UTe₂ is a rare superconductor believed to exhibit unique spin-triplet pairing, potentially possessing topological properties. The pairing mechanism remains unclear, with debate surrounding the role of ferromagnetic (FM) or antiferromagnetic (AFM) fluctuations. Understanding the magnetic properties of UTe₂ is crucial for elucidating its superconducting behavior. This study employs muon spin rotation/relaxation (µSR) to investigate the magnetic properties of independently grown UTe₂ single crystals, aiming to clarify the nature of magnetic fluctuations and their connection to the observed superconducting state. The importance stems from the potential of spin-triplet superconductors for applications in spintronics and topological quantum computing. The material's low critical temperature (Tc) near 2 K, large anisotropic upper critical field, and re-emergence of superconductivity above Hc2 at high magnetic fields further highlight its unconventional properties. While experimental indications point towards spin-triplet pairing, the microscopic mechanism and the influence of intrinsic magnetic inhomogeneities remain central open questions. This study specifically addresses the impact of these inhomogeneities on the interpretation of existing experimental data and seeks to provide a more comprehensive understanding of UTe2's low-temperature behavior. The ubiquitous residual linear term in the specific heat (C) and the low-temperature upturn in C/T versus T, observed in many samples, are also investigated in connection with the magnetic properties.

Previous studies on UTe₂ have provided various experimental indications of spin-triplet Cooper pairing. These include a negligible decrease in local spin susceptibility in the superconducting state (from 125Te-NMR Knight shift measurements), a large anisotropic upper critical field exceeding the Pauli paramagnetism limit in conventional superconductors, and the re-emergence of superconductivity at high magnetic fields applied in specific directions. Scanning tunneling spectroscopy has also suggested chiral in-gap surface states, indicative of a nontrivial band topology. Furthermore, observations of a double phase transition in specific heat and a finite polar Kerr effect have proposed a two-component superconducting order parameter that breaks time-reversal symmetry. However, the underlying pairing mechanism remains a topic of debate. Some suggest that FM fluctuations near a quantum critical point drive superconductivity, while others propose the dominance of AFM fluctuations. Inelastic neutron scattering experiments initially indicated AFM fluctuations, but later studies suggested the observed excitations are due to the heavy electron band structure, leaving the question of dominant interactions unresolved. Theoretical models have explored both FM and AFM fluctuation-mediated pairing, as well as Hund's and Kondo interaction-driven pairing independent of inter-site exchange. The double phase transition in specific heat, initially attributed to a two-component order parameter, is not universally observed, leading to suggestions of spatial inhomogeneity. A residual linear term in the specific heat and a low-temperature upturn in C/T vs. T are also present, with origins yet to be definitively established. These observations are discussed in the context of similar phenomena in other heavy-fermion superconductors, such as UPt3, URu2Si2, UPd2Al3, and CeCoIn5. Potential explanations include a residual normal state component, resonant impurity scattering, or magnetic origins. The existing literature highlights inconsistencies and the need for a more comprehensive investigation to reconcile the diverse experimental observations and theoretical interpretations.

This study employed muon spin rotation/relaxation (µSR) measurements on three independently grown UTe₂ single crystals to investigate its magnetic properties. The samples were prepared with varying degrees of crystallographic alignment: Sample S1 was a randomly oriented mosaic of single crystals, while samples S2 and S3 were plate-like single crystals with their c-axes oriented perpendicular to the flat surfaces. Zero-field (ZF), longitudinal-field (LF), and weak transverse-field (WTF) µSR measurements were performed using an Oxford Instruments top-loading dilution refrigerator. The samples were mounted on silver sample holders and measurements were conducted over a wide temperature range. The ZF µSR data were fit using a two-component exponential relaxation function plus a non-relaxing contribution (Equation 1) to account for magnetic regions and non-magnetic/rapidly fluctuating regions. The LF µSR data was analyzed to understand the effect of applied magnetic fields on relaxation and ascertain the nature of internal field fluctuations. In the WTF µSR experiments, a two-component Gaussian relaxation function (Equation 2) was used for fitting the experimental data. The data analysis involved careful consideration of the amplitude and relaxation rate parameters, accounting for the non-relaxing contribution from the sample holder and distinguishing between relaxation from different parts of the sample. Density functional theory (DFT) calculations were used to determine the most likely muon stopping site in UTe₂. Specific heat measurements using both adiabatic heat pulse and quasi-adiabatic thermal relaxation techniques were performed to obtain the temperature dependence of the specific heat for comparison with the µSR results. The combination of µSR and specific heat data provides a comprehensive perspective on the magnetic behavior of UTe₂.

