Search

We report a systematic study of the $5d$-electron-doped system $\mathrm{Ce}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ir}}_{x})}_{2}{\mathrm{Al}}_{10}$ $(0\ensuremath{\le}x\ensuremath{\le}0.15)$. With increasing $x$, the orthorhombic $b$ axis decreases slightly while accompanying changes in $a$ and $c$ leave the unit cell volume almost unchanged. Inelastic neutron scattering, along with thermal and transport measurements, reveal that for the Kondo semiconductor ${\mathrm{CeFe}}_{2}{\mathrm{Al}}_{10}$, the low-temperature energy gap, which is proposed to be a consequence of strong $c\text{\ensuremath{-}}f$ hybridization, is suppressed by a small amount of Ir substitution for Fe and that the system adopts a metallic ground state with an increase in the density of states at the Fermi level. The charge or transport gap collapses (at $x=0.04$) faster than the spin gap with Ir substitution. Magnetic susceptibility, heat capacity, and muon spin relaxation measurements demonstrate that the system undergoes long-range antiferromagnetic order below a N\'eel temperature ${T}_{\mathrm{N}}$ of 3.1(2) K for $x=0.15$. The ordered moment is estimated to be smaller than 0.07(1) ${\ensuremath{\mu}}_{\mathrm{B}}$/Ce, although the trivalent state of Ce is confirmed by Ce ${L}_{3}$-edge x-ray absorption near edge spectroscopy. It is suggested that the $c\text{\ensuremath{-}}f$ hybridization gap, which plays an important role in the unusually high ordering temperatures observed in $\mathrm{Ce}{T}_{2}{\mathrm{Al}}_{10}$ ($T$ = Ru and Os), may not be necessary for the onset of magnetic order with a low ${T}_{\mathrm{N}}$ seen here in $\mathrm{Ce}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ir}}_{x})}_{2}{\mathrm{Al}}_{10}$.

The linear magnetoelectric effect and multiferroicity phenomena occur independently due to breaking inversion symmetry below the magnetically ordered state of either transition metal or rare-earth ions. Here, we report the occurrence of a linear magnetoelectric effect and magnetic field-induced ferromagnetism and ferroelectricity below ${T}_{\mathrm{N}}^{R}$ in the orthorhombic green phases ${R}_{2}\mathrm{BaCu}{\mathrm{O}}_{5}$ ($R=\mathrm{Dy}$ and Ho). They undergo a long-range antiferromagnetic ordering of ${\mathrm{Cu}}^{2+}$ (${T}_{\mathrm{N}}^{\mathrm{Cu}}=18.5$ and 17.5 K) and ${R}^{3+}$ ions (${T}_{\mathrm{N}}^{\mathrm{Dy}}=10.7\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${T}_{\mathrm{N}}^{\mathrm{Ho}}=8\phantom{\rule{0.16em}{0ex}}\mathrm{K}$). The neutron diffraction study reveals that these compounds undergo a first-order magnetic transition from the high-temperature centrosymmetric antiferromagnetic phase (${P}_{\mathrm{b}}{112}_{1}/n$) to the low-temperature noncentrosymmetric phases $Pn{m}^{\ensuremath{'}}a$ (Dy) and $P{112}_{1}^{\ensuremath{'}}/a$ (Ho), which allow linear magnetoelectric coupling. This is consistent with field-induced electric polarization, below ${T}_{\mathrm{N}}^{R}$, which varies linearly up to \ensuremath{\sim}1.2 T. Above a critical field $({H}_{\mathrm{c}}g1.2\phantom{\rule{0.16em}{0ex}}\mathrm{T})$, both compounds exhibit metamagnetic transitions with magnetization close to the saturation value ${M}_{s} \ensuremath{\sim}10.1\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$ (Dy) and $\ensuremath{\sim}11.8\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$ (Ho) at 7 T. Above the metamagnetic transition, a new polar state appears with large electric polarization, indicating field-induced ferroelectricity. We discuss the important role of $4f\text{\ensuremath{-}}3d$ coupling in determining the ground state magnetic structure responsible for the magnetoelectric coupling in both compounds.

