Symmetry of magnetic correlations in spin-triplet superconductor UTe2

The temperature dependence of the low-energy magnetic excitations in the spin-triplet superconductor UTe$_2$ was measured via inelastic neutron scattering in the normal and superconducting states. The imaginary part of the dynamic susceptibility follows the behavior of interband correlations in a hybridized Kondo lattice with an appropriate characteristic energy. These excitations are a lower-dimensional analogue of phenomena observed in other Kondo lattice materials, such that their presence is not necessarily due to dominance of ferromagnetic or antiferromagnetic correlations. The onset of superconductivity alters the magnetic excitations noticeably on the same energy scales, suggesting that these changes originate from additional electronic structure modification.

Spin-triplet superconductivity was recently discovered in UTe 2 1 . The superconductivity is characterized by large and anisotropic upper critical fields that all exceed the paramagnetic limit, pointing to unconventional spin-triplet pairing 1,2 . Superconductivity is limited by a magnetic phase transition at 35 T 3,4 , and the field-polarized state contains another reentrant superconducting phase above 40 T 3 . Superconductivity in UTe 2 is believed to be topologically nontrivial because of observations of chiral in-gap surface states 5 , a double transition in specific heat, and broken time reversal symmetry as detected by optical Kerr rotation 6 , which suggest the presence of a complex, two-component superconducting order parameter. Consistent with a p-wave orbital symmetry, the superconducting gap is nodal [7][8][9] .
Superconductivity emerges from a renormalized electronic structure of hybridized felectrons. UTe 2 exhibits archetypal heavy fermion features, namely a large low-temperature specific heat and local maxima in temperature-dependent electrical resistivity and magnetic susceptibility below room temperature 1 , a Kondo hybridization gap in scanning tunneling spectroscopy 5 , quadratic temperature dependence of low-temperature resistivity 10 , linear temperature dependence of thermoelectric power 11 , and a Drude peak in optical conductvity 12 . Angle resolved photoemission (ARPES) measurements show that the band structure of UTe 2 is dominated by two intersecting one-dimensional sheets 13 . The heavy electron states result from hybridization between these highly-dispersive bands with felectron states near the chemical potential, as suggested by dynamical mean field theory (DMFT) calculations 12,13 , while ARPES also reveals an additional Fermi pocket that is three-dimensional and potentially heavy. We performed a series of inelastic neutron scattering experiments in the crystallographic a-b plane that demonstrate the detailed energy-dependence and anisotropy of the magnetic excitations. The excitations evolve over a broad range of temperatures, from the weakly correlated high-temperature state into the superconducting state below 1.6 K. These excitations are signatures of the heavy electron band structure, similar to several other Kondo lattice systems, but with a lower dimensionality due to the UTe 2 structure. They do not a priori imply a tendency toward a specific type of long-range magnetic order. These measurements also show that the change in the excitation spectrum in the superconducting state is a phenomenon that occurs over energies of several meV, suggesting a substantial change in magnetic correlations at low temperatures.
The scattered neutron intensity S, measured as a function of transfer of momentum Q and energy E, is proportional to a temperature factor times the imaginary part of the dynamic Another outstanding feature is the width in E of the excitatations in UTe 2 , which is comparable to the peak excitation energy, even at Q values where the excitations are sharpest.
Despite these large widths, which imply substantially shortened excitation lifetimes or a distribution of transitions, the excitations are clearly peaked at nonzero E -therefore, these are inelastic features that are separated from the ground state by a finite energy gap. The peak energy of 4 meV matches well the hybridization gap determined in scanning tunneling spectroscopy measurements 5 , suggesting a connection to the electronic structure.
The temperature dependence of the excitations at K = 1.4 is shown in Fig. 3. Cooling below 5 K into the superconducting state yields an excitation spectrum that appears to remain mostly the same. In contrast, on warming from 5 K to 20 K, the intensity decreases and the peak position increases slightly, but the excitations maintain their Q-dependence and energy gap. Importantly, they do not move to lower E and become quasielastic, as might occur to magnetic correlations at temperatures above a magnetic phase transition. To account for this hybridization, it will be necessary to carry out further electronic structure and magnetic susceptibility calculations with higher energy resolution. Available calculations suggest that the strongest atomic exchange interaction in UTe 2 is ferromagnetic, between uranium dimers, with antiferromagnetic correlations parallel to the chains along the a-axis 13,30 , but this does not readily explain the measured χ (Q, E). The observed b-axis modulation has been considered to arise from the electronic structure, either Fermi surface nesting or RKKY exchange 18 . However, calculations to date have not yet addressed an important experimental point, namely that the measured χ (Q, E) is peaked at small but finite energy, not at zero energy, the latter condition relevant to static magnetic order.
Generally, given that these excitations appear to follow the temperature dependence of the b-axis bulk magnetic susceptibility, we expect that they will be quite robust as a function of magnetic field and could play a role in the magnetic transition at 35 T, and by extension, in the magnetically ordered phase above 1.5 GPa [31][32][33] .
The situation at lowest temperatures, in the superconducting state, brings an interesting twist. As Fig. 3 shows, the magnetic excitation spectrum is similar at 0.2 K and 5 K.
Indeed, a significant difference is not expected at these energies, given the 1.  (Fig. 4e,f), when compared to the data at 5 K (Fig. 2).
This behavior suggests that in the superconducting state, χ changes on energy scales even larger than 1 meV, and that previously reported feature reflects a larger change in the magnetic excitation spectrum. Such a broad change is difficult to reconcile with an interpretation in terms of a superconducting spin resonance. Since these magnetic excitations have their origin in the heavy fermion band structure, low-temperature changes in the electronic structure are likely responsible, and this is evidence that the superconducting state involves heavy quasiparticles. The change in the magnetic excitations may additionally correlate with low-temperature changes in the magnetic response in muon spin relaxation 15 and nuclear magnetic resonance 34 inside the superconducting state.
In summary, inelastic neutron scattering measurements reveal magnetic excitations that are consistent with Kondo lattice phenomena. Specifically, the excitations follow BZ edges, obey the paramagnetic structural symmetry, and the temperature evolution of the heavy fermion bulk magnetic susceptibility along the b-axis. By analogy with other Kondo lattice compounds, these excitations are not directly related to an incipient magnetic ordered state.
In the superconducting state, the magnetic excitations near [0, 1.4, 0] decrease in energy, likely related to a change in the electronic structure.

I. METHODS
Single crystals of UTe 2 were synthesized by the chemical vapor transport method using iodine as the transport agent 35 . The crystals are from synthesis batches that have been previously characterized 1,3 and exhibit consistent properties.
Crystal orientation was determined by Laue x-ray diffraction performed with a Photonic Science x-ray measurement system. 1.2 g of single crystals, ranging in mass from 0.01 g to 0.1 g were coaligned and affixed to two copper plates using CYTOP fluoropolymer and

II. DATA AVAILABILITY
The data that support the results presented in this paper and other findings of this study are available from the corresponding author upon reasonable request.

III. ACKNOWLEDGMENTS
We

IV. COMPETING INTERESTS
The authors declare no competing interests. correlations between local f electrons and light bands are weakest. e) As temperature increases, the total spectral weight decreases but the magnetic susceptibility remains peaked at the same q value until it is no longer detectable above background. f) This behavior follows closely the temperaturedependence of the bulk magnetic susceptibility χ along the b-axis (K direction) 1 , which shows a hump structure characteristic of heavy fermion Kondo lattices (1 cm 3 /mol = 4π × 10 −6 m 3 /mol).
The letters indicate the temperatures of the corresponding neutron data.