Control of magnetoelectric coupling in the ${\mathrm{Co}}_2\mathrm{Y}$-type hexaferrites

We comprehensively investigated the magnetic, ferroelectric, and ME properties of ${\mathrm{Ba}}_{2-x}{\mathrm{Sr}}_x{\mathrm{Co}}_2{\left({\mathrm{Fe}}_{1-y}{\mathrm{Al}}_y\right)}_{12}{\mathrm{O}}_{22}$ single crystals in broad doping ranges of Sr $(1.0\le x\le 1.8)$ and Al $(0.00\le y\le 0.08)$. Most of the investigated compounds exhibit an intriguing coexistence of two apparently competing magnetic phases: a transverse conical (TC) and alternating longitudinal conical (ALC) spin structure. The magnetic properties show that the ${\mathrm{Ba}}_{0.2}{\mathrm{Sr}}_{1.8}{\mathrm{Co}}_2{\left({\mathrm{Fe}}_{0.96}{\mathrm{Al}}_{0.04}\right)}_{12}{\mathrm{O}}_{22}$ crystal has the highest ordering temperature and largest volume fraction of the ALC phase at zero H; further, after the application of an in-plane H, it exhibits a maximized volume fraction of the metastable TC phase, resulting in the highest ME susceptibility and electric polarization at all temperatures below 300 K. Our findings demonstrate that securing the thermal stability of the ALC phase is a crucial prerequisite to achieve optimized ME coupling in ${\mathrm{Co}}_2\mathrm{Y}$-type hexaferrites, pointing to a general strategy applicable to other hexaferrites as well.

Figure 1

(a) The crystal structure of ${\mathrm{Co}}_2\mathrm{Y}$-type hexaferrites and (b) a magnified view of the structure around the interface of the magnetic blocks. Both Fe and Co ions can occupy the center of the oxygen octahedra or tetrahedra. Orange and blue colors represent Fe or Co ions in the magnetic L and S blocks, respectively, while purple spheres represent Ba or Sr sites. The yellow triangle indicates the spin network with geometrical spin frustration related to helical spin ordering in the ${\mathrm{Co}}_2\mathrm{Y}$-type hexaferrites. (c) Schematic representation of the spin configuration of the ${\mathrm{Co}}_2\mathrm{Y}$-type hexaferrites without (left) and with (right) the application of an in-plane magnetic field ($H_{ab}$). ALC refers to an alternating conical spin ordering pattern, and TC represents a transverse conical spin ordering pattern.

Figure 2

(a) Field-induced electric polarization behavior of ${\mathrm{Ba}}_{2-x}{\mathrm{Sr}}_x{\mathrm{Co}}_2{\left({\mathrm{Fe}}_{1-y}{\mathrm{Al}}_y\right)}_{12}{\mathrm{O}}_{22}$ single crystals under the application of in-plane magnetic fields ($H_{ab}$, $H\text{//}\left[100\right]$). $\mathrm{\Delta }{P}_{\mathrm{Max}}$ indicates the difference between extreme values, $P_{\mathrm{Max}}-P_{\mathrm{Min}}$. Electric polarization is calculated through the integration of the ME current. (b) Temperature dependence of $\mathrm{\Delta }{P}_{\mathrm{Max}}$ and maximum dP/dH values. (c) Summary of $\mathrm{\Delta }{P}_{\mathrm{Max}}$ and maximum dP/dH as a function of $y$ at 10 and 300 K, demonstrating that the specimen with $x=1.8$ and $y=0.04$ has the highest magnetic-field-induced polarization and ME susceptibility at both temperatures.

Figure 3

(a) In-plane magnetization $M_{ab}$ of ${\mathrm{Ba}}_{0.2}{\mathrm{Sr}}_{1.8}{\mathrm{Co}}_2{\left({\mathrm{Fe}}_{0.96}{\mathrm{Al}}_{0.04}\right)}_{12}{\mathrm{O}}_{22}$ from 10 to 350 K measured at a bias magnetic field ${\mu }_0{H}_{\mathrm{M}}=20\mathrm{mT}$ after field cooling (FC) at various magnetic fields, demonstrating the metastable nature of the TC phase. (b) The red and black curves represent the $M_{ab}$ of ${\mathrm{Ba}}_{0.2}{\mathrm{Sr}}_{1.8}{\mathrm{Co}}_2{\left({\mathrm{Fe}}_{1-y}{\mathrm{Al}}_y\right)}_{12}{\mathrm{O}}_{22}$ measured under ${\mu }_0{H}_{\mathrm{M}}=20\mathrm{mT}$ during the warming process after FC at 5 T (5T-FC) and zero-field cooling (ZFC), respectively. (c) Upper and lower panels schematically show dominant spin configurations (ALC or TC) and the corresponding free-energy landscape, respectively, when the system is subject to different temperature and magnetic-field conditions sequentially from (1) to (4): (1) ZFC at 10 K, (2) the application of ${\mu }_{0}H=5\mathrm{T}$ at 10 K, (3) turning off the field to 0 T at 10 K, and finally (4) increasing the temperature up to 300 K at 0 T. The black (most white gray) curve represents the schematic free-energy landscape at each step (the previous step). The brightness from white to black indicates the intermediate free-energy landscapes upon the variation of the magnetic field or temperature. Note that to represent the ALC or TC phase, we only draw the L block for simplicity.

Figure 4

(a) Magnetization curves along the $ab$ (orange) and $c$ (blue) direction measured under the application of ${\mu }_0{H}_{\mathrm{M}}=20\mathrm{mT}$ during the warming process after ZFC. Magnetic phases are divided into 5: ALC, $ab$-FiM1 (ferrimagnetic along the $ab$ plane), $c$-FiM1 (ferrimagnetic along the $c$ axis), FiM2 (canted ferrimagnetic tilted between the $ab$ plane and $c$ axis), and PM (paramagnetic). ALC, $ab$-FiM1, and $c$-FiM1 phases are highlighted by green, orange, and blue shadows, respectively. $T_{\mathrm{ALC}}$ (green solid line) denotes the transition temperature from ALC to the FiM1 phase. $T_{\mathrm{a}}$ indicates the temperature of the magnetic-anisotropy transition from the $ab$-plane to the tilted direction. $T_{\mathrm{c}}$ is the Curie temperature, showing a paramagnetic-to-ferrimagnetic transition. $T^{*}$ indicates a local spin-ordering transition in the Fe-O-Fe bonds. (b) Magnetic phase diagram constructed from the magnetization curves in 4(a). The red arrows represent the spin structures in the phases. The long and short arrows indicate the spin in the L and S blocks, respectively. The ALC, $ab$-FiM1, and $c$-FiM1 phases are shown in green, red, and blue, respectively, to coincide with 4(a). The black dashed line indicates a trace of $T_{\mathrm{c}}$ drawn as a guide to the eye. (c) Plots of the inverse of $\left(M_{ab}+M_c\right)/2$ (left axis) and $|M_{ab}-M_c|/\left(M_{ab}+M_c\right)$ (right axis) against the Al doping ratio $y$ at 300 K, demonstrating that the $y=0.04$ specimen has the smallest average values of $M_{ab}$ and $M_c$ and the most isotropic magnetization curves.