Excitations and magnetization density distribution in the dilute ferromagnetic semiconductor ${\mathrm{Yb}}_{14}{\mathrm{MnSb}}_{11}$

${\mathrm{Yb}}_{14}{\mathrm{MnSb}}_{11}$ is a rare example of a Kondo lattice compound with ferromagnetic dominated RKKY interactions. As a ferromagnetic semiconductor with $T_c\approx 53$ K, it is also a potential compound for exploration of spintronic devices. Here we describe measurements which answer remaining questions regarding the energy scales of the exchange interactions, the valence, and the magnetization density distribution in this system. We find that the system consists of RKKY exchange coupled ${\mathrm{Mn}}^{2+}$ sites with nearest and next nearest exchange interactions dominating the magnetic spectrum with no significant magnetization density localized on other atomic sites. The extended spread of a negative magnetization around each of the Mn ions supports a Kondo screening cloud scenario for ${\mathrm{Yb}}_{14}{\mathrm{MnSb}}_{11}$.

Figure 1

(a) Crystal and magnetic structure of ${\mathrm{Yb}}_{14}{\mathrm{MnSb}}_{11}$ with $c$-axis vertical [15]. The red/black sites are the Mn/Sb sites. Only Mn and Sb(2) sites are shown for clarity [12]. The single red tetrahedron illustrates the Mn-Sb(2) coordination. The dashed gray line is the unit cell. The blue and dashed bonds between Mn sites represent $J_0$ and $J_1$ exchange. (b) Refined magnetization density superimposed on the nuclear crystal structure. Red volumes show magnetization density centered on the Mn site at a 0.025 level. Green volumes show negative magnetization density distributed within the unit cell at a 0.025 level on Yb and Sb atomic positions. (c) Intensity as a function of temperature for the (220) Bragg peak. Red line is a power-law fit using $T>35$ K data. Data were collected for approximately 2 s per point. (d) $T=5$ K magnetic form factor as a function of wave-vector transfer for the examined magnetic reflections where only Mn sites contribute to the scattering intensity. Lines are fits using the ${\mathrm{Mn}}^{2+}/{\mathrm{Mn}}^{3+}$ (red solid/dashed blue) valence. For presentation, data are binned in units of 0.25 Å${}^{-1}$ for $Q\ge 3.75$ Å${}^{-1}$.

Figure 2

$T=5$ K single crystal INS measurements and model of the spin-wave spectra. (a) and (c) Integrated between 5 and 7 meV. (b) and (d) Integrated between 3 and 5 meV. Model spectra (see text) are overlayed as contour lines at the 75% and 25% intensity level. Data are folded about principal axes to improve statistics. Integration normal to the planes shown is $\pm 0.2$ rlu.

Figure 3

$T=5$ K single crystal $E_i=27.5$ meV INS measurements. Data are folded about the principal axes and the $L=4,L=2,H=K=0$, and $H=K=1$ axes to improve statistics. The range of integration normal to the orthogonal axes shown is $\pm 0.15$ for the $H$ and $K$ directions and $\pm 0.2$ for the $L$ direction. (c) Average of scattering intensity along both the $\left(HH0\right)$ and $\left(H+1H-10\right)$ directions. Black circles are peak positions determined from fitting constant wave-vector scans. The vertical error bar is the fitted standard deviation in the peak position. The horizontal error bar is the range of integration to generate the constant wave-vector scan. Gray square points are the fitted peak positions from constant energy scans through the $E_i=15$ meV measurement in the vicinity of the (004) magnetic Bragg peak. The horizontal error bar is the standard deviation in peak position, and the vertical error bar is the range of energy transfer used to generate the constant energy scan. The solid white line is the fitted spin-wave dispersion described in the text.