Effect of spin fluctuations on the magnetic equation of state of ferromagnetic or nearly ferromagnetic metals

The case of itinerant magnetism in CaMn2Al10: self-consistent renormalisation (SCR) theory study

We have applied the powerful self-consistent renormalization theory of spin fluctuations for the system CaMn₂Al₁₀discovered in 2015 and was conjectured to be an itinerant magnet. We have calculated the inverse static i.e. (paramagnetic) susceptibility and have compared it with the experimental data (Steinkeet al2015Phys. Rev.B92020413). The agreement is very good. We have calculated spin fluctuations at various temperatures and have also estimated the strength of the electronic correlation i.e. (U = 0.3136 eV) in the Hubbard Hamiltonian. Based on our quantitative explanation of the inverse static i.e. (paramagnetic) susceptibility data within the framework of self-consistent renormalization theory, we can decisively conclude CaMn₂Al₁₀exhibits the phenomena of itinerant magnetism. Further, our density functional theory (DFT) and DFT + U calculations corroborate the strong Mn-Al hybridization which is the key to the itinerant magnetism in this system. Our estimated correlations strength will provide a foundation for further studies of itinerant magnetism in this system.

Influence of Ni content on structural, magnetocaloric and electrical properties in manganite La0.6Ba0.2Sr0.2Mn1-x Ni x O3 (0 ≤ x ≤ 0.1) type perovskites

We present a detailed study on the physical properties of La0.6Ba0.2Sr0.2Mn1-x Ni x O3 samples (x = 0.00, 0.05 and 0.1). The ceramics were fabricated using the sol-gel route. Structural refinement, employing the Rietveld method, disclosed a rhombohedral R3̄c phase. The magnetization vs. temperature plots show a paramagnetic-ferromagnetic (PM-FM) transition phase at the T C (Curie temperature), which decreases from 354 K to 301 K. From the Arrott diagrams M 2 vs. μ 0 H/M, we can conclude the phase transition is of the second order. Based on measurements of the isothermal magnetization around T C, the magnetocaloric effects (MCEs) have been calculated. The entropy maximum change (-ΔS M) values are 7.40 J kg-1 K-1, 5.6 J kg-1 K-1 and 4.48 J kg-1 K-1, whereas the relative cooling power (RCP) values are 232 J kg-1, 230 J kg-1 and 156 J kg-1 for x = 0.00, 0.05 and 0.10, respectively, under an external field (μ 0 H) of 5 T. Through these results, the La0.6Ba0.2Sr0.2Mn1-x Ni x O3 (0 ≤ x ≤ 0.1) samples can be suggested for use in magnetic refrigeration technology above room temperature. The electrical resistivity (ρ) vs. temperature plots exhibit a transition from metallic behavior to semiconductor behavior in the vicinity of T M-SC. The adiabatic small polaron hopping (ASPH) model is applied in the PM-semiconducting part (T > T MS). Throughout the temperature range, ρ is adjusted by the percolation model. This model is based on the phase segregation of FM-metal clusters and PM-insulating regions.

Spin fluctuations yield zT enhancement in ferromagnets

Thermal fluctuation of local magnetization intercoupled with charge carriers and phonons offers a path to enhance thermoelectric performance. Thermopower enhancement by spin fluctuations (SF) has been observed before. However, the crucial evidence for enhancing thermoelectric-figure-of-merit (zT) by SF has not been reported until now. Here we report that the SF leads to nearly 80% zT enhancement in ferromagnetic CrTe near and below T_C ∼ 335 K. The ferromagnetism is originated from the collective electronic and localized magnetic moments. The field-dependent transport properties demonstrate the profound impact of SF on the electrons and phonons. Under an external magnetic field, the enhancement in thermopower is suppressed, and the thermal conductivity is enhanced, evidencing the existence of a strong SF. The anomalous thermoelectric transport properties are analyzed based on theoretical models, and a good agreement with experimental data is found. This study contributes to the fundamental understanding of SF for designing high-performance spin-driven thermoelectrics.

