Microscopic evidence of a field-induced critical spin-liquid state in a frustrated metal

Abstract

A field-induced quantum spin liquid (QSL) state is an extraordinary phenomenon, hitherto unobserved in metallic frustrated compounds. Recent bulk measurements have revealed intriguing field-induced magnetic states in metallic frustrated CePdAl. However, the nature of these field-induced states, potentially including a QSL state, remains unclear due to the lack of detailed microscopic investigation. To elucidate these field-induced states, we employed the transverse-field muon spin relaxation/rotation (TF-$μ$SR) technique, applying various magnetic fields parallel to the c-axis in single-crystalline CePdAl over a broad temperature range (100~K-100~mK). Our $μ$SR data indicate that field-induced low-temperature states for fields B$\leq B_{c2}(=3.4~T)$ exhibit long-range magnetic order, whereas for B>$B_{c2}$ they yield contrasting behavior. Notably, at 3.75 T, the transverse relaxation rate ($λ_T$) diverges following a power-law dependence below 800~mK along with an indication of finite frustration, whereas the Knight shift is temperature independent. These observations corroborate the signature of a critical spin-liquid (CSL) with antiferromagnetic spin fluctuations. Furthermore, at 4.3 T, a non-Fermi liquid state is observed where frustration is absent. This comprehensive microscopic study strongly suggests the existence of a CSL state in a metallic frustrated system.

Figures (4)

• Figure 1: Temperature-field magnetic phase diagram has been constructed from ref. PhysRevLett.118.107204 for CePdAl when applied magnetic field is along the crystalligraphic c-axis. Blue stars and brown circles represent $T_s$ and $T_N$ from bulk measurements PhysRevLett.118.107204. Orange star and pink circle represent $T_s$ and $T_N$ estimated from zero field $\mu$SR measurements PhysRevB.105.L180402. NFL, FL and CSL represents non-Fermi liquid, Fermi-liquid and critical spin liquid respectively.
• Figure 2: (a), (b) and (c) show the temperature evolution of FFT $\mu$SR spectra at an applied field of 3 T, 3.75 T and 4.3 T respectively. The dashed lines are the guide to eyes and the shaded region in (a) represents LRO state. The left peak (line-1) and right peak (line-2) represent site-1 and site-2 respectively and the middle peak is the background contribution.
• Figure 3: (a) and (b) show the temperature dependence of knight shift ($K_\mu$%) and relaxation rate ($\lambda_T$) at different magnetic fields (B$\leq B_{c2}$) for site-1. (c) and (d) represent the temperature dependence of knight shift (K%) and relaxation rate ($\lambda_T$) at different magnetic fields (B$\leq B_{c2}$) for site-2. $T_s$ depicts a energy scale discussed in text. AFMO represent the antiferromagnetic ordered state. The dashed lines are the guide to eyes.
• Figure 4: (a) and (b) represent the temperature evolution of knight shift and relaxation rate ($\lambda_T$) for both of sites at 3.75 T ($AF_3$). (c) and (d) represent the temperature evolution of knight shift and relaxation rate ($\lambda_T$) for both of sites at 4.3 T ($AF_3$). The dashed lines are the guide to eyes. The red lines represents power-law behavior.