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Register a new userAnisotropic response of spin susceptibility in the superconducting state of UTe$_2$ probed with $^{125}$Te-NMR measurement
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To investigate spin susceptibility in a superconducting (SC) state, we measured the $^{125}$Te-nuclear magnetic resonance (NMR) Knight shifts at magnetic fields ($H$) up to 6.5 T along the $b$ and $c$ axes of single-crystal UTe$_2$, a promising candidate for a spin-triplet superconductor. In the SC state, the Knight shifts along the $b$ and $c$ axes ($K_b$ and $K_c$, respectively) decreased slightly and the decrease in $K_b$ was almost constant up to 6.5 T. The reduction in $K_c$ decreased with increasing $H$, and $K_c$ was unchanged through the SC transition temperature at 5.5 T, excluding the possibility of spin-singlet pairing. Our results indicate that spin susceptibilities along the $b$ and $c$ axes slightly decrease in the SC state in low $H$, and the $H$ response of SC spin susceptibility is anisotropic in the $bc$ plane. We discuss the possible $d$-vector state within the spin-triplet scenario and suggest that the dominant $d$-vector component for the case of $H parallel b$ changes above 13 T, where $T_{rm c}$ increases with increasing $H$.
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UTe$_2$ is a recently discovered promising candidate for a spin-triplet superconductor. In contrast to conventional spin-singlet superconductivity, spin-triplet superconductivity possesses spin and angular momentum degrees of freedom. To detect these degrees of freedom and obtain the solid evidence of spin-triplet superconductivity in UTe$_2$, we performed $^{125}$Te-NMR measurement. We previously reported that the shoulder signal appears in NMR spectra below the superconducting (SC) transition temperature $T_{rm c}$ in $H parallel b$, and that a slight decrease in the Knight shift along the $b$ and $c$ axes ($K_b$ and $K_c$, respectively) below $T_{rm c}$ at a low magnetic field $H$. To clarify the origin of the shoulder signal and the trace of the decrease in $K_b$, we compared the $^{125}$Te-NMR spectra obtained when $H~parallel~b$ and $H~parallel~c$ and measured the $^{125}$Te-NMR spectra for $H~parallel~b$ up to 14.5~T. The intensity of the shoulder signal observed for $H~parallel~b$ has a maximum at $sim 6$~T and vanishes above 10~T, although the superconductivity is confirmed by the $chi_{rm AC}$ measurements, which can survive up to 14.5~T (maximum $H$ in the present measurement). Moreover, the decrease in $K_b$ in the SC state starts to be small around 7~T and almost zero at 12.5~T. This indicates that the SC spin state gradually changes with the application of $H$. Meanwhile, in $H~parallel~c$, unexpected broadening without the shoulder signals was observed below $T_{rm c}$ at 1~T, and this broadening was quickly suppressed with increasing $H$. We construct the $H$--$T$ phase diagram for $H~parallel~b$ and $H~parallel~c$ based on the NMR measurements and discuss possible SC states with the theoretical consideration. We suggest that the inhomogeneous SC state characterized by the broadening of the NMR spectrum originates from the spin degrees of freedom.
We have performed the $^{125}$Te-nuclear magnetic resonance (NMR) measurement in the field along the $b$ axis on the newly discovered superconductor UTe$_2$, which is a candidate of a spin-triplet superconductor. The nuclear spin-lattice relaxation rate divided by temperature $1/T_1T$ abruptly decreases below a superconducting (SC) transition temperature $T_c$ without showing a coherence peak, indicative of UTe$_2$ being an unconventional superconductor. It was found that the temperature dependence of $1/T_1T$ in the SC state cannot be understood by a single SC gap behavior but can be explained by a two SC gap model. The Knight shift, proportional to the spin susceptibility, decreases below $T_c$, but the magnitude of the decrease is much smaller than the decrease expected in the spin-singlet pairing. Rather, the small Knight-shift decrease as well as the absence of the Pauli-depairing effect can be interpreted by the spin triplet scenario.
The orthorhombic uranium dichalcogenide UTe$_2$ displays superconductivity below 1.7 K, with the anomalous feature of retaining 50$%$ of normal state (ungapped) carriers, according to heat capacity data from two groups. Incoherent transport that crosses over from above 50 K toward a low temperature, Kondo lattice Fermi liquid regime indicates strong magnetic fluctuations and the need to include correlation effects in theoretical modeling. We report density functional theory plus Hubbard U (DFT+U) results for UTe$_2$ to provide a platform for modeling its unusual behavior, focusing on ferromagnetic (FM, time reversal breaking) long range correlations along the ${hat a}$ axis as established by magnetization measurements and confirmed by our calculations. States near the Fermi level are dominated by the $j=frac{5}{2}$ configuration, with the $j_z=pmfrac{1}{2}$ sectors being effectively degenerate and half-filled. Unlike the small-gap insulating nonmagnetic electronic spectrum, the FM Fermi surfaces are large (strongly metallic) and display low dimensional features, reminiscent of the FM superconductor UGe$_2$.
In order to determine the superconducting paring state in the ferromagnetic superconductor UCoGe, ^{59}Co NMR Knight shift, which is directly related to the microscopic spin susceptibility, was measured in the superconducting state under magnetic fields perpendicular to spontaneous magnetization axis: ^{59}K^{a, b}. ^{59}K^{a, b} shows to be constant, but does not decrease below a superconducting transition. These behaviors as well as the invariance of the internal field at the Co site in the superconducting state exclude the spin-singlet pairing, and can be interpreted with the equal-spin pairing state with a large exchange field along the c axis, which was studied by Mineev [Phys. Rev. B 81, 180504 (2010)].
Recent observations [A.~Pustogow et al. Nature 574, 72 (2019)] of a drop of the $^{17}$O nuclear magnetic resonance (NMR) Knight shift in the superconducting state of Sr$_2$RuO$_4$ challenged the popular picture of a chiral odd-parity paired state in this compound. Here we use polarized neutron scattering to show that there is a $34 pm 6$ % drop in the magnetic susceptibility at the ruthenium site below the superconducting transition temperature. Measurements are made at lower fields $H sim tfrac{1}{3} H_{c2}$ than a previous study allowing the suppression to be observed. Our results are consistent with the recent NMR observations and rule out the chiral odd-parity $mathbf{d}=hat{mathbf{z}}(k_xpm ik_y)$ state. The observed susceptibility is consistent with several recent proposals including even-parity $B_{1g}$ and odd-parity helical states.
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