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Spin-dependent thermoelectric properties are investigated

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Itinerate ferromagnetism-induced Stoner excitation favors thermoelectric transport

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Spin fluctuation contribution dominates spin-wave to the transport properties in CrTe

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Spin fluctuations boost zT by 80% near and below the transition temperature in CrTe

Skyrmion Phase in MnSi Thin Films Grown on Sapphire by a Conventional Sputtering

Topologically protected chiral skyrmions are an intriguing spin texture that has attracted much attention because of fundamental research and future spintronic applications. MnSi with a non-centrosymmetric structure is a well-known material hosting a skyrmion phase. To date, the preparation of MnSi crystals has been investigated by using special instruments with an ultrahigh vacuum chamber. Here, we introduce a facile way to grow MnSi films on a sapphire substrate using a relatively low vacuum environment of conventional magnetron sputtering. Although the as-grown MnSi films have a polycrystalline nature, a stable skyrmion phase in a broad range of temperatures and magnetic fields is observed via magnetotransport properties including phenomenological scaling analysis of the Hall resistivity contribution. Our findings provide not only a general way to prepare the materials possessing skyrmion phases but also insight into further research to stimulate more degrees of freedom in our inquisitiveness.

The Characteristic Properties of Magnetostriction and Magneto-Volume Effects of Ni2MnGa-Type Ferromagnetic Heusler Alloys

In this article, we review the magnetostriction and magneto-volume effects of Ni₂MnGa-type ferromagnetic Heusler alloys at the martensitic, premartensitic, and austenitic phases. The correlations of forced magnetostriction (ΔV/V) and magnetization (M), using the self-consistent renormalization (SCR) spin fluctuation theory of an itinerant electron ferromagnet proposed by Takahashi, are evaluated for the ferromagnetic Heusler alloys. The magneto-volume effect occurs due to the interaction between the magnetism and volume change of the magnetic crystals. The magnetic field-induced strain (referred to as forced magnetostriction) and the magnetization are measured, and the correlation of magnetostriction and magnetization is evaluated. The forced volume magnetostriction ΔV/V at the Curie temperature, T_C is proportional to M⁴, and the plots cross the origin point; that is, (M⁴, ΔV/V) = (0, 0). This consequence is in good agreement with the spin fluctuation theory of Takahashi. An experimental study is carried out and the results of the measurement agree with the theory. The value of forced magnetostriction is proportional to the valence electron concentration per atom (e/a). Therefore, the forced magnetostriction reflects the electronic states of the ferromagnetic alloys. The magnetostriction near the premartensitic transition temperature (T_P) induces lattice softening; however, lattice softening is negligible at T_C. The forced magnetostriction at T_C occurs due to spin fluctuations of the itinerant electrons. In the martensitic and premartensitic phases, softening of the lattice occurs due to the shallow hollow (potential barrier) of the total energy difference between the L2₁ cubic and modulated 10M or 14M structures. As a result, magnetostriction is increased by the magnetic field.

Spin-fluctuation and spin-relaxation effects of single adatoms from first principles

Single adatoms offer an exceptional playground for studying magnetism and its associated dynamics at the atomic scale. Here we review recent results on single adatoms deposited on metallic substrates, based on time-dependent density functional theory. First we analyze quantum zero-point spin-fluctuations (ZPSF) as calculated from the fluctuation-dissipation theorem, and show how they affect the magnetic stability by modifying the magnetic anisotropy energy. We also assess the impact of ZPSF in the limit of small hybridization to the substrate characteristic of semi-insulating substrates, connecting to recent experimental investigations where magnetic stability of a single adatom was achieved for the first time. Secondly, we inspect further the dynamics of single adatoms by considering the longitudinal and transverse spin-relaxation processes, whose time-scales are analyzed and related to the underlying electronic structure of both the adatom and the substrate. Thirdly, we analyze spin-fluctuation modes of paramagnetic adatoms, i.e. adatoms where the Stoner criterion for magnetism is almost fulfilled. Interestingly, such modes can develop well-defined peaks in the meV range, their main characteristics being determined by two fundamental electronic properties, namely the Stoner parameter and the density of states at the Fermi level. Furthermore, simulated inelastic scanning tunneling spectroscopy curves reveal that these spin-fluctuation modes can be triggered by tunneling electrons, opening up potential applications also for paramagnetic adatoms. Lastly, an overview of the outstanding issues and future directions is given.

