Superconductivity Reinforced by Magnetic Field and the Magnetic Instability in Uranium Ferromagnets
Dai Aoki, Tatsuma D. Matsuda, Frederic Hardy, Christoph Meingast, Valentin Taufour, Elena Hassinger, Ilya Sheikin, Carley Paulsen, Georg Knebel, Hisashi Kotegawa, Jacques Flouquet
备注：
6 pages, 9 figures, proceedings of ICHE2010 in Tokyo, to be published in J. Phys. Soc. Jpn. Suppl
We review our recent results on ferromagnetic superconductors, URhGe and UCoGe. High quality single crystals of both compounds were successfully grown. The specific heat shows a clear jump related to the superconducting transition in UCoGe. The finite values of C/T at 0K are discussed in terms of the self-induced vortex state and the value of the ordered moment. With increasing fields for H // b-axis in URhGe, the jump of thermal expansion increases and shifts to lower temperature. The re-entrant and S-shaped superconducting phases for URhGe and UCoGe respectively are explained by the unusual field dependence of the effective mass, which is induced by the ferromagnetic instability when the field is applied along the hard magnetization b-axis. The magnetic fluctuations are very sensitive to the field orientation. This is reflected in the Hc2 and the anisotropy of the effective mass.
Recent advances on ferromagnetic superconductors, UGe2, URhGe and UCoGe are presented. The superconductivity (SC) peacefully coexists with the ferromagnetism (FM), forming the spin-triplet state of Cooper pairs. The striking new phenomena, such as SC reinforced by the magnetic field, are associated with Ising-type ferromagnetic fluctuations. A variety of ferromagnetic ordered moments between UGe2, URhGe and UCoGe affords to understand the relation between FM, tricriticality and SC.
We review our recent studies on ferromagnetic superconductors, UGe2, URhGe and UCoGe, together with the ferromagnetic quantum criticality and paramagnetic singularity on the Ising 5f-itinerant system UCoAl. Thanks to the variety of ordered moment in ferromagnetic superconductors from 1.5 muB to 0.05 muB, interesting systematic changes or similarities are clarified. All ferromagnetic superconductors show large upper critical field Hc2, and the field-reentrant (-reinforced) phenomena are observed in the field-temperature phase diagram, when the pressure or field direction is tuned for particular…
We study the critical behavior of dc magnetization in the uranium ferromagnet URhSi around the paramagnetic to ferromagnetic phase transition at T_C~ 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 beta for the temperature dependence of the spontaneous magnetization below TC, gamma for the magnetic susceptibility, and delta for the magnetic isotherm at T_C in URhSi have been determined as beta = 0.300 +- 0.002, gamma = 1.00 +- 0…
There is proposed a phenomenological theory of quasi-elastic neutron scattering in the itinerant ferromagnets UGe$_2$ and UCoGe based on their property that magnetization supported by the moments located at uranium atoms is not conserved quantity relaxing to equilibrium by the interaction with itinerant electrons subsystem. As result the line width of quasi elastic neutron scattering at $q\to 0$ acquires nonvanishing value at all temperatures but the Curie temperature.
A double-exchange mechanism for the emergence of ferromagnetism in cubic uranium compounds is proposed on the basis of a $j$-$j$ coupling scheme. The idea is {\it orbital-dependent duality} of $5f$ electrons concerning itinerant $Γ_8^-$ and localized $Γ_7^-$ states in the cubic structure. Since orbital degree of freedom is still active in the ferromagnetic phase, orbital-related quantum critical phenomenon is expected to appear. In fact, odd-parity p-wave pairing compatible with ferromagnetism is found in the vicinity of an orbital ordered phase. Furthermore, even-parity d-wave pairing with si…
We have studied the magnetic torque in uranium monosulfide (US) single crystals to explore the magnetic anisotropy in this material. Uranium monosulfide crystallizes in cubic, NaCl-type of crystal structure and exhibits the largest magneto-crystalline anisotropy observed in cubic systems. By performing detailed torque measurements we observe a strongly anisotropic behavior in the paramagnetic phase due to crystal defects and quadrupolar pair interactions. Our studies also confirm the presence of a large anisotropy in the ferromagnetic state of the US system with the <100>, <111>, and <110> dir…
We report the novel critical behavior of magnetization in low carrier concentration systems UTeS and USeS that exhibit the large negative magnetoresistance around the ferromagnetic transition temperatures T_C ~ 85 and 23 K, respectively. UTeS and USeS crystallize in the same orthorhombic TiNiSi-type crystal structure as those of uranium ferromagnetic superconductors URhGe and UCoGe. We determine the critical exponents, beta for the spontaneous magnetization M_s, gamma for the magnetic susceptibility chi, and delta for the magnetization isotherm at T_C with several methods. The ferromagnetic st…
