Logarithmic growth law in the two-dimensional Ising spin glass state resulting from the electron doping in single-layered manganites

TL;DR

This study demonstrates a logarithmic growth law in a two-dimensional spin-glass state within electron-doped manganites, supported by experimental ac-susceptibility data and droplet model scaling analysis.

Contribution

It provides experimental evidence for the logarithmic growth law in a 2D spin-glass state, derived from simple scaling arguments and ac-susceptibility measurements.

Findings

Logarithmic growth law confirmed in 2D spin-glass state

Scaling form derived and fitted well to experimental data

Identifies the 2D SG correlation development below T_N

Abstract

The ac-susceptibility of the electron doped single-layered manganite La$_{1.1}$Sr$_{0.9}$MnO$_4$ is analyzed in detail. A quasi two-dimensional (2$D$) antiferromagnetic (AFM) order with Ising anisotropy is stabilized below $T_N$ $\sim$ 80K. We show that below $T_N$, a rare 2$D$ spin-glass (SG) correlation develops with the same Ising anisotropy as the AFM state. Using simple scaling arguments of the droplet model, we derive a scaling form for the ac-susceptibility data of a 2$D$ SG, which our experimental data follows fairly well. Due to simplifications in this 2$D$ case, the proposed scaling form only contains two unknown variables $\psi\nu$ and $\tau_0$. Hence, the logarithmic growth law of the SG correlation predicted by the droplet model is convincingly evidenced by the scaling of our experimental data. The origin and nature of this 2$D$ SG state is also discussed.