Large magnetic entropy change and prediction of magnetoresistance using a magnetic field in La0.5Sm0.1Sr0.4Mn0.975In0.025O3

A detailed study of the structural, magnetic, magnetocaloric and electrical effect properties in polycrystalline manganite La_0.5Sm_0.1Sr_0.4Mn_0.975In_0.025O₃ is presented. The X-ray diffraction pattern is consistent with a rhombohedral structure with R3̄c space group. Experimental results revealed that our compound prepared via a sol-gel method exhibits a continuous (second-order) ferromagnetic (FM) to paramagnetic (PM) phase transition around the Curie temperature (T _C = 300 K). In addition, the magnetic entropy change was found to reach 5.25 J kg^-1 K^-1 under an applied magnetic field of 5 T, corresponding to a relative cooling power (RCP) of 236 J kg^-1. We have fitted the experimental data of resistivity using a typical numerical method (Gauss function). The simulation values such as maximum resistivity (ρ _max) and metal-semiconductor transition temperature (T _M-Sc), calculated from this function, showed a perfect agreement with the experimental data. The shifts of these parameters as a function of magnetic field for our sample have been interpreted. The obtained values of β and γ, determined by analyzing the Arrott plots, are found to be T _C = 298.66 ± 0.64 K, β = 0.325 ± 0.001 and γ = 1.25 ± 0.01. The critical isotherm M (T _C, μ ₀ H) gives δ = 4.81 ± 0.01. These critical exponent values are found to be consistent and comparable to those predicted by the three-dimensional Ising model with short-range interaction. Thus, the Widom scaling law is fulfilled.

Tuning Paramagnetic Spin Excitations of Single Adatoms

We predict the existence of paramagnetic spin excitations (PSE) in nonmagnetic single adatoms. Our calculations demonstrate that PSE develop a well-defined structure in the meV region when the adatom's Stoner criterion for magnetism is close to the critical point. We further reveal a subtle tunability and enhancement of PSE by external magnetic fields. Finally, we show how PSE can be detected as moving steps in the dI/dV signal of inelastic scanning tunneling spectroscopy, opening a potential route for experimentally accessing electronic properties of nonmagnetic adatoms, such as the Stoner parameter.

Weyl fermions and spin dynamics of metallic ferromagnet SrRuO3

Weyl fermions that emerge at band crossings in momentum space caused by the spin–orbit interaction act as magnetic monopoles of the Berry curvature and contribute to a variety of novel transport phenomena such as anomalous Hall effect and magnetoresistance. However, their roles in other physical properties remain mostly unexplored. Here, we provide evidence by neutron Brillouin scattering that the spin dynamics of the metallic ferromagnet SrRuO₃ in the very low energy range of milli-electron volts is closely relevant to Weyl fermions near Fermi energy. Although the observed spin wave dispersion is well described by the quadratic momentum dependence, the temperature dependence of the spin wave gap shows a nonmonotonous behaviour, which can be related to that of the anomalous Hall conductivity. This shows that the spin dynamics directly reflects the crucial role of Weyl fermions in the metallic ferromagnet.

Whilst Weyl fermions have characteristic effects in magnetotransport measurements in condensed matter systems, their effects on other properties remain unexplored. Here, the authors use neutron Brillouin scattering to evidence the interaction of Weyl fermions with the spin wave dynamics in SrRuO₃.

Quantum Critical Behavior in a Concentrated Ternary Solid Solution

The face centered cubic (fcc) alloy NiCoCr_x with x ≈ 1 is found to be close to the Cr concentration where the ferromagnetic transition temperature, T_c, goes to 0. Near this composition these alloys exhibit a resistivity linear in temperature to 2 K, a linear magnetoresistance, an excess –TlnT (or power law) contribution to the low temperature heat capacity, and excess low temperature entropy. All of the low temperature electrical, magnetic and thermodynamic properties of the alloys with compositions near x ≈ 1 are not typical of a Fermi liquid and suggest strong magnetic fluctuations associated with a quantum critical region. The limit of extreme chemical disorder in this simple fcc material thus provides a novel and unique platform to study quantum critical behavior in a highly tunable system.