We report a comprehensive investigation of the structural, magnetic, and electrical properties in a quasi-two-dimensional planar antiferromagnet ${\mathrm{BaNi}}_{2}{({\mathrm{PO}}_{4})}_{2}$, which crystallizes in the rhombohedral structure (space group $R\overline{3}$) consisting of honeycomb layers of ${\mathrm{Ni}}^{2+}$ ions. Magnetic susceptibility and heat capacity data reveal a long-range antiferromagnetic ordering of ${\mathrm{Ni}}^{2+}$ ions at ${T}_{N}=24$ K. Interestingly, an applied magnetic field induces a dielectric anomaly and an electric polarization at ${T}_{N}$ with the polarization proportional to the applied magnetic fields, demonstrating the linear magnetoelectric effect in ${\mathrm{BaNi}}_{2}{({\mathrm{PO}}_{4})}_{2}$ with a coupling coefficient of 1.67 ps/m. It is interesting to note that the magnetic symmetry associated with the magnetoelectric effect is ${\overline{1}}^{\ensuremath{'}}$, which allows all tensor elements of the magnetoelectric susceptibility.

We present the detailed structural and magnetic properties of ${\mathrm{Li}}_{2}{\mathrm{Mn}}_{3}{\mathrm{O}}_{7}$ from powder x-ray diffraction (XRD), dc susceptibility, heat capacity, ac susceptibility, thermoremanent magnetization, magnetic memory, and exchange bias effect. Rietveld refinement of XRD data reveals that this compound has a rhombhohedral structure composed of a layered triangular lattice. Onset of spin-glass transition was confirmed by dc magnetization and ac susceptibility measurements. Dynamic scaling laws were used to analyze and classify the glassy behavior of the compound. Magnetic field dependence of irreversible temperature follows the Almeida-Thouless line, which is characteristic for an Ising spin-glass system. Fitting of the frequency-dependent freezing temperature with a power law results in $z{\ensuremath{\nu}}^{\ensuremath{'}}=4.06\ifmmode\pm\else\textpm\fi{}0.06$, which indicates the critical exponent of the sluggish spin dynamics and ${\ensuremath{\tau}}_{0}=4.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ s is a characteristic time scale for a single spin-flip. Further evidence of cluster-glass behavior comes from the frequency dependence of the freezing temperature fitted with the Vogel-Fulcher law, which considers interaction between bigger magnetic entities. Values of fitting parameters are ${E}_{a}/{k}_{B}=27.62$ K and ${T}_{0}=9.57$ K, which confirm cluster-glass behavior. The presence of magnetic relaxation below freezing temperature and the magnetic memory effect confirms the nonequilibrium dynamics of the system through a number of metastable states. Moreover, observation of the exchange bias effect reflects the presence of intrinsic phase inhomogeneity. These results indicate that the triangular lattice causes a disordered ground state as a result of competing exchange interactions.

The magnetic ground state of $\mathrm{Co}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ has been a controversial issue because the ratio of nearest- (${J}_{1}$) to next-nearest-neighbor (${J}_{2}$) exchange interactions in the diamond lattice is close to the boundary between a spiral spin liquid and a long-range ordered antiferromagnetic ground state. Recently, Ghara et al. reported a linear magnetoelectric effect in a polycrystalline $\mathrm{Co}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ and attributed it to a long-range magnetic order. However, the magnetic ground state and the easy axis anisotropy remained unsolved. Here we propose the easy magnetic axis direction by comparing the results of magnetoelectric measurements in a high-quality single crystal with phenomenological calculations. From the value of polarization ratio $P||[1\text{\ensuremath{-}}10]$ measured under magnetic field applied along $H||[1\text{\ensuremath{-}}10]$ and $H||[001]$, we determined that the magnetic easy axis is along [111]. The single ion contribution of the magnetic ions located at the noncentrosymmetric environment is responsible for the magnetoelectric effect similar to that observed in other $A$-site magnetic spinel oxides, ${\mathrm{Co}}_{3}{\mathrm{O}}_{4}$, $\mathrm{Mn}{B}_{2}{\mathrm{O}}_{4}$ ($B=\mathrm{Al},\phantom{\rule{0.16em}{0ex}}\mathrm{Ga}$).

