Unusual slow magnetic fluctuations and critical slowing down in Sr$_{2}$Ir$_{1-x}$Rh$_{x}$O$_{4}$

TL;DR

This study reveals slow magnetic fluctuations and critical slowing down in Sr$_{2}$Ir$_{1-x}$Rh$_{x}$O$_{4}$ using muon spin relaxation, indicating coexistence of static and dynamic magnetic fields near magnetic transition temperatures.

Contribution

It provides the first detailed muon spin relaxation analysis of hidden magnetic order and critical slowing down in Sr$_{2}$Ir$_{1-x}$Rh$_{x}$O$_{4}$, highlighting the coexistence of static and dynamic magnetic fields.

Findings

Critical slowing down observed at specific temperatures.

Correlation times of spin fluctuations are in the nanosecond range.

Field dependencies match the Redfield relation.

Abstract

Hidden magnetic order of Sr$_2$Ir$_{1-x}$Rh$_x$O$_4$, $x = 0.05$ and 0.1, has been studied using muon spin relaxation spectroscopy. In zero applied field and weak longitudinal fields ($\mu_0H_L \lesssim 2$~mT), muon spin relaxation data can be well described by exponentially-damped static Lorentzian Kubo-Toyabe functions, indicating that static and dynamic local fields coexist at each muon site. For $\mu_0H_L \gtrsim 2$~mT, the static rate is completely decoupled, and the exponential decay is due to dynamic spin fluctuations. In both zero field and $\mu_0H_L = 1$--2~mT, the temperature dependencies of the exponential muon spin relaxation rate exhibit maxima at 215~K for $x = 0.05$ and 175~K for $x = 0.1$, suggesting critical slowing down of electronic spin fluctuations. The field dependencies of the dynamic spin fluctuation rates can be well described by the Redfield relation. The correlation time of this electronic spin fluctuation is in the range of~2--5~ns for Sr$_2$Ir$_{0.9}$Rh$_{0.1}$O$_4$, and shorter than 2~ns for Sr$_2$Ir$_{0.95}$Rh$_{0.05}$O$_4$. The rms fluctuating field is on the order of 1 mT, which is consistent with the polarized neutron diffraction cross-section.