Chemical composition tuning of the anomalous Hall effect in isoelectronic L10FePd(1-x)Pt(x) alloy films

The anomalous Hall effect (AHE) in L1(0)FePd(1-x)Pt(x) alloy films is studied both experimentally and theoretically. We find that the intrinsic contribution (σ(AH)(int)) to the AHE can be significantly increased, whereas the extrinsic side-jump contribution (σ(AH)(sj)) can be continuously reduced from being slightly larger than σ(AH)(int) in L1(0) FePd to being much smaller than σ(AH)(int) in L1(0) FePt, by increasing the Pt composition x. We show that this chemical composition tuning of the intrinsic contribution is afforded by the stronger spin-orbit coupling strength on the Pd/Pt site when the lighter Pd atoms are replaced by the heavier Pt atoms. Our results provide a means of manipulating the competing AHE mechanisms in ferromagnetic alloys for fully understanding the AHE and also for technological applications of ferromagnetic alloys.

Anisotropic critical magnetic fluctuations in the ferromagnetic superconductor UCoGe

We report neutron scattering measurements of critical magnetic excitations in the weakly ferromagnetic superconductor UCoGe. The strong non-Landau damping of the excitations we observe, although unusual, has been found in another related ferromagnet, UGe(2) at zero pressure. However, we also find that there is a significant anisotropy of the magnetic correlation length in UCoGe that contrasts with an almost isotropic length for UGe(2). The values of the magnetic correlation length and damping are found to be compatible with superconductivity on small Fermi-surface pockets. The anisotropy may be important to explain why UCoGe is a superconductor at zero pressure while UGe(2) is not.

Extended dynamic spin-fluctuation theory of metallic magnetism

A dynamic spin-fluctuation theory that directly takes into account nonlocality of thermal spin fluctuations and their mode-mode interactions is developed. The Gaussian approximation in the theory is improved by a self-consistent renormalization of the mean field and spin susceptibility due to the third-and fourth-order terms of the free energy, respectively. This eliminates the fictitious first-order phase transition, which is typical for the Gaussian approximation, and yields a proper second-order phase transition. The effect of nonlocal spin correlations is enhanced by taking into account uniform fluctuations in the single-site mean Green function. Explicit computational formulae for basic magnetic characteristics are obtained. The extended theory is applied to the calculation of magnetic properties of Fe-Ni Invar. Almost full agreement with experiment is achieved for the magnetization, Curie temperature, and local and effective magnetic moments.

Direct observation of paramagnons in palladium

We report an inelastic neutron scattering study of the spin fluctuations in the nearly ferromagnetic element palladium. Dispersive over-damped collective magnetic excitations or "paramagnons" are observed up to 128 meV. We analyze our results in terms of a Moriya-Lonzarich-type spin-fluctuation model and estimate the contribution of the spin fluctuations to the low-temperature heat capacity. In spite of the paramagnon excitations being relatively strong, their relaxation rates are large. This leads to a small contribution to the low-temperature electronic specific heat.

Skyrmion lattices in metallic and semiconducting B20 transition metal compounds

High pressure studies in MnSi suggest the existence of a non-Fermi liquid state without quantum criticality. The observation of partial magnetic order in a small pocket of the pressure versus temperature phase diagram of MnSi has additionally inspired several proposals of complex spin textures in chiral magnets. We used neutron scattering to observe the formation of a two-dimensional lattice of skyrmion lines, a type of magnetic vortices, under applied magnetic fields in metallic and semiconducting B20 compounds. In strongly disordered systems the skyrmion lattice is hysteretic and extends over a large temperature range. Our study experimentally establishes magnetic materials lacking inversion symmetry as an arena for new forms of spin order composed of topologically stable spin textures.

Quantum order in the chiral magnet MnSi

Systems lacking inversion symmetry, such as selected three-dimensional compounds, multilayers and surfaces support Dzyaloshinsky-Moriya (DM) spin-orbit interactions. In recent years DM interactions have attracted great interest, because they may stabilize magnetic structures with a unique chirality and non-trivial topology. The inherent coupling between the various properties provided by DM interactions is potentially relevant for a variety of applications including, for instance, multiferroic and spintronic devices. The, perhaps, most extensively studied material in which DM interactions are important is the cubic B20 compound MnSi. We review the magnetic field and pressure dependence of the magnetic properties of MnSi. At ambient pressure this material displays helical order. Under hydrostatic pressure a non-Fermi liquid state emerges, where a partial magnetic order, reminiscent of liquid crystals, is observed in a small pocket. Recent experiments strongly suggest that the non-Fermi liquid state is not due to quantum criticality. Instead it may be the signature of spin textures and spin excitations with a non-trivial topology.

