Multiferroic $M$-Type Hexaferrites with a Room-Temperature Conical State and Magnetically Controllable Spin Helicity

Magnetic and magnetoelectric (ME) properties have been studied for single crystals of Sc-doped $M$-type barium hexaferrites. Magnetization ($M$) and neutron diffraction measurements revealed that by tuning Sc concentration a longitudinal conical state is stabilized up to above room temperatures. ME measurements have shown that a transverse magnetic field ($H$) can induce electric polarization ($P$) at lower temperatures and that the spin helicity is nonvolatile and endurable up to near the conical magnetic transition temperature. It was also revealed that the response (reversal or retention) of the $P$ vector upon the reversal of $M$ varies with temperature. In turn, this feature allows us to control the relation between the spin helicity and the $M$ vectors with $H$ and temperature.

Figure 1

(a)–(d) Schematics of (a) crystal and (b)–(d) magnetic structures of ${\mathrm{BaFe}}_{12-x-\delta }{\mathrm{Sc}}_x{\mathrm{Mg}}_{\delta }{\mathrm{O}}_{19}$ ($\delta =0.05$) for $T<T_{\mathrm{cone}}$ under (b) zero, (c) tilted, and (d) transverse $H$. Black arrows represent the net moment of each spin block $R$ and $R^{\prime }$. (e) Dotted (red, solid) line indicates $M$ for $x=1.6$ in $H=500\mathrm{Oe}$ along the [001]([100]) direction. Solid (blue) line indicates $M$ in $H=100\mathrm{Oe}$ along [100] direction for $x=1.75$ multiplied by a factor of 5. (f),(g) $T$ dependence of (f) position of the magnetic superlattice reflection at (0 0 $4+\tau$), calculated value of $\phi$, (g) integrated intensity of the superlattice reflection at (0 0 $4+\tau$), and ME response measured at 10 K after cooling down from $T_{\mathrm{w}}$. ME responses are normalized by that measured at 10 K immediately after the initial ME poling procedure (see main text). Inset shows the evolution of the magnetic superlattice peaks near $T_{\mathrm{cone}}$ for $x=1.75$. The residual peak on (0 0 5) at 380 K is due to the multiple scattering.

Figure 2

(a) Initial magnetization curves measured along [100]. (b) $H$-induced $P$ measured along [120] under the application of $H$ along [100]. (c) Phase diagram obtained from the data presented in (a) and (b). Open circles represent $H$ at which $M$ shows inflection and $P$ starts to decrease, and the closed circle shows the extrapolated value at which $P$ becomes zero. The expected magnetic structure is schematically shown for each phase. (d) Initial magnetization curves measured along the tilted direction by 45° from [001] toward [100]. (e) $H$-induced $P$ measured along [120] under the application of $H$ along tilted direction from [001] toward [100] by 45°.

Figure 3

(a),(b) Schema of expected domain-wall structures between positive and negative $M_c$ regions at (a) 10 K and (b) 30 K. (c),(d) $M\mathrm{\text{−}}H$ curves measured at 10 K and 30 K, respectively. In (c), dashed (blue) and solid (red) lines indicate $M$ measured after zero-filed and field ($H=-250\mathrm{Oe}$) cooling, respectively. (e),(f) $P\mathrm{\text{−}}H$ hysteresis measured along the [120] direction at (e) 10 K and (f) 30 K. In (e), the sample was initially cooled down to 10 K under the application of negative $E$ ($-3\mathrm{kV}/\mathrm{cm}$) and $H$ ($-250\mathrm{Oe}$). Then $E$ was switched off and $H$ was swept. (f) was measured after preparing the $+P$ and $+M_c$ state.