Theory of Pairing Assisted Spin Polarization in Spin-Triplet Equal Spin Pairing: Origin of Extra Magnetization in Sr<sub>2</sub>RuO<sub>4</sub> in Superconducting State

Miyake, Kazumasa

doi:10.7566/jpsj.83.053701

Cited by 22 publications

(28 citation statements)

References 20 publications

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“…However, in such a non-unitary state, the additional spin polarization would be along the c-axis, and thus is not relevant to the present observation. Rather, we point out that the extra magnetization in the SC state is a natural consequence of the ESP state formed by the strongly correlated electrons as discussed in the recent theoretical paper [27]. We will next examine this possi-bility.…”

Section: Fig 2: (Color Online) (A)mentioning

confidence: 85%

“…This may lead to an additional spin polarization in the SC state, and this polarization is enhanced in the strongly correlated electron system; to gain the free energy associated with the SC condensation, the up-spin and down-spin pairs are redistributed with each other. Based on this mechanism, the ratio of the extra magnetization δm to the normal magnetization m n (at T = 0 K) is calculated as [27],…”

Section: Fig 2: (Color Online) (A)mentioning

confidence: 99%

“…(Note that the sign of magnetic moment of electron and 3 He is opposite.) We reformulate Takagi's discussion and extend it to the ground state under the magnetic field H [27]. To begin with, we assume the ξ dependence of the DOS N (ξ) without the magnetic field H is given by…”

Section: Fig 2: (Color Online) (A)mentioning

confidence: 99%

“…[27]. The magnetization m n in the normal state under the magnetic field H is given by m n ∼ = 2µ Note that this ratio vanishes as long as the particle-hole symmetry is retained (α = 0).…”

Section: Fig 2: (Color Online) (A)mentioning

confidence: 99%

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Spin polarization enhanced by spin-triplet pairing inSr2RuO4probed by NMR

et al. 2015

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We report a novel phenomenon intimately related to the spin-triplet superconductivity. It is well known that the spin susceptibility decreases below the superconducting transition temperature in almost all superconductors because of spin-singlet pair formation, while it may remain unchanged in a handful of spin-triplet exceptions. Here we report the observation in Sr2RuO4 with nuclear magnetic resonance (NMR) that the spin susceptibility originating from the Ru-4d electron slightly increases by ∼ 2% of total and becomes inhomogeneous in the superconducting state. These are reasonably explained if the electron pairs form the equal-spin-pairing (ESP) in the mixed state. A similar phenomenon was predicted for superfluid 3 He forty years ago, but had never been demonstrated in any superconductor. Ru [5,6] nuclei are unchanged in the SC state. The unchanged spin susceptibility, which was supported also from the polarized neutron scattering measurements [7], strongly suggests that the equal-spin-pairing (ESP) state of the spin-triplet superconductivity is realized in SRO, in which the SC pairs consist of the up-up (| ↑↑ ) or down-down (| ↓↓ ) pairs. In addition, the µSR [8] and Kerr-effect [9] measurements in the SC state suggest the broken time-reversal symmetry. Unlike heavy-fermion systems, the effect of spin-orbit coupling should be relatively weak, the pairing state in SRO would be closely analogous to the case of superfluid 3 He. By taking the experimental results into account, the chiral p-wave spin-triplet state, which is analogous to the A-phase of superfluid 3 He [10], has been considered as the most promising candidate for the SC pairing state [11,12].However, toward the establishment of this pairing state, there still remains a controversy since the superconductivity is strongly suppressed with a first-order transition under the in-plane magnetic fields near the SC critical field H c2 as shown in Fig. 1 (a) [13,14]. In addition, sharp magnetization jump with the hysteresis at H c2 was observed when the magnetic field is exactly parallel to the ab plane at 0.1 K [15]. These are phenomena usually expected in a spin-singlet superconductor [16,17]. Furthermore, non-detection of some of the behaviors expected for the chiral p-wave state (e.g. chiral edge current [18][19][20] and splitting of T c by in-plane magnetic fields of any magnitude [21]) casts some doubts on this pairing state. Therefore, convincing evidence for establishing the SC pairing state in SRO, particularly finding a new phenomenon specific to the pairing state, has been desired.In this paper, we report, from the "double-site" Knight-shift measurement in the SC state, which is the reliable method to subtract the Meissner effect from the observed Knight shift, that the spin susceptibility of SRO becomes inhomogeneous and its average slightly increases in the SC state. The small increase of spin susceptibility cannot be explained with a singlet-pairing state but consistently interpreted with the ESP state in triplet superconductivity. As far as ...

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Section: Fig 2: (Color Online) (A)mentioning

confidence: 85%

Section: Fig 2: (Color Online) (A)mentioning

confidence: 99%

Section: Fig 2: (Color Online) (A)mentioning

confidence: 99%

Section: Fig 2: (Color Online) (A)mentioning

confidence: 99%

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Spin polarization enhanced by spin-triplet pairing inSr2RuO4probed by NMR

et al. 2015

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“…An isotropic gap which does not change sign can result from an on-site interaction, which is not possible for equal spin pairing in a single-orbital model, but could result from a local attraction between electrons with equal spins on different orbitals. The pairing potential has the form ∆ [14,44].…”

