Electronic charge transfer driven by spin cycloidal structure

Muon spin rotation and resonant soft x-ray scattering experiments on prototype multiferroics $R{\mathrm{Mn}}_2{\mathrm{O}}_5$ ($R$ = Y, Sm) are used to demonstrate that the local electric displacements are driven by the spin-current (SC) mechanism. Small local electric displacements were evaluated by observing spin polarization at ligand O ions, for which implanted muons served as an extremely sensitive probe. Our results for ${\mathrm{YMn}}_2{\mathrm{O}}_5$ provide evidence that the spin polarization of O ions forming a spin cycloid chain with Mn spins increases in proportion to the vector spin chirality (${\mathbf{S}}_i\times {\mathbf{S}}_j$) of the Mn ions. This relationship strongly indicates that the charge transfer between O and Mn ions is driven by the SC mechanism, which leads to the ferroelectricity accompanying O spin polarization.

Figure 1

(a) Energy spectra of RSXS around the O $K$ edge in $R{\mathrm{Mn}}_2{\mathrm{O}}_5$ ($R$ = Y, Sm). Each measurement was performed in the CM phase (26 K for ${\mathrm{YMn}}_2{\mathrm{O}}_5$; 18 K for ${\mathrm{SmMn}}_2{\mathrm{O}}_5$) of each material. (b) Azimuth angle dependence of RSXS intensity at O $K$ edge ($E=530$ eV) in ${\mathrm{YMn}}_2{\mathrm{O}}_5$. The red curve represents the calculated values with the magnetic structure of O2 ions [shown in Fig. 4]. The inset shows the scattering geometry at azimuthal angle $\psi ={90}^{\circ }$. By definition, $\psi ={90}^{\circ }$ indicates that the $b^{*}$ axis is perpendicular to the scattering plane.

Figure 2

(a) Crystal structure of $R{\mathrm{Mn}}_2{\mathrm{O}}_5$. Site1 and Site2 represent candidate muon stopping sites indicated by vasp calculations. (b),(c) FFT spectra of TF-$\mu \mathrm{SR}$ at each temperature under an external magnetic field along the $c$ axis for ${\mathrm{YMn}}_2{\mathrm{O}}_5$ and ${\mathrm{SmMn}}_2{\mathrm{O}}_5$. The dashed line represents 813 MHz. (d),(e) Contour map of the local magnetic field (shown in terms of the frequency shift ${\gamma }_{\mu }{\mathit{B}}_{\mathrm{loc}}/2\pi$) in the $ab$ plane around Site1 and Site2. Positive (negative) indicates parallel (antiparallel) to the external magnetic field. (f),(g) Hartree potential in the $ac$ and $ab$ planes around Site1.

Figure 3

(a) Time spectra of ZF-$\mu \mathrm{SR}$ for ${\mathrm{SmMn}}_2{\mathrm{O}}_5$ at 8 K in the CM phase and (b) FFT of the time spectrum with ${\mathit{P}}_{\mu }\left|\right|b$. (c) Magnetic structure in the CM phase of ${\mathrm{SmMn}}_2{\mathrm{O}}_5$. Red and black arrows represent the magnetic moments of Sm and Mn ions, respectively. Site$1^{{(}^{\prime })}$ correspond to muon stopping sites. (d),(e) Contour map of ${\mathit{B}}_{\mathrm{loc}}$ in the $ac$ plane around Site1 and Site$1^{\prime }$. The magnitude is represented by the corresponding muon spin precession frequency (${\gamma }_{\mu }{B}_{\mathrm{loc}}/2\pi$). Dashed lines represent the contour of the Hartree potential shown in Fig. 2.

Figure 4

(a) Time spectra and (b) FFT spectra of ZF-$\mu \mathrm{SR}$ for ${\mathrm{YMn}}_2{\mathrm{O}}_5$ at 32 K and 10 K. (c) Magnetic structure of Mn and O2 ions in the CM phase of ${\mathrm{YMn}}_2{\mathrm{O}}_5$ projected onto the $ac$ plane. Black and green arrows represent the magnetic moments of Mn and O2 ions, respectively. The magnitude of magnetic moments at O2 sites is exaggerated for clarity. Filled blue circles represent muon stopping sites Site$1_i^{{(}^{\prime })}$ ($i=1,2$). (d) Calculation of ${\mathit{B}}_{\mathrm{loc}}$ at Site$1_i^{{(}^{\prime })}$ for $T=10$ K. Filled circles (triangles) represent calculated values at Site$1_i^{{(}^{\prime })}$ with only Mn magnetic moments. Open circles and triangles represent calculated values with Mn and O magnetic moments. The data are plotted over different chemical unit cells along the $c$ axis. The line represents the magnitude of ${\mathit{B}}_{\mathrm{loc}}$ ($\sim 88.9$ MHz) and dashed lines represent the distribution width $\mathrm{\Delta }B\sim 70$ MHz. (e) Temperature dependence of the amplitude of the oxygen magnetic moments at O$2_i$ and O$2_{i^{\prime }}$ sites (${\mathbf{m}}_{\mathrm{O}{2}_{\mathit{i}}}$ and ${\mathbf{m}}_{\mathrm{O}{2}_{{\mathit{i}}^{\prime }}}$), ${\sigma }_{+}-{\sigma }_{-}$, and the electric polarization ($P_{\mathrm{s}}$). The ${\sigma }_{+}-{\sigma }_{-}$ data are taken from Ref. [18]. The values of $P_{\mathrm{s}}$ corresponding to temperatures below 18 K, ${\mathbf{m}}_{\mathrm{O}{2}_{\mathit{i}}}$, and ${\mathbf{m}}_{\mathrm{O}{2}_{{\mathit{i}}^{\prime }}}$, are exaggerated for clarity.