arXiv subjects

D. Aoki

Publications and source records attributed to D. Aoki.

At least 37 records · Page 2Linked to original sources

arXiv2021

Unconventional Superconductivity in UTe2

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 of the 5f Uranium electrons, as well as the shift of the U valence appear as key parameters in the rich phase diagrams discovered recently under extreme conditions like low temperature, high magnetic field, and pressure. We discuss macroscopic and microscopic experiments at low temperature to clarify the normal phase properties at ambient pressure. Special attention will be given to the occurrence of a metamagnetic transition at Hm = 35 T for a magnetic field applied along the hard magnetic axis b. Adding external pressure leads to strong changes in the magnetic and electronic properties with a direct feedback on superconductivity. Attention will be given on the possible evolution of the Fermi surface as a function of magnetic field and pressure. Superconductivity in UTe2 is extremely rich exhibiting various unconventional behaviors which will be highlighted. It shows an exceptionally huge superconducting upper critical field with a re-entrant behavior under magnetic field and the occurrence of multiple superconducting phases in the temperature field, pressure phase diagram. There is evidence for spin-triplet pairing. The different theoretical approaches will be described. Notably we discuss that UTe2 is a possible example for the realization of a fascinating topological superconductor.

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arXiv2021

Pairing interaction in superconducting UCoGe tunable by magnetic field

The mechanism of unconventional superconductivity, such as high-temperature-cuprate, Fe-based, and heavy-fermion superconductors, has been studied as a central issue in condensed-matter physics. Spin fluctuations, instead of phonons, are considered to be responsible for the formation of Cooper pairs, and many efforts have been made to confirm this mechanism experimentally. Although a qualitative consensus seems to have been obtained, experimental confirmation has not yet been achieved. This is owing to a lack of the quantitative comparison between theory and experiments. Here, we show a semi-quantitative comparison between the superconducting-transition temperature ($T_{\rm SC}$) and spin fluctuations derived from the nuclear magnetic resonance (NMR) experiment on the ferromagnetic (FM) superconductor UCoGe, in which the FM fluctuations and superconductivity are tunable by external fields. The enhancement and abrupt suppression of $T_{\rm SC}$ by applied fields, as well as the pressure variation of $T_{\rm SC}$ around the FM criticality are well understood by the change in the FM fluctuations on the basis of the single-band spin-triplet theoretical formalism. The present comparisons strongly support the theoretical formalism of spin-fluctuation-mediated superconductivity, particularly in UCoGe.

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arXiv2021

Disappearance of spin glass behavior in ThCr2Si2-type intermetallic PrAu2Si2

It is unexpected that a spin-glass transition, which generally occurs only in the system with some form of disorder, was observed in the ThCr2Si2-type compound PrAu2Si2 at a temperature of ~3 K. This puzzling phenomenon was later explained based on a novel dynamic frustration model that does not involve static disorder. We present the results of re-verification of the reported spin-glass behaviors by measuring the physical properties of three polycrystalline PrAu2Si2 samples annealed under different conditions. Indeed, in the sample annealed at 827 C for one week, a spin-glass transition does occur at a temperature of Tf=2.8 K as that reported previously in the literature. However, it is newly found that the spin-glass effect is actually more pronounced in the as-cast sample, and almost completely disappears in the well-annealed (at 850 C for 4 weeks) sample. The apparent sample dependence of the magnetic characteristics of PrAu2Si2 is discussed by comparing it with similar phenomena observed in the isomorphic compounds URh2Ge2 and CeAu2Si2. Our experimental results strongly suggest that the spin-glass behavior observed in the as cast and insufficient annealed samples is most likely due to the presence of small amount of crystalline impurities and/or partial site disorder on the Au and Si sublattices, and thus is not the inherent characteristic of ideal ThCr2Si2-type PrAu2Si2. The perfectly ordered PrAu2Si2 should be regarded as a paramagnetic system with obvious crystal-field effects.