Comprehensive muon-spin-rotation/relaxation (\ensuremath{\mu}SR) and neutron powder-diffraction (NPD) studies supported via bulk measurements have been performed on the ordered double-perovskite ${\mathrm{Sr}}_{2}\mathrm{YbRu}{\mathrm{O}}_{6}$ to investigate the nature of the magnetic ground state. Two sharp transitions at ${T}_{\mathrm{N}1}\ensuremath{\sim}42\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${T}_{\mathrm{N}2}\ensuremath{\sim}36\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ have been observed in the static and dynamic magnetization measurements, coinciding with the heat-capacity data. In order to confirm the origin of the observed phase transitions and the magnetic ground state, microscopic evidences are presented here. An initial indication of long-range magnetic ordering comes from a sharp drop in the muon initial asymmetry and a peak in the relaxation rate near ${T}_{\mathrm{N}1}$. NPD confirms that the magnetic ground state of ${\mathrm{Sr}}_{2}\mathrm{YbRu}{\mathrm{O}}_{6}$ consists of an antiferromagnetic (AFM) structure with interpenetrating lattices of parallel $\mathrm{Y}{\mathrm{b}}^{3+}$ and $\mathrm{R}{\mathrm{u}}^{5+}$ moments lying in the $ab$ plane and adopting an A-type AFM structure. Intriguingly, a small but remarkable change is observed in the long-range ordering parameters at ${T}_{\mathrm{N}2}$ confirming the presence of a weak spin reorientation (i.e., change in spin configuration) transition of Ru and Yb moments, as well as a change in the magnetic moment evolution of the $\mathrm{Y}{\mathrm{b}}^{3+}$ spins at ${T}_{\mathrm{N}2}$. The temperature-dependent behavior of the $\mathrm{Y}{\mathrm{b}}^{3+}$ and $\mathrm{R}{\mathrm{u}}^{5+}$ moments suggests that the $4d$ electrons of $\mathrm{R}{\mathrm{u}}^{5+}$ play a dominating role in stabilizing the long-range-ordered magnetic ground state in the double-perovskite ${\mathrm{Sr}}_{2}\mathrm{YbRu}{\mathrm{O}}_{6}$ whereas only the $\mathrm{Y}{\mathrm{b}}^{3+}$ moments show an arrest at ${T}_{\mathrm{N}2}$. The observed magnetic structure and the presence of a ferromagnetic interaction between Ru and Yb ions are explained with use of the Goodenough-Kanamori-Anderson rules. Possible reasons for the presence of the second magnetic phase transition and of a compensation point in the magnetization data are linked to competing mechanisms of magnetic anisotropy.

The magnetic ground state of the B -site ordered double perovskite S r 2 DyRu O 6 has been investigated using muon spin rotation and relaxation (µSR), neutron powder diffraction (NPD), and inelastic neutron scattering (INS), in addition to heat capacity and magnetic susceptibility (AC and DC) measurements. A clear signature of a long-range ordered magnetic ground state has been observed in the heat capacity data, which exhibits two sharp anomalies at 39.5 and 36 K found as well in the magnetic data. Further supporting evidence consistent with long-range magnetic ordering comes from a sharp drop in the muon initial asymmetry and a peak in the relaxation rate at 40 K, along with a weak anomaly near 36 K. Based on temperature dependent NPD, the low temperature magnetic structure contains two interpenetrating lattices of D y 3 + and Ru 5 + , forming an antiferromagnetic ground state below 39.5 K with magnetic propagation vector k = ( 0 , 0 , 0 ) . The magnetic moments of D y 3 + and Ru 5 + at 3.5 K are pointing along the crystallographic b axis with values of μ Dy = 4.92 ( 10 ) μ B and μ Ru = 1.94 ( 7 ) μ B , respectively. The temperature dependence of the Ru 5 + moments follows a mean field type behavior, while that of the D y 3 + moments exhibits a deviation indicating that the primary magnetic ordering is induced by the order of the 4 d electrons of Ru 5 + rather than that of the proper 4 f D y 3 + electrons. The origin of the second anomaly observed in the heat capacity data at 36 K must be connected to a very small spin reorientation as the NPD studies do not reveal any clear change in the observed magnetic Bragg peaks’ positions or intensities between these two transitions. INS measurements reveal the presence of crystal field excitations (CEF) in the paramagnetic state with overall CEF splitting of 73.8 meV, in agreement with the point change model calculations, and spin wave excitations below 9 meV at 7 K. Above T N , the spin wave excitations transform into a broad diffuse scattering indicating the presence of short-range dynamic magnetic correlations.