We investigate the physical properties of a single crystal of uranium telluride U$_{7}$Te$_{12}$. We have confirmed that U$_{7}$Te$_{12}$ crystallizes in the hexagonal structure with three nonequivalent crystallographic uranium sites. The paramagnetic moments are estimated to be approximately 1 $μ_{\rm B}$ per the uranium site, assuming a uniform moment on all the sites. A ferromagnetic phase transition occurs at $T_{\rm C}=48$ K, where the in-plane magnetization increases sharply, whereas the out-of-plane component does not increase significantly. With decreasing temperature further below $T_…
Strong magnetocrystalline anisotropy is a well-known property of uranium compounds. The almost isotropic ferromagnetism in $\mathrm{U_{4}Ru_{7}Ge_{6}}$ reported in this paper represents a striking exception. We present results of magnetization, AC susceptibility, thermal expansion, specific heat and electrical resistivity measurements performed on a $\mathrm{U_{4}Ru_{7}Ge_{6}}$ single crystal at various temperatures and magnetic fields and discuss them in conjunction with results of first-principles electronic-structure calculations. $\mathrm{U_{4}Ru_{7}Ge_{6}}$ behaves as an itinerant 5$f$-el…
Magnetic properties of uranium and neptunium compounds showing the coexistence of Kondo screening effect and ferromagnetic order are investigated within the Anderson lattice Hamiltonian with a two-fold degenerate $f$-level in each site, corresponding to $5f^2$ electronic configuration with $S=1$ spins. A derivation of the Schrieffer-Wolff transformation is presented and the resulting Hamiltonian has an effective $f$-band term, in addition to the regular exchange Kondo interaction between the $S=1$ $f$-spins and the $s=1/2$ spins of the conduction electrons. The obtained effective Kondo lattice…
The spin-triplet state is most likely realized in uranium ferromagnetic superconductors, UGe2, URhGe, UCoGe. The microscopic coexistence of ferromagnetism and superconductivity means that the Cooper pair should be realized under the strong internal field due the ferromagnetism, leading to the spin-triplet state with equal spin pairing. The field-reinforced superconductivity, which is observed in all three materials when the ferromagnetic fluctuations are enhanced, is one of the strong evidences for the spin-triplet superconductivity. We present here the results of a newly discovered spin-tripl…
We have carried out an analysis of magnetic data in 69 uranium, 7 neptunium and 4 plutonium ferromagnets with the spin fluctuation theory developed by Takahashi (Y. Takahashi, J. Phys. Soc. Jpn. 55, 3553 (1986)). The basic and spin fluctuation parameters of the actinide ferromagnets are determined and the applicability of the spin fluctuation theory to actinide 5f system has been discussed. Itinerant ferromagnets of the 3d transition metals and their intermetallics follow a generalized Rhodes-Wohlfarth relation between p_eff/p_s and T_C/T_0, viz., p_eff/p_s ~ (T_C/T_0)^(-3/2). Here, p_s, p_eff…
Analogous to the Hall effect, the Nernst effect is the generation of a transverse voltage due to a temperature gradient in the presence of a perpendicular magnetic field. The Nernst effect has promise for thermoelectric applications and as a probe of electronic structure. In magnetic materials, a so-called anomalous Nernst effect (ANE) is possible in zero magnetic field. Here we report a colossal ANE reaching 23 $μ$V/K in the ferromagnetic metal UCo$_{0.8}$Ru$_{0.2}$Al. Uranium's $5f$ electrons provide strong electronic correlations that lead to narrow bands, which are a known route to produci…
Thanks to the discovery in the last decade of three uranium ferromagnetic superconductors, UGe2, URhGe and UCoGe, the fascinating aspects of the interplay between the triplet state of Cooper pairing and ferromagnetism have emerged. Furthermore, as the ferromagnetic properties in the normal state are quite different with respect to the proximity of the ferromagnetic-paramagnetic instabilities, the feedback with the coexistence of superconductivity gives rise to quite different boundaries in pressure and magnetic field. Special attention is given on the location of the materials with respect to …
Uranium dipnictide USb$_2$ reflects enigmatic properties posing a substantial challenge for a microscopic modeling. Among others, it develops a nonstandard antiferromagnetic order of a $\uparrow\downarrow\downarrow\uparrow$-type along [001] crystallographic direction, and under pressure it undergoes transition to the ferromagnetic phase. Here we propose a minimal low-energy model of USb$_2$ which, as we demonstrate at the mean-field level, accommodates physical mechanism for mentioned observations. Relying on the obtained results we also comment on the features of magnetism observed in other U…
Thermal expansion, magnetostriction and magnetization measurements under magnetic field and hydrostatic pressure were performed on a $\mathrm{UAu_{2}Si_{2}}$ single crystal. They revealed a large anisotropy of magnetoelastic properties manifested by prominent length changes leading to a collapse of the unit-cell volume accompanied by breaking the fourfold symmetry (similar to that in $\mathrm{URu_{2}Si_{2}}$ in the hidden-order state) in the antiferromagnetic state as consequences of strong magnetoelastic coupling. The magnetostriction curves measured at higher temperatures confirm a bulk char…