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arXiv2021

Magnetic reshuffling and feedback on superconductivity in UTe2 under pressure

The discovery of superconductivity in the heavy-fermion paramagnet UTe$_2$ has attracted a lot of attention, particularly due to the reinforcement of superconductivity near pressure- and magnetic-field-induced magnetic quantum phase transitions. A challenge is now to characterize the effects of combined pressure and magnetic fields applied along variable directions in this strongly anisotropic paramagnet. Here, we present an investigation of the electrical resistivity of UTe$_2$ under pressure up to 3~GPa and pulsed magnetic fields up to 58~T along the hard magnetic crystallographic directions $\mathbf{b}$ and $\mathbf{c}$. We construct three-dimensional phase diagrams and show that, near the critical pressure, a field-enhancement of superconductivity coincides with a boost of the effective mass related to the collapse of metamagnetic and critical fields at the boundaries of the correlated paramagnetic regime and magnetically-ordered phase, respectively. Beyond the critical pressure, field-induced transitions precede the destruction of the magnetically-ordered phase, suggesting an antiferromagnetic nature. By bringing new elements about the interplay between magnetism and superconductivity, our work appeals for microscopic theories describing the anisotropic properties of UTe$_2$ under pressure and magnetic field.

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arXiv2021

Feedback of superconductivity on the magnetic excitation spectrum of UTe$_{2}$

We investigate the spin dynamics in the superconducting phase of UTe$_{2}$ by triple-axis inelastic neutron scattering on a single crystal sample. At the wave-vector $\bf{k_1}$=(0, 0.57, 0), where the normal state antiferromagnetic correlations are peaked, a modification of the excitation spectrum is evidenced, on crossing the superconducting transition, with a reduction of the relaxation rate together with the development of an inelastic peak at $Ω$ $\approx$ 1 meV. The low dimensional nature and the the $a$-axis polarization of the fluctuations, that characterise the normal state, are essentially maintained below $T_{sc}$. The high ratio $Ω/k_{B}T_{sc}$ $\approx$ 7.2 contrasts with the most common behaviour in heavy fermion superconductors.

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arXiv2021

Low-dimensional antiferromagnetic fluctuations in the heavy-fermion paramagnetic ladder UTe$_2$

Inelastic-neutron-scattering measurements were performed on a single crystal of the heavy-fermion paramagnet UTe$_2$ above its superconducting temperature. We confirm the presence of antiferromagnetic fluctuations with the incommensurate wavevector $\mathbf{k}_1=(0,0.57,0)$. A quasielastic signal is found, whose momentum-transfer dependence is compatible with fluctuations of magnetic moments $μ\parallel\mathbf{a}$, with a sine-wave modulation of wavevector $\mathbf{k}_1$ and in-phase moments on the nearest U atoms. Low dimensionality of the magnetic fluctuations, consequence of the ladder structure, is indicated by weak correlations along the direction $\mathbf{c}$. These fluctuations saturate below the temperature $T_1^*\simeq15$~K, in possible relation with anomalies observed in thermodynamic, electrical-transport and nuclear-magnetic-resonance measurements. The absence or weakness of ferromagnetic fluctuations, in our data collected at temperatures down to 2.1 K and energy transfers from 0.6 to 7.5 meV, is emphasized. These results constitute constraints for models of magnetically-mediated superconductivity in UTe$_2$.

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arXiv2021

Anomalous Anisotropy of the Lower Critical Field and Meissner Effect in UTe2

We report on low temperature susceptibility and magnetization measurements made on single crystals of the recently discovered heavy-fermion superconductor UTe$_2$ and compare the results with the two ambient pressure ferromagnetic superconductors URhGe and UCoGe. Hysteresis curves in the superconducting phase show a familiar diamond shape superimposed on a large paramagnetic background. The Meissner state was measured by zero field cooling in small fields of a few Oe as well as ac susceptibility measurements in small fields and resulted in 100\% shielding, with a sharp transition. However the field cooling Meissner-Ochsenfeld effect (expulsion of flux) was negligible in fields greater than just a few Oe, but becomes nearly 30\% of the perfect diamagnetic signal when the field was reduced to 0.01~Oe. The critical current due to flux pinning was studied by ac susceptibility techniques. Over the range in fields and temperature of this study, no signature of a ferromagnetic transition could be discerned. The lower critical field $H_{\rm c1}$ has been measured along the three crystalographic axes, and surprisingly, the anisotropy of $H_{\rm c1}$ contradicts that of the upper critical field. We discuss this discrepancy and show that it may provide additional support for a magnetic field-dependent pairing mediated by ferromagnetic fluctuations in UTe$_2$.

