Sawtooth lattice multiferroic ${\mathrm{BeCr}}_2{\mathrm{O}}_4$: Noncollinear magnetic structure and multiple magnetic transitions

Noncollinear magnetic structures and multiple magnetic phase transitions in a sawtooth lattice antiferromagnet consisting of ${\mathrm{Cr}}^{3+}$ are experimentally identified in this work, thereby proposing the scenario of magnetism-driven ferroelectricity in a sawtooth lattice. The title compound, ${\mathrm{BeCr}}_2{\mathrm{O}}_4$, displays three magnetic phase transitions at low temperatures—at $T_{N1}\approx 7.5$ K, at $T_{N2}\approx 25$ K, and at $T_{N3}\approx 26$ K—revealed through magnetic susceptibility, specific heat, and neutron diffraction in this work. These magnetic phase transitions are found to be influenced by externally applied magnetic fields. Isothermal magnetization curves at low temperatures below the magnetic transitions indicate the antiferromagnetic nature of ${\mathrm{BeCr}}_2{\mathrm{O}}_4$ with two spin-flop-like transitions occurring at $H_{c1}\approx 29$ kOe and $H_{c2}\approx 47$ kOe. Our high-resolution x-ray and neutron diffraction studies, performed on single crystal and powder samples, unambiguously determined the crystal structure as orthorhombic $Pbnm$. By performing the magnetic superspace group analysis of the neutron diffraction data at low temperatures, the magnetic structure in the temperature range $T_{N3,N2}<T<T_{N1}$ is determined to be the polar magnetic space group $P21nm.1^{\prime }\left(00g\right)0s0s$ with a cycloidal magnetic propagation vector ${\mathbf{k}}_1=(0,0,0.090\left(1\right))$. The magnetic structure in the newly identified phase below $T_{N1}$ is determined as $P21/b.1^{\prime }\left[b\right]\left(00g\right)00s$ with the magnetic propagation vector ${\mathbf{k}}_2=(0,0,0.908\left(1\right))$. The cycloidal spin structure determined in our work is usually associated with electric polarization, thereby making ${\mathrm{BeCr}}_2{\mathrm{O}}_4$ a promising multiferroic belonging to the sparsely populated family of sawtooth lattice antiferromagnets.

Figure 1

(a) Synchrotron x-ray diffraction pattern of ${\mathrm{BeCr}}_2{\mathrm{O}}_4$ at 295 K along with a Rietveld fit using $Pbnm$ space group. The circles are the experimentally measured intensities, and the solid line is the calculated pattern. Top and bottom vertical bars mark the positions of the expected Bragg reflections for ${\mathrm{BeCr}}_2{\mathrm{O}}_4$ and ${\mathrm{Cr}}_2{\mathrm{O}}_3$, respectively. The blue horizontal line at the bottom is the difference between the measured and calculated patterns. The indices of a few major reflections are indicated. (b) A clinographic view of the orthorhombic unit cell of ${\mathrm{BeCr}}_2{\mathrm{O}}_4$. (c) The sawtooth arrangement formed by Cr atoms at $4a$ and $4c$ Wyckoff positions. The solid line indicates the unit cell boundary.

Figure 2

(a) Magnetic susceptibility, ${\chi }_{\mathrm{dc}}\left(T\right)$, of ${\mathrm{BeCr}}_2{\mathrm{O}}_4$ measured at an applied field of 1 kOe. The inset magnifies the derivative, $d{\chi }_{\mathrm{dc}}\left(T\right)/dT$, in the low-temperature region, revealing a double-peak anomaly of two nearby transitions. (b) The magnetic susceptibility at different values of applied magnetic fields from 0.1 to 80 kOe. (c),(d) Derivatives $d{\chi }_{\mathrm{dc}}\left(T\right)/dT$ identifying three transitions at $T_{N1}\approx 7.5$ K, $T_{N2}\approx 25$ K, and $T_{N3}\approx 26$ K. (e) The isothermal magnetization $M\left(H\right)$ at different temperatures in the range 2–50 K. (f) The derivative, $dM/dH$, revealing the presence of field-induced magnetic transitions.

Figure 3

(a) The low-temperature specific heat of ${\mathrm{BeCr}}_2{\mathrm{O}}_4$ plotted as $C_p/T$ vs $T^2$. Three phase transitions at $T_{N1}\approx$ 7.5 K, $T_{N2}\approx$ 25 K, and $T_{N3}\approx$ 26 K are present, indicated by dashed vertical lines. The inset shows the total specific heat of ${\mathrm{BeCr}}_2{\mathrm{O}}_4$ and ${\mathrm{BeAl}}_2{\mathrm{O}}_4$ in the range 2–300 K in logarithmic scales. (b) The specific heat of ${\mathrm{BeCr}}_2{\mathrm{O}}_4$ under the application of different magnetic fields. $T_{N2}$ and $T_{N3}$ are suppressed by the fields, while $T_{N1}$ (indicated by an arrow) is field-independent. (c) The $H-T$ phase diagram of ${\mathrm{BeCr}}_2{\mathrm{O}}_4$ constructed from the phase-transition points extracted from the specific heat and magnetic susceptibility. The inset shows the critical fields $H_{c1}$ and $H_{c2}$ identified in the derivatives of magnetization isotherms.

Figure 4

A color map of temperature evolution of diffraction patterns of ${\mathrm{BeCr}}_2{\mathrm{O}}_4$ as a function of $d$-spacing. Magnetic phase transitions, at approximately $T_{N2,N3}$ (top horizontal dashed line) and $T_{N1}$ (bottom horizontal line), are discernible with the appearance of additional Bragg reflections.

Figure 5

Time-of-flight neutron diffraction data of ${\mathrm{BeCr}}_2{\mathrm{O}}_4$ at three different temperatures are shown along with Rietveld refinement results at (a) 30 K ($T>T_{N3}$), (b) 10 K ($T_{N1}<T<T_{N2,N3}$), and (c) 2 K ($T<T_{N1}$). Best fits to the experimental data were obtained for the superspace group $P21nm.1^{\prime }\left(00g\right)0s0s$ at 10 K and $P21/b.1^{\prime }\left[b\right]\left(00g\right)00s$ at 2 K. The insets show a section of diffraction pattern where few additional Bragg peaks are observed compared to the 30 K data. Arrangement of ${\mathrm{Cr}}^{3+}$ spins viewed along the $b$ direction at (d) 10 K and (e) 2 K.