We report the discovery of linear magnetoelectric effect in the well-known green phase compound, Sm2BaCuO5, which crystallizes in the centrosymmetric orthorhombic (Pnma) structure. Magnetization and specific heat measurements reveal the long-range antiferromagnetic ordering of Cu2+ and Sm3+-ions moments at TN1 = 23 K and TN2 = 5 K, respectively. Applied magnetic field induces dielectric anomaly at TN1 whose magnitude increases with field, which results in significant (1.7%) magnetocapacitance effect. On the other hand, the dielectric anomaly observed in zero-applied magnetic field at TN2 shows a small (0.4%) magnetocapacitance effect. Interestingly, applied magnetic field induces an electric polarization below TN1 and the polarization varies linearly up to the maximum applied field of 9 T with the magnetoelectric coefficient {\alpha} ~ 4.4 ps/m, demonstrating high magnetoelectric coupling. Below TN2, the electric polarization decreases from 35 to 29 {\mu}C/m2 at 2 K and 9 T due to ordering of Sm-sublattice. The observed linear magnetoelectricity in Sm2BaCuO5 is explained using symmetry analysis., Comment: 22 pages, 5 figures (to be published in Phys. Rev. B)

We report a spin-driven ferroelectricity below the helical spin ordering temperature in a nonoxide mineral $\mathrm{MnS}{\mathrm{b}}_{2}{\mathrm{S}}_{4}$, which crystallizes in a centrosymmetric monoclinic $\mathrm{HgB}{\mathrm{i}}_{2}{\mathrm{S}}_{4}$ structure. At $\mathrm{T}\ensuremath{\sim}25\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, the dielectric constant shows an anomaly and the spontaneous electric polarization begins to develop. The polarization obtained from pyroelectric current measurement can be switched by reversing the direction of poling electric field. Interestingly, upon applying magnetic field parallel to the electric field, the polarization is enhanced nearly six times above a critical field $H||E\ensuremath{\sim}5\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, demonstrating large magnetoelectric effect in this system. Below $\mathrm{T}\ensuremath{\sim}25\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, this compound is known to exhibit an unusual magnetic structure where the spiral spins lie in the ac plane but propagate along the $b$ axis with an angle of $\ensuremath{\sim}{133}^{\ensuremath{\circ}}$ between the adjacent magnetic moments. The origin of ferroelectric ordering has been attributed to the inverse Dzyaloshinskii-Moriya type interaction in accordance with local symmetry considerations.