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arXiv2021

Origin of the 30 T transition in CeRhIn$_5$ in tilted magnetic fields

We present a comprehensive ultrasound study of the prototypical heavy-fermion material CeRhIn$_5$, examining the origin of the enigmatic 30 T transition. For a field applied at 2$^\circ$ from the $c$ axis, we observed two sharp anomalies in the sound velocity, at $B_m \approx$ 20 T and $B^* \approx$ 30 T, in all the symmetry-breaking ultrasound modes at low temperatures. The lower-field anomaly corresponds to the well-known first-order metamagnetic incommensurate-to-commensurate transition. The higher-field anomaly takes place at 30 T, where an electronic-nematic transition was previously suggested to occur. Both anomalies, observed only within the antiferromagnetic state, are of similar shape, but the corresponding changes of the ultrasound velocity have opposite signs. Based on our experimental results, we suggest that a field-induced magnetic transition from a commensurate to another incommensurate antiferromagnetic state occurs at $B^*$. With further increasing the field angle from the $c$ axis, the anomaly at $B^*$ slowly shifts to higher fields, broadens, and becomes smaller in magnitude. Traced up to 30$^\circ$ from the $c$ axis, it is no longer observed at 40$^\circ$ below 36 T.

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arXiv2021

Specific heat of CeRhIn$_5$ in high magnetic fields: Magnetic phase diagram revisited

CeRhIn$_5$ is a prototypical antiferromagnetic heavy-fermion compound, whose behavior in a magnetic field is unique. A magnetic field applied in the basal plane of the tetragonal crystal structure induces two additional phase transitions. When the magnetic field is applied along, or close to, the $c$ axis, a new phase characterized by a pronounced in-plane electronic anisotropy emerges at $B^* \approx$ 30 T, well below the critical field, $B_c \simeq$ 50 T, to suppress the antiferromagnetic order. The exact origin of this new phase, originally suggested to be an electronic-nematic state, remains elusive. Here we report low-temperature specific-heat measurements in CeRhIn$_5$ in high static magnetic fields up to 36 T applied along both the $a$ and $c$ axes. For fields applied along the $a$ axis, we confirmed the previously suggested phase diagram, and extended it to higher fields. This allowed us to observe a triple point at $\sim$ 30 T, where the first-order transition from an incommensurate to commensurate magnetic structure merges into the onset of the second-order antiferromagnetic transition. For fields applied along the $c$ axis, we observed a small but distinct anomaly at $B^*$, which we discuss in terms of a possible field-induced transition, probably weakly first-order. We further suggest that the transition corresponds to a change of magnetic structure. We revise magnetic phase diagrams of CeRhIn$_5$ for both principal orientations of the magnetic field based entirely on thermodynamic anomalies.

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arXiv2021

Robust Fermi-Surface Morphology of CeRhIn$_5$ across the Putative Field-Induced Quantum Critical Point

We report a comprehensive de Haas--van Alphen (dHvA) study of the heavy-fermion material CeRhIn$_5$ in magnetic fields up to 70~T. Several dHvA frequencies gradually emerge at high fields as a result of magnetic breakdown. Among them is the thermodynamically important $β_1$ branch, which has not been observed so far. Comparison of our angule-dependent dHvA spectra with those of the non-$4f$ compound LaRhIn$_5$ and with band-structure calculations evidences that the Ce $4f$ electrons in CeRhIn$_5$ remain localized over the whole field range. This rules out any significant Fermi-surface reconstruction, either at the suggested nematic phase transition at $B^{*}\approx$ 30~T or at the putative quantum critical point at $B_c \simeq$ 50~T. Our results rather demonstrate the robustness of the Fermi surface and the localized nature of the 4$f$ electrons inside and outside of the antiferromagnetic phase.

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arXiv2020

Comparison of two superconducting phases induced by a magnetic field in UTe2

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 in the (b,c) plane. Here we explore the phase diagram of UTe2 under these two magnetic-field directions. Zero-resistance measurements permit to confirm unambiguously that superconductivity is established beyond Hm in the tilted-field direction. While superconductivity is locked exactly at fields either smaller (for a H || b), or larger (for H tilted by $\simeq27°$ from b to c), than Hm, the variations of the Fermi-liquid coefficient in the electrical resistivity and of the residual resistivity are surprisingly similar for the two field directions. The resemblance of the normal states for the two field directions puts constraints for theoretical models of superconductivity and implies that some subtle ingredients must be in play.

