraction measurements reveal a novel magnetic ground state of Ba{0.60}K{0.40}Mn2As2 in which itinerant ferromagnetism (FM) below a Curie temperature TC = 100 K arising from the doped conduction holes coexists with collinear antiferromagnetism (AFM) of the Mn local moments that order below a Neel temperature TN = 480 K. The FM ordered moments are aligned in the tetragonal ab-plane and are orthogonal to the AFM-ordered Mn moments that are aligned along the c-axis. The magnitude an…
We discuss the form of the damping of magnetic excitations in a metal near a ferromagnetic instability. The paramagnon theory predicts that the damping term should have the form $Ω/Γ(q)$ with $Γ(q) \propto q$ (the Landau damping). However, the experiments on uranium metallic compounds UGe$_2$ and UCoGe showed that $Γ(q)$ tends to a constant value at vanishing $q$. A non-zero $Γ(0)$ is impossible in systems with one type of carriers (either localized or itinerant) because it would violate the spin conservation. It has been conjectured recently that a non-zero $Γ(q)$ in UGe$_2$ and UCoGe may be …
A comprehensive theory is developed that describes the coexistence of p-wave, spin-triplet superconductivity and itinerant ferromagnetism. It is shown how to use field-theoretic techniques to derive both conventional strong-coupling theory, and analogous gap equations for superconductivity induced by magnetic fluctuations. It is then shown and discussed in detail that the magnetic fluctuations are generically stronger on the ferromagnetic side of the magnetic phase boundary, which substantially enhances the superconducting critical temperature in the ferromagnetic phase over that in the parama…
The electronic and magnetic properties of cobalt-based layered oxypnictides, LaCoOX (X = P, As), are investigated. LaCoOP and LaCoOAs show metallic type conduction, and the Fermi edge is observed by hard x-ray photoelectron spectroscopy. Ferromagnetic transitions occur at 43 K for LaCoOP and 66 K for LaCoOAs. Above the transition temperatures, temperature dependence of the magnetic susceptibility follows the Curie-Weiss law. X-ray magnetic circular dichroism (XMCD) is observed at the Co L2,3-edge, but not at the other edges. The calculated electronic structure shows a spin polarized ground sta…
$A$Co$_2$Se$_2$ ($A$=K,Rb,Cs) is a homologue of the iron-based superconductor, $A$Fe$_2$Se$_2$. From a comprehensive study of RbCo$_2$Se$_2$ via measurements of magnetization, transport, neutron diffraction, angle-resolved photoemission spectroscopy, and first-principle calculations, we identify a ferromagnetic order accompanied by an orbital-dependent spin-splitting of the electronic dispersions. Furthermore, we identify the ordered moment to be dominated by a $d_{x^2-y^2}$ flatband near the Fermi level, which exhibits the largest spin splitting across the ferromagnetic transition, suggesting…
Ferromagnetism and superconductivity are antagonistic phenomena. Their coexistence implies either a modulated ferromagnetic order parameter on a lengthscale shorter than the superconducting coherence length or a weak exchange coupling between the itinerant superconducting electrons and the localized ordered spins. In some iron based pnictide superconductors the coexistence of ferromagnetism and superconductivity has been clearly demonstrated. The nature of the coexistence, however, remains elusive since no clear understanding of the spin structure in the superconducting state has been reached …
We investigate thermodynamic phases, including the phase of coexistence of superconductivity and ferromagnetism, the possible phase transitions of first and second order, and the shape of the phase diagram in mean-field approximation for a phenomenological model of spin-triplet ferromagnetic superconductors. The results are discussed in view of application to metallic ferromagnets as UGe$_2$, ZrZn$_2$, URhGe, and Fe.