The doubly ordered perovskites $\mathrm{Na}Ln\mathrm{MnW}{\mathrm{O}}_{6}$ ($Ln=\mathrm{La}$, Nd, and Tb), $\mathrm{Na}Ln\mathrm{FeW}{\mathrm{O}}_{6}$ ($Ln=\mathrm{La}$ and Nd), and $\mathrm{Na}Ln\mathrm{CoW}{\mathrm{O}}_{6}$ ($Ln=\mathrm{Sm}\ensuremath{-}\mathrm{Er}$, Yb, and Y) have been reported to be potential multiferroics because of their polar crystal structure ($P{2}_{1}$) and antiferromagnetic ordering of the transition-metal ions at low temperatures. In these materials, the octahedral rotation resulting from the layered ordering of cations at the $A$-site and the rock-salt ordering of cations at the $B$-site is suggested to be responsible for ferroelectric polarization. However, the ferroelectricity of these compounds has never been confirmed experimentally. Here we report an experimental demonstration of nonswitchable electric polarization below the magnetic ordering temperatures in two representative compounds, namely $\mathrm{NaYMnW}{\mathrm{O}}_{6}$ and $\mathrm{NaHoCoW}{\mathrm{O}}_{6},$ with smaller $Ln$-ions synthesized by high pressure and high temperatures. These compounds crystallize in the polar structure ($P{2}_{1}$) and undergo antiferromagnetic ordering at ${T}_{\mathrm{N}}\ensuremath{\sim}9\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, where a dielectric anomaly occurs in zero magnetic field. While the conventional $P\ensuremath{-}E$ loop measurements suggest the absence of ferroelectric polarization in the paramagnetic state, the pyroelectric current measurements across the magnetic ordering temperature show a nonswitchable change in polarization ($\mathrm{\ensuremath{\Delta}}P$) at ${T}_{\mathrm{N}}$, indicating a large energy barrier between the two polar states. The change in polarization at $Tl{T}_{\mathrm{N}}$ under magnetic field reveals magnetoelectric coupling.

La2NiMnO6 has been reported to exhibit a paramagnetic to ferromagnetic transition with a transition temperature of similar to 260 K. However, most of its magnetic properties, such as the saturation ...

The $A$-site cation-ordered spinel $\mathrm{LiFeC}{\mathrm{r}}_{4}{\mathrm{O}}_{8}$ is a unique system which manifests properties of the frustrated pyrochlore lattice, including the breathing distortion and antiferromagnetic coupling between $A$ and $B$ sites. This compound crystallizes in a cubic spinel structure with a noncentrosymmetric space group $(F\overline{4}3m)$, where $\mathrm{L}{\mathrm{i}}^{+}$ and $\mathrm{F}{\mathrm{e}}^{3+}$ ions are ordered in a zinc-blende-type manner at the $A$ site and $\mathrm{C}{\mathrm{r}}^{3+}$ ions at the $B$ site form a breathing pyrochlore lattice. It undergoes a ferrimagnetic transition at ${T}_{\mathrm{N}}\ensuremath{\sim}94\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, below which temperature-dependent magnetization data exhibit a maximum at ${T}_{\mathrm{SG}}\ensuremath{\sim}60\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, corresponding to a spin-gap arising from breathing distortion. At low temperature $({T}_{\mathrm{MS}}\ensuremath{\sim}23\phantom{\rule{0.16em}{0ex}}\mathrm{K})$, concurrent structural $(I\overline{4}m2)$ and magnetic phase transitions occur because of significant geometrical frustration of the pyrochlore lattice, giving rise to a complex conical magnetic order. Intriguingly, the observed dielectric anomalies at all three magnetic transition temperatures in zero applied magnetic field indicate the occurrence of magnetodielectric effects. Further, the temperature dependence of Raman modes shows three distinct anomalous behaviors that correlate with the dielectric anomalies at ${T}_{\mathrm{N}},{T}_{\mathrm{SG}}$, and ${T}_{\mathrm{MS}}$, which suggest the presence of spin-lattice coupling.