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arXiv2020

Magnetic structure of Cd-doped CeIrIn$_5$

We report the magnetic structure of nominally 10% Cd-doped CeIrIn$_5$, CeIr(In$_{0.9}$Cd$_{0.1}$)$_5$, determined by elastic neutron scattering. Magnetic intensity was observed only at the ordering wave vector $Q_{AF} = (1/2,1/2,1/2)$, commensurate with the crystal lattice. A staggered moment of 0.47(3)$μ_B$ at 1.8 K resides on the Ce ion. The magnetic moments are found to be aligned along the crystallographic $c$ axis. This is further confirmed by magnetic susceptibility data, which suggest the $c$ axis to be the easy magnetic axis. The determined magnetic structure is strikingly different from the incommensurate antiferromagnetic ordering of the closely related compound CeRhIn$_5$, in which the magnetic moments are antiferromagnetically aligned within the tetragonal basal plane.

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arXiv2020

Pairing symmetry of an intermediate valence superconductor CeIr3 investigated using muSR measurements

We have investigated the bulk and microscopic properties of the rhombohedral intermediate valence superconductor CeIr$_3$ by employing magnetization, heat capacity, and muon spin rotation and relaxation ($μ$SR) measurements. The magnetic susceptibility indicates bulk superconductivity below $T_\mathrm{C} = 3.1$~K. Heat capacity data also reveal a bulk superconducting transition at $T_\mathrm{C} = 3.1$~K with a second weak anomaly near 1.6~K. At $T_{\mathrm{C}}$, the jump in heat capacity $ΔC$/$γT_{\mathrm{C}} \sim 1.39(1)$, is slightly less than the BCS weak coupling limit of 1.43. Transverse-field $μ$SR measurements suggest a fully gapped, isotropic, $s$-wave superconductivity with 2$Δ(0)/k_{\mathrm{B}}T_{\mathrm{C}} = 3.76(3)$, very close to 3.56, the BCS gap value for weak-coupling superconductors. From the temperature variation of magnetic penetration depth, we have also determined the London penetration depth $λ_{\mathrm{L}}(0) = 435(2)$~nm, the carriers' effective mass enhancement $m^{*} = 1.69(1)m_{\mathrm{e}}$ and the superconducting carrier density $n_{\mathrm{s}} = 2.5(1)\times 10^{26}$ carriers m$^{-3}$. The fact that LaIr$_3$, with no $4f$-electrons, and CeIr$_3$ with $4f^{n}$ electrons where $n \le 1$-electron (Ce ion in a valence fluctuating state), both exhibit the same $s$-wave gap symmetry indicates that the physics of these two compounds is governed by the Ir-$d$ band near the Fermi-level, which is in agreement with previous band structure calculations.

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arXiv2019

Multiple superconducting phases in a nearly ferromagnetic system

Multiple superconducting order parameters are extremely rare. Here we show that a very small pressure can induce this phenomenon in the recently discovered heavy fermion superconductor UTe2. This nearly ferromagnetic system shows several intriguing phenomena, including an extraordinary reinforcement of superconductivity in very strong magnetic fields. We find that pressure can tune the system to a more correlated state and probable magnetic order. The superconducting critical temperature is strongly enhanced, reaching almost 3K, a new record for Ce- and U-based heavy fermion superconductors. Most spectacularly under pressure we find a transition within the superconducting state, putting UTe2 among the very rare systems having multiple superconducting phases. UTe2 under pressure is a treasure trove of several of the most fascinating phenomena in unconventional superconductivity and may well be a keystone in their understanding.

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arXiv2019

High-field moment polarization in the itinerant ferromagnet URhSi

We report a high-magnetic-field study of the itinerant ferromagnet URhSi. Magnetization and electrical resistivity were measured under magnetic fields $μ_0H$ up to 58~T applied along the directions $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$ of the orthorhombic structure and temperatures $T$ ranging from 1.5 to 50 K. For $\mathbf{H}\parallel\mathbf{b}$, pseudo-metamagnetism at $μ_0H_m\simeq30-40$~T is associated with a broad step in the magnetization and a maximum in the resistivity. The properties of URhSi are discussed and compared with those of the isostructural superconducting ferromagnets URhGe and UCoGe and of the superconducting paramagnet UTe$_2$.

