${\mu }^{+}\text{SR}$ investigation of local magnetic order in ${\text{LiCrO}}_2$

In order to elucidate the magnetic nature of the lithium chromium dioxide ${\text{LiCrO}}_2$, in which the ${\text{Cr}}^{3+}$ ions form a two-dimensional triangular lattice in the ${\text{CrO}}_2$ plane, we have performed a positive muon-spin rotation and relaxation $\left({\mu }^{+}\text{SR}\right)$ experiment using a powder sample in the temperature range 1.7–155 K. Weak-transverse-field measurements indicated the existence of a bulk antiferromagnetic (AF) transition at $T_N=61.2\text{K}$. Below $T_N$, zero-field (ZF) ${\mu }^{+}\text{SR}$ measurements demonstrated the formation of static long-range order; the observed ZF spectrum was well reproduced by the AF spin structure proposed by neutron measurements. The $\text{ZF-}{\mu }^{+}\text{SR}$ measurements also indicated that ${\text{LiCrO}}_2$ is a pure paramagnet for $T\ge 62.5\text{K}$, since its internal magnetic field $\left(H_{\text{int}}\right)$ can be explained by solely nuclear magnetic moments. This means that, contrary to previous suggestions by susceptibility and heat capacity measurements, no short-range order exists for $T\ge 62.5\text{K}$. However, $\text{ZF-}{\mu }^{+}\text{SR}$ detected the change in $H_{\text{int}}$ from a low-$T$ static state to a high-$T$ dynamic state at 115 K, most likely connected to a change in the position/motion of the Li ions.

Figure 1

(Color online) Crystal structure of ${\text{LiCrO}}_2$ showing (a) alternating stacks of Li and ${\text{CrO}}_2$ layers along the $c$ axis and (b) top view along the $c$ axis demonstrating the triangular configuration of the Cr ions.

Figure 2

Temperature dependence of (a) magnetic susceptibility $\left(\chi \right)$ and (b) inverse $\chi$ for the powder sample of ${\text{LiCrO}}_2$. $\chi$ was measured in field-cooling (FC) mode with magnetic field $H=10\text{kOe}$.

Figure 3

(Color online) Temperature dependence of the $\text{wTF}\left(=30\text{Oe}\right)$ ${\mu }^{+}\text{SR}$ time spectra. Solid lines represent the fitting result using Eq. (1).

Figure 4

Temperature dependences of (a) normalized asymmetries ($A_{\text{TF}}$ and $A_{\text{fast}}$), (b) exponential relaxation rates (${\lambda }_{\text{TF}}$ and ${\lambda }_{\text{fast}}$), and (c) magnetic susceptibility $\left(\chi \right)$. The data in (a) and (b) were obtained by fitting the wTF spectra using Eq. (1). $\chi$ was measured both in FC and zero-field-cooling (ZFC) mode with magnetic field $H=100\text{Oe}$.

Figure 5

(Color online) Temperature-dependent $\text{ZF-}{\mu }^{+}\text{SR}$ spectra for ${\text{LiCrO}}_2$. Solid lines represent the fitting result using Eq. (2). Each spectrum is offset by 0.1 for clarity of display.

Figure 6

(Color online) Temperature dependences of (a) muon precession frequencies $f_{\text{AF}1}\left(={\omega }_{\text{AF}1}^{\mu }/2\pi \right)$ and $f_{\text{AF}2}\left(={\omega }_{\text{AF}2}^{\mu }/2\pi \right)$, (b) exponential relaxation rates (${\lambda }_{\text{AF}1}$ and ${\lambda }_{\text{AF}2}$), and (c) ${\lambda }_{\text{tail}}$. The data were obtained by global fitting of all the ZF spectra using Eq. (2), with common $A_{\text{AF}1}\left(=0.10678\right)$, $A_{\text{AF}2}\left(=0.07424\right)$, $A_{\text{tail}}\left(=0.05898\right)$, and ${\varphi }_1={\varphi }_2=0$.

Figure 7

(Color online) Temperature dependences of (a) $\text{ZF-}{\mu }^{+}\text{SR}$ spectrum above $T_N$ and (b) the field distribution width $\left(\Delta \right)$ shown as triangles and field fluctuation rate $\left(\nu \right)$ as circles. The data in (b) were obtained by fitting the ${\mu }^{+}\text{SR}$ time spectra to Eq. (3). Closed symbols are obtained from a global fit to ZF spectra only, while open symbols are obtained from a global fit to both ZF and longitudinal field $\left(\text{LF}=20\text{Oe}\right)$ spectra at 65 and 140 K. The solid horizontal line in (b) represents a common ${\Delta }_{\text{measure}}^{\text{PM}}\left(=0.3124\times {10}^6{\text{s}}^{-1}\right)$ for a global fit, while the dashed horizontal line shows a prediction from dipole field calculations ${\Delta }_{\text{calc}}^{\text{PM}}$. Dotted curve serves as a guide for the eyes.

Figure 8

(Color online) (a) Field distribution for ${\text{LiCrO}}_2$ predicted from dipole field calculations (vertical bars) using the spin structure from Ref. 12, (b) calculated $\text{ZF-}{\mu }^{+}\text{SR}$ time spectrum (thick solid line) and the fit curve using Eq. (2) (thin solid line) and Eq. (2) with ${\varphi }_i=0$ (thin broken line), and (c) measured $\text{ZF-}{\mu }^{+}\text{SR}$ time spectrum at 1.7 K. In the calculations, we used ${\mu }_{\text{ord}}=2.7{\mu }_B$, where ${\mu }_{\text{ord}}$ is the magnitude of the ordered moment of the Cr ions estimated by neutron measurements (Ref. 12). The calculated ZF spectrum was obtained by Eq. (4) with ${\lambda }_i=0$.