Magnetic properties of Ni(3)Al and Ni(3)Ga: emergent states and the possible importance of a tri-critical point

We present a study of the magnetic properties of the itinerant-electron systems Ni(3)Al and Ni(3)Ga at ambient pressure. In both compounds the magnetization and susceptibility show a non-Fermi liquid form. We test these properties using a mean-field model of enhanced spin fluctuations on the border of ferromagnetism in three dimensions with no adjustable parameters. While Ni(3)Al is found to be explained well by the standard form of such a model, the data on Ni(3)Ga require us to extend the model to take into account the fact that this system lies close to a tri-critical point. We suggest that such a quantum tri-critical point may be a key feature in the understanding of quantum critical systems more generally.

Magnetic excitations in an itinerant ferromagnet near quantum criticality

We determine the initial temperature dependence of the exchange splitting Delta(T) in the weak itinerant ferromagnet ZrZn2 (T{C}=28 K) using the de Haas-van Alphen effect. There is a large decrease in Delta with temperature in the range 0.5< or =T< or =4 K. A comparison of Delta(T) with the magnetization M(T) shows that the dominant process responsible for the reduction of M is not the thermal excitation of spin waves, but a repopulation of the spin- upward arrow and spin- downward arrow Fermi surfaces. This contrasts with the behavior in Fe where there is no observable change in Delta and the thermal excitation of spin waves is the only observable spin-flipping process at low temperatures.

Magnetic field and pressure dependence of small angle neutron scattering in MnSi

We report small angle neutron scattering of spontaneous and magnetic field aligned components of the helical spin polarization in MnSi for temperatures T down to 0.35 K, at pressures p up to 21 kbar, and magnetic field B up to 0.7 T. The parameter range of our study spans the first order transition between helical order and partial magnetic order at p{c}=14.6 kbar, which coincides with the onset of an extended regime of non-Fermi liquid resistivity. Our study suggests that MnSi above p{c} is not dominated by the remnants of the first order transition at p{c}, but that an unidentified mechanism favors stabilization of a new ground state other than helical order.

Non-Fermi Liquid Metal Without Quantum Criticality

A key question in condensed matter physics concerns whether pure three-dimensional metals can always be described as Fermi liquids. Using neutron Larmor diffraction to overcome the traditional resolution limit of diffraction experiments, we studied the lattice constants of the cubic itinerant-electron magnet manganese silicide (MnSi) at low temperatures and high pressures. We were able to resolve the nature of the phase diagram of MnSi and to establish that a stable, extended non-Fermi liquid state emerges under applied pressure without quantum criticality. This suggests that new forms of quantum order may be expected even far from quantum phase transitions.

Developments of the theory of spin fluctuations and spin fluctuation-induced superconductivity

Theory of spin fluctuations as developed in the past 30 years have played important roles in the theory of magnetism in metals, particularly in elucidating the properties around the magnetic instability or quantum critical points. Recently the theory has been extended to deal with the spin fluctuaion-mediated superconductivity with anisotropic order parameters in strongly correlated electron systems. These theoretical developments are briefly reviewed and the high temperature superconductivity of cuprates and organic and heavy electron superconductors are discussed in the light of these theories.

Linear magnetization dependence of the intrinsic anomalous Hall effect

The anomalous Hall effect is investigated experimentally and theoretically for ferromagnetic thin films of Mn5Ge3. We have separated the intrinsic and extrinsic contributions to the experimental anomalous Hall effect and calculated the intrinsic anomalous Hall conductivity from the Berry curvature of the Bloch states using first-principles methods. The intrinsic anomalous Hall conductivity depends linearly on the magnetization, which can be understood from the long-wavelength fluctuations of the spin orientation at finite temperatures. The quantitative agreement between theory and experiment is remarkably good, not only near 0 K but also at finite temperatures, up to about approximately 240 K (0.8TC).

de Haas-van Alphen effect in ZrZn2 under pressure: crossover between two magnetic states

We report measurements of the de Haas-van Alphen effect in ZrZn2 under hydrostatic pressures up to 21 kbar where the Curie temperature vanishes. The exchange splitting of a Fermi surface changes in behavior with increasing magnetic field, which is qualitatively consistent with the behavior of the high-field magnetization, suggesting the existence of a crossover between two distinct magnetic states. These and previously unexplained findings may be understood in terms of a p-T-B phase diagram qualitatively similar to that of the ferromagnetic superconductor UGe2.