The critical behavior of dc magnetization in the uranium ferromagnet URhAl with the hexagonal ZrNiAl-type crystal structure has been studied around the ferromagnetic transition temperature T_C. The critical exponent beta for the temperature dependence of the spontaneous magnetization below T_C, gamma for the magnetic susceptibility, and delta for the magnetic isotherm at T_C have been obtained with a modified Arrott plot, a Kouvel-Fisher plot, the critical isotherm analysis and the scaling analysis. We have determined the critical exponents as beta = 0.287 +- 0.005, gamma = 1.47 +- 0.02, and d…
Uranium dioxide (UO$_2$) remains a formidable challenge for first-principles approaches, due to the complex interplay among spin-orbit coupling, Mott physics, magnetic ordering, and crystal distortions. Here we use DFT+$U$ to explore UO$_2$ at zero temperature, incorporating all the aforementioned phenomena. The technical challenge is to navigate the many metastable electronic states produced by DFT+$U$, which is acomplished using $f$-orbital occupation matrix control to search for the ground state. We restrict our search to the high-symmetry ferromagnetic phase, including spin-orbit coupling,…
We report a polarized neutron diffraction study conducted to reveal the nature of the weak ferromagnetic moment in the superconducting ferromagnet UCoGe. We find that the ordered moment in the normal phase in low magnetic fields (B // c) is predominantly located at the U atom and has a magnitude of about 0.1 muB at 3 T, in agreement with bulk magnetization data. By increasing the magnetic field the U moment grows to about 0.3 muB in 12 T and most remarkably, induces a substantial moment (about 0.2 muB) on the Co atom directed antiparallel to the U moment. The anomalous polarizability of the Co…
The field-reentrant (field-reinforced) superconductivity on ferromagnetic superconductors is one of the most interesting topics in unconventional superconductivity. The enhancement of effective mass and the induced ferromagnetic fluctuations play key roles for reentrant superconductivity. However, the associated change of the Fermi surface, which is often observed at (pseudo-) metamagnetic transition, can also be a key ingredient. In order to study the Fermi surface instability, we performed Hall effect measurements in the ferromagnetic superconductor URhGe. The Hall effect of URhGe is well ex…
In most unconventional superconductors, like the high-Tc cuprates, iron pnictides, or heavy fermion systems, superconductivity emerges in the proximity of an electronic instability. Identifying unambiguously the pairing mechanism remains nevertheless an enormous challenge. Among these systems, the orthorhombic uranium ferromagnetic superconductors have a unique position, notably because magnetic fields couple directly to ferromagnetic order, leading to the fascinating discovery of the re-emergence of superconductivity in URhGe at high field. Here we show that uniaxial stress is a remarkable to…
We prepared single crystals in UCo1-xRhxGe and UIr1-xRhxGe systems to establish a complex dU-U-T (dU-U is the shortest interatomic uranium distance and T is temperature) magnetic phase diagram. This recognized a characteristic maximum in magnetic susceptibility at temperature Tmax along the b axis as an important parameter. Three magnetically ordered regions can be distinguished within this scope; first a ferromagnetic region with Curie temperature < Tmax, second a ferromagnetic region with Curie temperature = Tmax and finally an antiferromagnetic region existing on the UIrGe side with Néel te…
Magnetic structure of tetragonal UAu$_2$Si$_2$ was investigated by single-crystal neutron diffraction experiments. Below $T_{\rm N}$ = 20 K it orders antiferromagnetically with a propagation vector of $k = (2/3, 0, 0)$ and magnetic moments of uranium ions pointing along the tetragonal $c$-axis. Weak signs of the presence of a ferromagnetic component of magnetic moment were traced out.Taking into account a group theory calculation and experimental results of magnetization and $^{29}$Si-NMR, the magnetic structure is determined to be a squared-up antiferromagnetic structure, with a stacking sequ…
Spin angular momentum transfer in magnetic bilayers offers the possibility of ultrafast and low-loss operation for next-generation spintronic devices. We report the field- and temperature- dependent measurements on the magnetization precessions in Co$_2$FeAl/(Ga,Mn)As by time-resolved magneto-optical Kerr effect (TRMOKE). Analysis of the effective Gilbert damping and phase shift indicates a clear signature of an enhanced dynamic exchange coupling between the two ferromagnetic (FM) layers due to the reinforced spin pumping at resonance. The temperature dependence of the dynamic exchange-couplin…