We report the discovery of magnetoelectric multiferroicity in a family of oxides, $R\mathrm{FeW}{\mathrm{O}}_{6}$ ($R=\mathrm{Dy}$, Eu, Tb, and Y) that crystallize in a polar aeschynite-type structure ($Pna{2}_{1}$) with an ordered arrangement of $\mathrm{F}{\mathrm{e}}^{3+}$ and ${\mathrm{W}}^{6+}$ ions. Magnetization and analysis of neutron-diffraction data of $\mathrm{DyFeW}{\mathrm{O}}_{6}$ reveal a commensurate noncollinear antiferromagnetic ordering of $\mathrm{F}{\mathrm{e}}^{3+}$ spins (${T}_{\mathrm{N}}^{\mathrm{Fe}}\ensuremath{\sim}18\phantom{\rule{0.16em}{0ex}}\mathrm{K}$), which induce Dy spins to order at the same temperature. A sudden change in electric polarization $(\mathrm{\ensuremath{\Delta}}P)$ appears in all the compounds at ${T}_{\mathrm{N}}^{\mathrm{Fe}}=15--18\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The electric polarization is sensitive to an applied magnetic field, and the coupling between different magnetic $R$-ion and Fe-ion moments suppresses the polarization to a different extent. Although the measured polarization in polycrystalline $\mathrm{DyFeW}{\mathrm{O}}_{6}$ at 3.5 K is about $3\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{C}/{\mathrm{m}}^{2}$, a simple calculation of the ionic contribution to polarization with formal charges is $75\phantom{\rule{0.16em}{0ex}}560\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{C}/{\mathrm{m}}^{2}$ and it is of the form $\mathbf{P}=({p}_{x},0,{p}_{z})$ where, ${p}_{x}$ comes from magnetic ordering and ${p}_{z}$ is associated with the polar structure in the paramagnetic state. These findings open up an avenue to explore further new polar magnets with rare-earth/transition-metal ions in the ordered aeschynite-type structure.

It is known that the orbital disordered orthorhombic ($Pnma$) perovskite, $\mathrm{YV}{\mathrm{O}}_{3}$, undergoes a transition to the $G$-type orbital ordered monoclinic phase $(P{112}_{1}/a)$ at ${T}_{G\ensuremath{-}\mathrm{OO}}\ensuremath{\sim}200\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ followed by a first-order transition to the $C$-type orbital ordered orthorhombic phase ($Pnma$) at ${T}_{S}\ensuremath{\sim}77\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. In contrast, using the high-angular-resolution synchrotron x-ray powder diffraction technique, we find that the $C$-type orbital ordered phase appears at ${T}_{N}=116\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and coexists with the $G$-type monoclinic phase down to ${T}_{S}\ensuremath{\sim}77\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The coexistence of different orbital ordered states in the temperature range ${T}_{S}lTl{T}_{N}$ is discussed based on large octahedral distortion caused by smaller Y ions present at the $A$ site of the perovskite. Intriguingly, the temperature evolution of the coexistence of the $G$- and $C$-type orbital ordered phases and associated magnetic structures could be responsible for the temperature-induced magnetization reversal observed in the temperature interval ${T}_{S}lTl{T}_{N}$. We also discuss that the correlation of phase coexistence and magnetization reversal is present in other $R\mathrm{V}{\mathrm{O}}_{3}$ systems.

The ground state of the frustrated $A$-site magnetic spinel $\mathrm{CoA}{\mathrm{l}}_{2}{\mathrm{O}}_{4}$ has been a controversial issue whether it is a collinear antiferromagnetic ordering or a spiral spin-liquid state, as the ratio of the two competing interactions ${J}_{2}/{J}_{1}$ lies close to the boundary between these two ground states. Here we address the magnetic ground state in $\mathrm{CoA}{\mathrm{l}}_{2}{\mathrm{O}}_{4}$ with different amounts of $\mathrm{C}{\mathrm{o}}^{2+}/\mathrm{A}{\mathrm{l}}^{3+}$ site disorder from the study of magnetoelectric effect and Monte Carlo simulations. $\mathrm{CoA}{\mathrm{l}}_{2}{\mathrm{O}}_{4}$ with low site disorder exhibits a linear magnetoelectric effect below the magnetic ordering temperature. With increasing disorder, the magnetoelectric effect is suppressed and the sample with $14%$ disorder exhibits a spin glass behavior without the magnetoelectric effect. Monte Carlo simulations support the experimental findings and suggest that the site disorder suppresses long-range antiferromagnetic order and induces a spin glass state. Since the linear magnetoelectric effect requires a long-range magnetic ordering, we suggest that the ground state of $\mathrm{CoA}{\mathrm{l}}_{2}{\mathrm{O}}_{4}$ with low site disorder is a collinear antiferromagnet.