Magnetic excitations in the ferromagnetic superconductor UGe2

We report that the uniform magnetization is not conserved in the magnetic excitation spectrum of UGe2. The measured spectrum is therefore different from that in d-electron ferromagnetic metals in a way that would facilitate magnetically mediated superconductivity.

Fermi-liquid breakdown in the paramagnetic phase of a pure metal

Fermi-liquid theory (the standard model of metals) has been challenged by the discovery of anomalous properties in an increasingly large number of metals. The anomalies often occur near a quantum critical point--a continuous phase transition in the limit of absolute zero, typically between magnetically ordered and paramagnetic phases. Although not understood in detail, unusual behaviour in the vicinity of such quantum critical points was anticipated nearly three decades ago by theories going beyond the standard model. Here we report electrical resistivity measurements of the 3d metal MnSi, indicating an unexpected breakdown of the Fermi-liquid model--not in a narrow crossover region close to a quantum critical point where it is normally expected to fail, but over a wide region of the phase diagram near a first-order magnetic transition. In this regime, corrections to the Fermi-liquid model are expected to be small. The range in pressure, temperature and applied magnetic field over which we observe an anomalous temperature dependence of the electrical resistivity in MnSi is not consistent with the crossover behaviour widely seen in quantum critical systems. This may suggest the emergence of a well defined but enigmatic quantum phase of matter.

Ferromagnetic superconductivity driven by changing Fermi surface topology

We introduce a simple but powerful zero temperature Stoner model to explain the unusual phase dia-gram of the ferromagnetic superconductor, UGe2. Triplet superconductivity is driven in the ferromagnetic phase by tuning the majority spin Fermi level through one of two peaks in the paramagnetic density of states (DOS). Each peak is associated with a metamagnetic jump in magnetization. The twin-peak DOS may be derived from a tight-binding, quasi-one-dimensional band structure, inspired by previous band-structure calculations.

Evidence for weak itinerant long-range magnetic correlations in UGe2

Positive muon spin relaxation measurements performed on the ferromagnet UGe2 reveal, in addition to the well-known localized 5f-electron density responsible for the bulk magnetic properties, the existence of itinerant quasistatic magnetic correlations. Their critical dynamics is well described by the conventional dipolar Heisenberg model. These correlations involve small magnetic moments.

Non-Fermi-liquid nature of the normal state of itinerant-electron ferromagnets

A century of research on magnetic phenomena had led to the view that the normal state of itinerant-electron ferromagnets such as Fe, Ni and Co could be described in terms of the standard model of the metallic state or its extension known as the nearly ferromagnetic Fermi liquid theory. In recent years, however, a large body of observations has accumulated from various complex intermetallic systems that raises the possibility that this assumption might be wrong. Here we examine this issue by means of high-precision measurements of the electrical transport and magnetic properties of pure ferromagnets-in particular, MnSi-in which the Curie temperature is tuned towards absolute zero by the application of hydrostatic pressure. With this method, it is possible for us to study the normal state over an extraordinarily large range of temperature of up to five orders of magnitude above the Curie temperature. Our results using MnSi reveal a particularly striking combination of properties-most notably a T3/2 power law for the resistivity-showing clearly that the normal state of this itinerant-electron ferromagnet cannot be described in terms of the standard model of metals.

Coexistence of superconductivity and ferromagnetism in URhGe

The discovery of superconductivity at high pressure (albeit over a restricted range) in the ferromagnetic material UGe2 raised the possibility that bulk superconductivity might be found in other ferromagnets. The exact symmetry of the paired state and the dominant mechanism responsible for the pairing, however, remain unidentified. Meanwhile, the conjecture that superconductivity could occur more generally in ferromagnets has been fuelled by the recent observation of a low-temperature transition that suggests an onset of superconductivity in high-quality crystals of the itinerant-ferromagnet ZrZn2 (ref. 2), although the thermodynamic signature of this transition could not be detected. Here we show that the ferromagnet URhGe is superconducting at ambient pressure. In this case, we find the thermodynamic signature of the transition-its form is consistent with a superconducting pairing of a spin-triplet type, although further testing with cleaner samples is needed to confirm this. The combination of superconductivity and ferromagnetism may thus be more common and consequently more important than hitherto realized.