Magnetic structures and excitations in a multiferroic Y-type hexaferrite ${\mathrm{BaSrCo}}_2{\mathrm{Fe}}_{11}{\mathrm{AlO}}_{22}$

We have investigated magnetic orders and excitations in a Y-type hexaferrite ${\mathrm{BaSrCo}}_2{\mathrm{Fe}}_{11}{\mathrm{AlO}}_{22}$ (BSCoFAO), which was reported to exhibit spin-driven ferroelectricity at room temperature [S. Hirose, K. Haruki, A. Ando, and T. Kimura, Appl. Phys. Lett. 104, 022907 (2014)]. By means of magnetization, electric polarization, and neutron-diffraction measurements using single-crystal samples, we establish a $H-T$ magnetic phase diagram for magnetic field perpendicular to the $c$ axis ($H_{\perp c}$). This system exhibits an alternating longitudinal conical (ALC) magnetic structure in the ground state, and it turns into a non-co-planar commensurate magnetic order with spin-driven ferroelectricity under $H_{\perp c}$. The field-induced ferroelectric phase remains as a metastable state after removing magnetic field below $\sim 250$ K. This metastability is the key to understanding of magnetic field reversal of the spin-driven electric polarization in this system. Inelastic polarized neutron-scattering measurements in the ALC phase reveal a magnetic excitation at around 7.5 meV, which is attributed to spin components oscillating in a plane perpendicular to the cone axis. This phasonlike excitation is expected to be an electric-field active magnon, i.e., electromagnon excitation, in terms of the magnetostriction mechanism.

Figure 1

(a) The crystal structure of a Y-type hexaferrite with the hexagonal basis $(a,b,c)$ and rhombohedral basis ($a_R,b_R,c_R$). For BSCoFAO, $A$ sites are occupied by Ba or Sr. $M$ sites mainly contain Fe, and are partly substituted by Co and Al. Schematic models of the (b) proper-screw, (c) LC, (d) ALC, and (e) double-fan structures (and the staggered collinear and cycloidal components) on the basis of the block approximation.

Figure 2

(a) Temperature dependence of magnetization under a magnetic field of 100 Oe parallel and perpendicular to the $c$ axis. The data for heating runs were measured after zero-field cooling. (b, c) Temperature dependence of (b) integrated intensities of the commensurate magnetic (CM) and incommensurate magnetic (ICM) reflections and (c) the wave vector of the incommensurate magnetic modulation $q_{\mathrm{IC}}$ on cooling.

Figure 3

Temperature dependence of the unpolarized neutron-diffraction profile on the $(1,0,l)$ line measured on ZFC.

Figure 4

(a) Schematics showing relationships between the directions of $\kappa , p_{\mathrm{N}}$, and crystallographic axes and the Cartesian coordinate $xyz$. (b, c) Polarized neutron-diffraction profiles along the (b) $(0,0,l)$ and (c) $(1,0,l)$ lines measured with $p_{\mathrm{N}}$ parallel to the $x$ axis at 5.2 K after ZFC. (d, e) Observed and calculated $l$ dependence of $P_f/P_0$ for (d) $(0,0,l)$ and (e) $(1,0,l)$ lines.

Figure 5

Magnetization curves measured under $H_{\parallel c}$ and $H_{\perp c}$ at (a) 400, (b) 300, and (c) 150 K. Insets show magnifications of low-field regions of the $M-H_{\perp c}$ curves.

Figure 6

(a, d) $M-H_{\perp c}$ curves measured after ZFC at (a) 300 and (d) 150 K. Doubled arrows indicate the inflection points, which may correspond to the transition to the intermediate phase (see text for details). Magnetic field dependence of integrated intensities of magnetic and nuclear reflections on the $(0,0,l)$ line measured at (b) 289 and (e) 150 K, and those on the $(1,0,l)$ lines measured at (c) 289 and (f) 150 K. The magnetic field was applied along the [010] direction. The sample was cooled in zero magnetic field before each measurement. Filled and open symbols denote the data points measured in field-increasing and -decreasing processes, respectively. In (b), (c), (e), and (f), triangular, circular, and square symbols show the integrated intensities of nuclear, incommensurate magnetic, and commensurate magnetic reflections, respectively.

Figure 7

$H_{\perp c}-T$ magnetic phase diagram of BSCoFAO for (a) $H_{\perp c}$-increasing process after ZFC and (b) $H_{\perp c}$-decreasing process.

Figure 8

(a) Comparison of $H_{\perp c}$ dependence of $P$ and magnetization at 150 K. Right-bottom and left-top insets show a magnification of the low-field region and a schematic showing the shape of the sample, orientation of the crystallographic axes, and directions of magnetic field and electric polarization. (b) Schematic illustrations showing possible spin arrangements during the magnetization reversal. (c–e) Displacement current (ME current) measured under sweeping magnetic field between $\pm 0.3$ T measured at (c) 200, (d) 250, and (e) 300 K.

Figure 9

(a, b) Unpolarized inelastic neutron-scattering spectra measured by constant-$Q$ scans on the (a) $(0,0,l)$ and (b) $(h,0,9+q_{\mathrm{IC}})$ lines, at $T=4.5$ K after ZFC. (c) Temperature dependence of the unpolarized constant-$Q$ profile at $(0,0,9+q_{\mathrm{IC}})$. Note that the data are shifted by 200 for each, to enhance the visibility. The dashed lines are guides to the eyes. (d) A reciprocal-lattice map of the $(h,0,l)$ scattering plane. (e) IPNS spectrum measured by constant-$Q$ scans with $p_{\mathrm{N}}$ parallel to $\kappa$ at $(0,0,9+q_{\mathrm{IC}})$ at 4.5 K after ZFC. (f, g) IPNS spectra measured by constant-$Q$ scans with $p_{\mathrm{N}}$ parallel to the $x$ axis (perpendicular to the scattering plane) at (f) $(0,0,9+q_{\mathrm{IC}})$ and (g) $(1,0,2.5)$ at 4.5 K after ZFC.

Figure 10

Schematic pictures of electromagnon modes in the (a) ALC phase in BSCoFAO and (b) FE3 phase of BMFO. Orange dotted arrows denote $p_{\text{local}}$ embedded in the crystal structure. Pairs of filled and open arrows qualitatively show deviations of the magnetic moments from their mean position in the (possible) electromagnon modes.