The µSR measurements revealed the presence of magnetic clusters in all three UTe₂ samples. A significant non-relaxing component in the ZF µSR signals suggests that a substantial volume fraction of the sample exhibits either negligible local fields or extremely fast spin fluctuations, even at very low temperatures. The ZF µSR data showed two exponentially relaxing components, with a fast-relaxing component attributed to magnetic regions with frozen or slowly fluctuating spins and a slow-relaxing component associated with paramagnetic regions with rapidly fluctuating electronic moments above ~0.2 K. The analysis of the data revealed that the fast relaxation rate (λ1) in sample S1 exhibits a temperature dependence that initially suggests a correlation with slow longitudinal magnetic fluctuations along the a-axis, but deviates from the typical behavior predicted near a FM instability. In samples S2 and S3 (c-axis aligned), a significant loss of initial amplitude in the ZF µSR signal was observed with decreasing temperature, suggesting an anisotropic distribution of local magnetic fields. The temperature dependence of the slower relaxation rate (λ2) in samples S2 and S3 shows an increase below 0.5 K and a plateau below ~0.12 K, with an abrupt change near Tc. The LF µSR data showed that application of an external field decoupled the muon spins from the internal fields and allowed the paramagnetic components to become dominant in the sample. The WTF µSR data and analysis of the missing amplitude of the signals confirmed the presence of a magnetic volume fraction in samples S2 and S3, whose evolution is halted at Tc. DFT calculations indicated a single muon site, contradicting previous interpretations of two sites, indicating the magnetic inhomogeneity observed is intrinsic. The magnetic volume fraction, estimated from both ZF and WTF data, exhibits a temperature dependence, increasing as the temperature decreases, but showing saturation at Tc. The data suggest that the freezing of magnetic clusters is an inhomogeneous process which starts well above Tc. The low-temperature upturn in C/T vs T in sample S1 was analyzed using the Schottky anomaly expression, revealing a level splitting much larger than expected from crystal electric field effects. The residual linear term in specific heat below Tc was observed to vary between samples, correlating with the magnetic volume fraction. The low temperature linear term was linked to the magnetic clusters and attributed to spin glass behavior

The findings demonstrate the ubiquitous presence of magnetic clusters in UTe₂, challenging the assumption of homogeneity in previous studies. The magnetic clusters, whose freezing is an inhomogeneous process starting well above Tc, are likely responsible for the residual linear term in the specific heat and the low-temperature upturn. The absence of a residual linear term in thermal conductivity suggests a magnetic origin for this behavior rather than a residual density of states. The correlation between the magnetic volume fraction and the residual linear term in different samples further supports this conclusion. The observation that the freezing of magnetic clusters is largely complete in the superconducting state suggests that these clusters do not directly cause the superconductivity. However, the impact of these clusters on other low-temperature experimental observations needs to be further considered. The findings have implications for the interpretation of various experimental results, including those related to the polar Kerr effect, inelastic neutron scattering resonance, and NMR measurements. Samples exhibiting a minimal residual linear term and a smaller Schottky anomaly are likely to be more representative of the intrinsic properties of UTe₂.

This study provides compelling evidence for the presence of ubiquitous magnetic clusters in UTe₂ that freeze in a disordered state at low temperatures. This inhomogeneous magnetic behavior is linked to the residual linear term in the specific heat and its low-temperature upturn. The findings challenge previous assumptions of sample homogeneity and highlight the importance of considering this magnetic inhomogeneity when interpreting low-temperature experimental results. Future studies should focus on improving sample quality to minimize magnetic inhomogeneity and facilitate a more precise determination of UTe₂'s intrinsic properties.

The study is limited to three samples, although these were from independent growths. Further investigation on a broader range of samples with varying degrees of disorder and impurity levels is needed to fully characterize the universality of the observed magnetic inhomogeneity. The analysis of the low-temperature upturn in specific heat did not consider broadening effects from the inhomogeneous nature of the cluster freezing. Moreover, the exact nature of the magnetic clusters (FM or AFM) cannot be definitively determined from the current data.