Superconductivity has again become a challenge following the discovery of unconventional superconductivity. Resistance-free currents have been observed in heavy-fermion materials, organic conductors and copper oxides. The discovery of superconductivity in a single crystal of $UGe_2$, $ZrZn_2$ and $URhGe$ revived the interest in the coexistence of superconductivity and ferromagnetism. The experiments indicate that: i)The superconductivity is confined to the ferromagnetic phase. ii)The ferromagnetic order is stable within the superconducting phase (neutron scattering experiments). iii) The speci…
We report the coexistence of ferromagnetic order and superconductivity in UCoGe at ambient pressure. Magnetization measurements show that UCoGe is a weak ferromagnet with a Curie temperature T_{C}= 3 K and a small ordered moment $m_{0}$= 0.03 $μ_B$. Superconductivity is observed with a resistive transition temperature T_{s} = 0.8 K for the best sample. Thermal-expansion and specific-heat measurements provide solid evidence for bulk magnetism and superconductivity. The proximity to a ferromagnetic instability, the defect sensitivity of T_{s}, and the absence of Pauli limiting, suggest triplet s…
We characterize the coexistence of itinerant ferromagnetism and spin-triplet superconductivity within a single mechanism involving local (Hund's rule) exchange among $d$ electrons. The ratio of transition temperatures and the spin anisotropy of the superconducting gap is estimated for $ZrZn_2$. The $A$ phase is stable in very low applied and molecular fields, whereas the $A1$ phases persists in higher fields. A small residual magnetic moment is present below the Stoner threshold in the superconducting phase.
A microscopic mean-field theory of the phase coexistence between ferromagnetism and superconductivity in the weakly ferromagnetic itinerant electron system is constructed, while incorporating a realistic mechanism for superconducting pairing due to the exchange of critical spin fluctuations. The self-consistent solution of the resulting equations determines the superconducting transition temperature which is shown to depend strongly on the exchange splitting. The effect of phase crossover from isotropic (Heisenberg-like) to uniaxial (Ising-like) spin fluctuations near the quantum phase transit…
Recent results for the coexistence of ferromagnetism and unconventional superconductivity with spin-triplet Cooper pairing are reviewed on the basis of the quasi-phenomenological Ginzburg-Landau theory. New results are reported. The results are discussed in view of applications to metallic compounds as UGe2, URhGe, ZrZn2.
In superconducting ferromagnets for which the Curie temperature $T_{m}$ exceeds the superconducting transition temperature $T_{c}$, it was suggested that ferromagnetic spin fluctuations could lead to superconductivity with p-wave spin triplet Cooper pairing. Using the Stoner model of itinerant ferromagnetism, we study the feedback effect of the p-wave superconductivity on the ferromagnetism. Below $T_{c}$, the ferromagnetism is enhanced by the p-wave superconductivity. At zero temperature, the critical Stoner value for itinerant ferromagnetism is reduced by the strength of the p-wave pairing p…
Recent results about the coexistence of ferromagnetism and unconventional superconductivity with spin-triplet Cooper pairing are reviewed on the basis of the quasi-phenomenological Ginzburg-Landau theory. The superconductivity in the mixed phase of coexistence of ferromagnetism and unconventional superconductivity is triggered by the spontaneous magnetization. The mixed phase is stable whereas the other superconducting phases that usually exist in unconventional superconductors are either unstable or metastable at relatively low temperatures in a quite narrow domain of the phase diagram and th…
The experimental results for ZrZn$_{2}$, URhGe, and in some pressure ranges also for UGe$_{2}$, have shown that the ferromagnetic superconductors are weak itinerant ferromagnets. Guided by these results we describe the phenomenon of coexistence between equal spin triplet pairing superconductivity (SC) and ferromagnetism (F) using the extended Stoner model, which includes in Hamiltonian the on-site Coulomb interaction, $U$, and occupation dependent hopping integral. We use Hartree-Fock (H-F) approximation and the Green functions technique. In the H-F approximation the on-site Coulomb interactio…
We argue that a single-band itinerant electron model with short-range interactions, proposed by Karchev et al. (cond-mat/9911489) and investigated further by Jackiewicz et al. (cond-mat/0302449), cannot describe the coexistence of superconducting and ferromagnetic order.