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arXiv2019

Ir 5$d$-band Derived Superconductivity in LaIr$_3$

We have studied the superconducting properties of LaIr$_3$ with a rhombohedral structure using magnetization, heat capacity, and muon-spin rotation/relaxation ($μ$SR) measurements. The zero-field cooled and field cooled susceptibility measurements exhibit a superconducting transition below $T_{\mathrm{C}}$ = 2.5 K. Magnetization measurements indicate bulk type-II superconductivity with upper critical field $μ_0H_{\mathrm{c2}}(0)$ = 3.84 T. Two successive transitions are observed in heat capacity data, one at $T_{\mathrm{C}}$ = 2.5 K and a second at 1.2 K below $T_{\mathrm{C}}$ whose origin remain unclear. The heat capacity jump reveals $ΔC$/$γT_{\mathrm{C}} \sim$ 1.0 which is lower than 1.43 expected for BCS weak coupling limit. Transverse field-$μ$SR measurements reveal a fully gapped $s-$wave superconductivity with 2$Δ(0)/k_{\mathrm{B}}T_{\mathrm{C}}$ = 3.31, which is small compared to BCS value 3.56, suggesting weak coupling superconductivity. Moreover the study of the temperature dependence of the magnetic penetration depth estimated using the transverse field-$μ$SR measurements gives a zero temperature value of the magnetic penetration depth $λ_{\mathrm{L}}(0)$ = 386(3) nm, superconducting carrier density $n_{\mathrm{s}}$ = 2.9(1) $\times$10$^{27}$ carriers $m^{-3}$ and the carriers' effective-mass enhancement $m^{*}$ = 1.53(1) $m_{\mathrm{e}}$. Our zero-field-$μ$SR measurements do not reveal the spontaneous appearance of an internal magnetic field below the transition temperature, which indicates that time-reversal symmetry is preserved in the superconducting state of LaIr$_3$.

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arXiv2019

Pressure-Induced Rotational Symmetry Breaking in URu$_2$Si$_2$

Phase transitions and symmetry are intimately linked. Melting of ice, for example, restores translation invariance. The mysterious hidden order (HO) phase of URu$_2$Si$_2$ has, despite relentless research efforts, kept its symmetry breaking element intangible. Here we present a high-resolution x-ray diffraction study of the URu$_2$Si$_2$ crystal structure as a function of hydrostatic pressure. Below a critical pressure threshold $p_c\approx3$ kbar, no tetragonal lattice symmetry breaking is observed even below the HO transition $T_{HO}=17.5$ K. For $p>p_c$, however, a pressure-induced rotational symmetry breaking is identified with an onset temperatures $T_{OR}\sim 100$ K. The emergence of an orthorhombic phase is found and discussed in terms of an electronic nematic order that appears unrelated to the HO, but with possible relevance for the pressure-induced antiferromagnetic (AF) phase. Existing theories describe the HO and AF phases through an adiabatic continuity of a complex order parameter. Since none of these theories predicts a pressure-induced nematic order, our finding adds an additional symmetry breaking element to this long-standing problem.

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arXiv2018

Anisotropic Kondo pseudo-gap in URu2Si2

A polarized electronic Raman scattering study reveals the emergence of symmetry dependence in the electronic Raman response of single crystalline URu$_{2}$Si$_{2}$ below the Kondo crossover scale $T_K\sim100K$. In particular, the development of a coherent Kondo pseudo-gap predominantly in the E$_g$ channel highlights strong anisotropy in the Kondo physics in URu$_{2}$Si$_{2}$ that has previously been neglected in theoretical models of this system. A calculation of the Raman vertices demonstrates that the strongest Raman vertex does indeed develop within the E$_g$ channel for interband transitions and reaches a maximum along the diagonals of the Brillouin zone, implying a d-wave-like geometry for the Kondo pseudo-gap. Below the hidden order phase transition at $T_{HO}= 17.5K$, the magnitude of the pseudo-gap is found to be enhanced. Moreover, the anisotropy of the pseudo-gap is similar in form to that proposed for the chiral d-wave (E$_g$) superconducting state that appears below $T_c=1.5K$.

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