Spin dynamics and a nearly continuous magnetic phase transition in an entropy-stabilized oxide antiferromagnet

The magnetic order and the spin dynamics in the antiferromagnetic entropy-stabilized oxide (${\mathrm{Mg}}_{0.2}{\mathrm{Co}}_{0.2}{\mathrm{Ni}}_{0.2}{\mathrm{Cu}}_{0.2}{\mathrm{Zn}}_{0.2}$)O (MgO-ESO) have been studied using muon spin relaxation ($\mu \mathrm{SR}$) and inelastic neutron scattering. We find that antiferromagnetic order develops gradually in the sample volume as it is cooled below 140 K, becoming fully ordered around 100 K. The spin dynamics show a critical slowing down in the vicinity of the transition, and the magnetic order parameter grows continuously in the ordered state. These results indicate that the antiferromagnetic transition is continuous but proceeds with a Gaussian distribution of ordering temperatures. The magnetic contribution to the specific heat determined from inelastic neutron scattering likewise shows a broad feature centered around 120 K. High-resolution inelastic neutron scattering further reveals an initially gapped spectrum at low temperature which sees an increase in a quasielastic contribution upon heating until the ordering temperature.

Figure 1

(a) Asymmetry spectra at representative temperatures above, below, and throughout the antiferromagnetic transition. Solid black curves are fits to the data using the model $a\left(t\right)=a_{0}exp{(-\lambda t)}^{\beta }$. (b) Temperature dependence of the relaxation rate $\lambda$ (blue triangles, left axis) and exponential power $\beta$ (gray circles, right axis) determined from the fits. The peak in $\lambda$ is characteristic of critical spin dynamics near a magnetic phase transition.

Figure 2

(a) Weak transverse field (wTF) asymmetry spectra at 230 K and 2 K. The large-amplitude oscillations at high temperature indicate a fully paramagnetic state, while the complete lack of oscillations at low temperature indicates the presence of static magnetism extending through the entire sample volume. (b) Temperature dependence of the zero-field (ZF) asymmetry amplitude $a_0$ determined from fits to the spectra. (c) Antiferromagnetically ordered volume fraction (blue circles, left axis) calculated from the $a_0$ values. The orange curve is a fit to the volume fraction data using a complementary error function, corresponding to the Gaussian distribution of Néel temperatures shown as the gray curve (right axis).

Figure 3

(a) Early-time portion of the zero-field $\mu \mathrm{SR}$ asymmetry spectra for MgO-ESO at representative temperatures. The solid black curves represent fits using a model described in the main text. (b) The Kubo-Toyabe relaxation rate $\mathrm{\Delta }$ (blue symbols) as a function of temperature extracted from the fits. The orange curve is a power law fit. (c) Simulated probability distribution of the magnetic field magnitude at a possible muon stopping site (blue curve), compared to the field distribution for a collection of completely randomly oriented spins corresponding to a KT distribution with $\mathrm{\Delta }=210\mu {\mathrm{s}}^{-1}$ (orange curve).

Figure 4

(a) Asymmetry spectra in longitudinal field (LF) of 0.3 T shown for representative temperatures. The solid black curves are fits using the model $a\left(t\right)=a_{0}exp{(-\lambda t)}^{\beta }$. (b) Temperature dependence of the relaxation rate $\lambda$ (blue circles, left axis) and exponential power $\beta$ (gray circles, right axis) determined from the fits. (c) Estimated spin fluctuation rate $\nu$ determined from $\lambda$ as described in the text.

Figure 5

Thermodynamic analysis using phonon properties determined from inelastic neutron scattering (INS) measurements combined with calorimetry. (a) Phonon density of states (DOS) extracted from INS. The red points give the DOS extracted from the measured scattering function before correcting for atomic cross sections and masses. The black points give the thermodynamic phonon DOS determined by correcting for cross sections and atomic contributions based on calculations of the phonon DOS shown in (b). The total calculated phonon DOS (black line) is well separated into Mg-site (red) and O (blue) contributions. (c) Measured heat capacity, $C_P$ (black points), along with the phonon contribution at constant volume ($C_V$) determined from the measured thermodynamic phonon DOS. A correction for volume expansion ($9Bv{\alpha }^{2}T$) is also included. (d) Magnetic contribution determined by subtracting the phonon contribution from the measured heat capacity. A very broad magnetic transition is evident.

Figure 6

(a) Inelastic neutron scattering (INS) spectra for MgO-ESO at representative temperatures obtained from integrating over the $Q$ range $1.1<Q<1.4{\AA }^{-1}$. The solid curves represent fits described in the main text. (b) Normalized weights of the magnon and quasielastic neutron scattering (QENS) components of the fits to the INS spectra as a function of temperature. See main text for additional details.