In strongly correlated materials, cooperative behavior of the electrons causes a variety of quantum ordered states that may, in some cases, coexist. It has long been believed, however, that such coexistence among ferromagnetic ordering, superconductivity and heavy-fermion behavior is impossible, as the first supports parallel spin alignment while the conventional understanding of the latter two phenomena assumes spin-singlet or anti-parallel spins. This understanding has recently been challenged by an increasing number of observations in uranium systems (UGe2, URhGe, UIr and UCoGe) in which su…
We report on a microscopic study of the evolution of ferromagnetism in the Ru substituted ferromagnetic superconductor (FM SC) UCoGe crystallizing in the orthorhombic TiNiSi-type structure. For that purpose, two single crystals with composition UCo0.97Ru0.03Ge and UCo0.88Ru0.12Ge have been prepared and characterized by magnetization, AC susceptibility, specific heat and electrical resistivity measurements. Both compounds have been found to order ferromagnetically below TC = 6.5 K and 7.5 K, respectively, which is considerably higher than the TC = 3 K of the parent compound UCoGe. The higher va…
We investigated the evolution of magnetism in the UIr1-xRhxGe system by the systematic study of high-quality single crystals. Lattice parameters of both parent compounds are very similar resulting in almost identical nearest interatomic uranium distance close to the Hill limit. We established the x-T phase diagram of the UIr1-xRhxGe system and found a discontinuous antiferromagnetic/ferromagnetic boundary at xcrit = 0.56 where a local minimum in ordering temperature and maximum of the Sommerfeld coefficient 175 mJ/mol K2 occurs in the UCoGe-URhGe-UIrGe system, signaling an increase in magnetic…
We report on microscopic study of the ferromagnetism enhancement in the Ru doped ferromagnetic superconductor (FM SC) UCoGe. For that purpose, two single crystals with composition UCo0.97Ru0.03Ge and UCo0.88Ru0.12Ge were prepared. Both single crystals were investigated by polarized neutron diffraction (PND) at low temperatures in magnetic fields and the latter one also by the soft X-ray magnetic circular dichroism (XMCD) method. UCo0.96Ru0.03Ge and UCo0.88Ru0.12Ge have been found ordering ferromagnetically below the Curie temperature TC = 6 K and 8.5 K, respectively, which are considerable hig…
We report the magnetoresistance in the novel spin-triplet superconductor UTe2 under pressure close to the critical pressure Pc, where the superconducting phase terminates, for field along the three a, b and c-axes in the orthorhombic structure. The superconducting phase for H // a-axis just below Pc shows a field-reentrant behavior due to the competition with the emergence of magnetic order at low fields. The upper critical field Hc2 for H // c-axis shows a quasi-vertical increase in the H-T phase diagram just below Pc, indicating that superconductivity is reinforced by the strong fluctuations…
The novel spin-triplet superconductor candidate UTe2 was discovered only recently at the end of 2018 and attracted enormous attention. We review key experimental and theoretical progress which has been achieved in different laboratories. UTe2 is a heavy-fermion paramagnet, but right after the discovery of superconductivity it has been expected to be close to a ferromagnetic instability showing many similarities to the U-based ferromagnetic superconductors, URhGe and UCoGe. The competition between different types of magnetic interactions and the duality between the local and itinerant character…
Superconductivity induced by a magnetic field near metamagnetism is a striking manifestation of magnetically-mediated superconducting pairing. After being observed in itinerant ferromagnets, this phenomenon was recently reported in the orthorhombic paramagnet UTe$_2$. Under a magnetic field applied along the hard magnetization axis b, superconductivity is reinforced on approaching metamagnetism at $μ_0H_m$ = 35 T, but it abruptly disappears beyond $H_m$. On the contrary, field-induced superconductivity was reported beyond $μ_0H_m$ = 40-50 T in a magnetic field tilted by $\simeq25-30°$ from b i…
Spin-triplet superconductivity is a condensate of electron pairs with spin-1 and an odd-parity wavefunction. A particularly interesting manifestation of triplet pairing is a chiral p-wave state which is topologically non-trivial and a natural platform for realizing Majorana edge modes. Triplet pairing is however rare in solid state systems and so far, no unambiguous identification has been made in any bulk compound. Since pairing is most naturally mediated by ferromagnetic spin fluctuations, uranium based heavy fermion systems containing f electron elements that can harbor both strong correlat…
Magnetic response of uranium dioxide (UO2) has been investigated through temperature and magnetic field dependent dc magnetization measurements. UO2 is a paramagnet at room temperature. The magnetic susceptibility, however, deviates from Curie-Weiss (CW) like paramagnetic behavior below T = 280 K. Further down the temperature UO2 undergoes phase transition to an antiferromagnetic state below TN = 30.6 K. The zero field cooled (ZFC) and field cooled (FC) magnetizations exhibit some distinct thermomagnetic irreversibility below TN. The temperature dependence of the FC magnetization is more like …
