Lattice modulation induced by magnetic order in the magnetoelectric helimagnet Ba${}_{0.5}$Sr${}_{1.5}$Zn${}_2$Fe${}_{12}$O${}_{22}$

By means of an electron diffraction technique, crystal-lattice modulations were investigated for a hexaferrite, Ba${}_{0.5}$Sr${}_{1.5}$Zn${}_2$Fe${}_{12}$O${}_{22}$, showing a helimagnetic order below $T_{\mathrm{N}}=320$ K. We observed a lattice modulation with a wave vector $\text{Q}=(0,0,3\delta )$ below $T_{\mathrm{N}}$. The value of $\delta$ varies between $~0.23$ and 0.5 as a function of temperature and corresponds well to that of the magnetic modulation vector. By applying magnetic fields, Ba${}_{0.5}$Sr${}_{1.5}$Zn${}_2$Fe${}_{12}$O${}_{22}$ was found to exhibit successive changes in the lattice modulation, accompanied by the modifications of the helical magnetic order. We concluded that the observed lattice modulation is induced by the helical magnetic order via exchange magnetostriction.

Figure 1

Schematic representation of (a) the crystal and (b) the magnetic structures of Ba${}_{2-x}$Sr${}_x$Zn${}_2$Fe${}_{12}$O${}_{22}$. In (a), the $L$ and $S$ denote the large and small magnetic moments, respectively. They correspond to arrows in (b). (c) Proposed magnetic structure models for the evolution of the $L$ and $S$ magnetic moments by applying magnetic fields.[23, 25]

Figure 2

(a) $[\overline{1}10]$-zone electron diffraction pattern of Ba${}_{0.5}$Sr${}_{1.5}$Zn${}_2$Fe${}_{12}$O${}_{22}$, obtained at 19 K. Arrows indicate the superlattice reflections. Inset shows the magnified image obtained from the boxed region. The contrast of the inset image was adjusted to facilitate visualization. Temperature profiles of the $00l$ systematic electron diffraction were obtained at (b) 310 K, (c) 300 K, (d) 200 K, and (e) 90 K. (f) The magnified images obtained from the boxed regions in panels (b)–(e). The contrast of each image was independently adjusted. (g) Temperature dependence of ${\delta }_{\mathrm{s}}$ in the lattice modulation wave vector ${\text{Q}}_{\mathrm{s}}=(0,0,3{\delta }_{\mathrm{s}})$. Temperature dependence of ${\delta }_{\mathrm{m}}$ reported in Ref. 24 is also shown.

Figure 3

The $00l$ systematic electron-diffraction patterns obtained in the magnetic fields of (a) 0 T, (b) 0.26 T, (c) 0.81 T, and (d) 1.97 T. These were obtained at 200 K. Arrows indicate the superlattice reflections. Lower right panels of the respective figures show magnified images around the superlattice reflections. Magnetic-field dependences of ${\delta }_{\mathrm{s}}$ are shown at temperatures of (e) 200 K, (f) 150 K, (g) 80 K, and (h) 20 K. (i) Phase diagram of Ba${}_{0.5}$Sr${}_{1.5}$Zn${}_2$Fe${}_{12}$O${}_{22}$, regarding the lattice modulation and temperature. Regions $\alpha$, $\beta$, $\gamma$, and $\delta$ correspond to the incommensurate, ${\delta }_{\mathrm{s}}=0.25$, ${\delta }_{\mathrm{s}}=0.5$, and ${\delta }_{\mathrm{s}}=0$ or 1 phases, respectively.

Figure 4

(a) Intensity profiles of the electron diffraction around the 009 reflection along $00l$ in 0.01 T at 80 K. Solid and dashed lines are profiles for field (0.01 T) cooling and zero-field cooling procedures, respectively. (b) Magnetic-field dependence of magnetization of Ba${}_{0.5}$Sr${}_{1.5}$Zn${}_2$Fe${}_{12}$O${}_{22}$. The magnetic fields perpendicular to the $c$ axis were applied at 20 K.