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confidence: 99%

Two-Gap Superconductivity inLaNiGa2with Nonunitary Triplet Pairing and Even Parity Gap Symmetry

et al. 2016

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The nature of the pairing states of superconducting LaNiC 2 and LaNiGa 2 has to date remained a puzzling question. Broken time reversal symmetry has been observed in both compounds and a group theoretical analysis implies a non-unitary triplet pairing state. However all the allowed non-unitary triplet states have nodal gap functions but most thermodynamic and NMR measurements indicate fully gapped superconductivity in LaNiC 2 . Here we probe the gap symmetry of LaNiGa 2 by measuring the London penetration depth, specific heat and upper critical field. These measurements demonstrate two-gap nodeless superconductivity in LaNiGa 2 , suggesting that this is a common feature of both compounds. These results allow us to propose a novel triplet superconducting state, where the pairing occurs between electrons of the same spin, but on different orbitals. In this case the superconducting wavefunction has a triplet spin component but isotropic even parity gap symmetry, yet the overall wavefunction remains antisymmetric under particle exchange. This model leads to a nodeless twogap superconducting state which breaks time reversal symmetry, and therefore accounts well for the seemingly contradictory experimental results. The breaking of symmetries in addition to gauge symmetry upon entering the superconducting state usually indicates an unconventional order parameter. Several materials have been found to break time reversal symmetry (TRS) in the superconducting state through the detection of spontaneous magnetic fields below T c using zero-field muon-spin relaxation (µSR [14], where it has been argued that as a result of the low symmetry of the orthorhombic crystal structures of both compounds, broken TRS necessarily implies non-unitary triplet superconductivity and all the TRS breaking states have nodes in the gap function [15]. Although evidence for nodal superconductivity was found from some measurements [16,17], recent specific heat [18,19], nuclear quadrapole relaxation [20] and penetration depth [19] measurements indicate fully gapped behavior in LaNiC 2 . In addition, evidence for two-gap superconductivity was found from the specific heat, superfluid density and upper critical field [19]. There have been fewer measurements of superconductivity in LaNiGa 2 [21], which has an orthorhombic centrosymmetric crystal structure in contrast to noncentrosymmetric LaNiC 2 , although fully gapped behavior was inferred from the specific heat [22].In this Letter, we suggest a solution to this apparent contradiction from measurements of the London penetration depth, specific heat and upper critical field, all of which consistently suggest the presence of two-gap superconductivity in LaNiGa 2 . Along with previous results of LaNiC 2 [19], we establish that nodeless, two-gap superconductivity is a common feature of these compounds. We propose that pairing between electrons with the same spins but on different orbitals gives rise to a triplet superconducting state with even parity pairing in both compounds, where the wave function re...

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Theoretical Studies on Off-Axis Phase Diagrams and Knight Shifts in UTe$$_2$$: Tetra-Critical Point, d-Vector Rotation, and Multiple Phases

Machida

2024

J Low Temp Phys

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Inspired by recent remarkable sets of experiments on UTe$$_2$$ 2 : discoveries of the fourth horizontal internal transition line running toward a tetra-critical point (TCP) at H = 15 T, the off-axis high-field phases, and abnormally large Knight shift (KS) drop below $$T_\textrm{c}$$ T c for $$H \parallel a$$ H ‖ a -magnetic easy axis, we advance further our theoretical work on the field (H)-temperature (T) phase diagram for $$H \parallel b$$ H ‖ b -magnetic hard axis which contains a positive sloped $$H_\textrm{c2}$$ H c2 departing from TCP. A nonunitary spin-triplet pairing with three components explains these experimental facts simultaneously and consistently by assuming that the underlying normal electron system with a narrow bandwidth characteristic to the Kondo temperature $$\sim$$ ∼ 30 K unsurprisingly breaks the particle-hole symmetry. This causes a special invariant term in Ginzburg–Landau (GL) free energy functional which couples directly with the 5f magnetic system, giving rise to the $$T_\textrm{c}$$ T c splitting and ultimately to the positive sloped $$H_\textrm{c2}$$ H c2 and the horizontal internal transition line connected to TCP. The large KS drop can be understood in terms of this GL invariance whose coefficient is negative and leads to a diamagnetic response where the Cooper pair spin is antiparallel to the applied field direction. The present scenario also accounts for the observed d-vector rotation phenomena and off-axis phase diagrams with extremely high $$H_\textrm{c2}$$ H c2 $$\gtrsim$$ ≳ 70 T found at angles in between the b- and c-axes and between the bc-plane and a-axis, making UTe$$_2$$ 2 a fertile playground for a possible topological superconductor.

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Theory of Pairing Assisted Spin Polarization in Spin-Triplet Equal Spin Pairing: Origin of Extra Magnetization in Sr₂RuO₄ in Superconducting State

Cited by 22 publications

References 20 publications

Spin polarization enhanced by spin-triplet pairing inSr2RuO4probed by NMR

Spin polarization enhanced by spin-triplet pairing inSr2RuO4probed by NMR

Two-Gap Superconductivity inLaNiGa2with Nonunitary Triplet Pairing and Even Parity Gap Symmetry

Theoretical Studies on Off-Axis Phase Diagrams and Knight Shifts in UTe$$_2$$: Tetra-Critical Point, d-Vector Rotation, and Multiple Phases

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Theory of Pairing Assisted Spin Polarization in Spin-Triplet Equal Spin Pairing: Origin of Extra Magnetization in Sr2RuO4 in Superconducting State

Cited by 22 publications

References 20 publications

Spin polarization enhanced by spin-triplet pairing inSr2RuO4probed by NMR

Spin polarization enhanced by spin-triplet pairing inSr2RuO4probed by NMR

Two-Gap Superconductivity inLaNiGa2with Nonunitary Triplet Pairing and Even Parity Gap Symmetry

Theoretical Studies on Off-Axis Phase Diagrams and Knight Shifts in UTe$$_2$$: Tetra-Critical Point, d-Vector Rotation, and Multiple Phases

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Theory of Pairing Assisted Spin Polarization in Spin-Triplet Equal Spin Pairing: Origin of Extra Magnetization in Sr₂RuO₄ in Superconducting State