Nematicity of correlated systems driven by anisotropic chemical phase separation

The origin of nematicity, i.e., in-plane rotational symmetry breaking, and in particular the relative role played by spontaneous unidirectional ordering of spin, orbital, or charge degrees of freedom, is a challenging issue of magnetism, unconventional superconductivity, and quantum Hall effect systems, discussed in the context of doped semiconductor systems such as ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}, {\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$, and Ga(Al)As/${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells, respectively. Here, guided by our experimental and theoretical results for ${\mathrm{In}}_{1-x}{\mathrm{Fe}}_x\mathrm{As}$, we demonstrate that spinodal phase separation at the growth surface (that has a lower symmetry than the bulk) can lead to a quenched nematic order of alloy components, which then governs low-temperature magnetic and magnetotransport properties, in particular the magnetoresistance anisotropy whose theory for the $C_{2v}$ symmetry group is advanced here. These findings, together with earlier data for ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$, show under which conditions anisotropic chemical phase separation accounts for the magnitude of transition temperature to a collective phase or merely breaks its rotational symmetry. We address the question to what extent the directional distribution of impurities or alloy components setting in during the growth may account for the observed nematicity in other classes of correlated systems.

Figure 1

The morphology of Fe-rich nanolamellae in single-crystalline InAs. (a) Schematic image of the nanolamellae and their orientation within the InAs matrix. Structural characterization by (b) top-view scanning electron microscopy (SEM), (c) cross-sectional bright-field transmission electron microscopy (TEM) in $\left[1\overline{1}0\right]$ zone axis geometry, and (d) high-resolution TEM of the area marked with the white rectangle in (c) point to the pseudomorphic growth of nanolamellae oriented in (110) planes of the single-crystalline (001) InAs wafer.

Figure 2

Chemical analysis of the nanolamellar structure. (a) High-angle annular dark-field scanning TEM image of the same specimen region as shown in the bright-field TEM micrograph of Fig. 1 together with the (b) iron, (c) indium, and (d) arsenic element distributions obtained by EDXS for the area marked with the white rectangle in (a).

Figure 3

Depth-dependent Fe concentration by secondary ion mass spectrometry (SIMS) and srim simulation.

Figure 4

Rutherford backscattering spectrometry random ($R$) and channeling ($C$) spectra for virgin InAs (squares and circles, respectively), an as-Fe-implanted InAs (triangles), and pulsed laser melting treated (solid lines) samples.

Figure 5

(a) Conversion electron Mössbauer spectroscopy (CEMS) spectrum recorded at room temperature fitted with two quadrupole-split emission lines exhibiting a broad distribution of the quadrupole splittings. Parameters can be found in the text. (b) Behavior of the quadrupole splitting for both distributions.

Figure 6

Magnetic properties of (In,Fe)As epilayers. (a) Magnetic-field-dependent magnetization measured at temperatures of 5, 50, 100, and 300 K. The inset shows the temperature dependence of the coercivity indicating its exponentially fast decay on temperature. (b) Field-cooled (FC) and zero-field-cooled (ZFC) temperature dependence of magnetization measured at 50, 200, and 500 Oe. (c) Solid line: thermoremanent magnetization (TRM); circles: its temperature cycling between the base temperature ($2<T_0<5$ K) and progressively higher temperatures ($T_1$–$T_6$) according to the pattern drawn in the inset. (d) Magnetization loops for the magnetic field along the $\left[1\overline{1}0\right]$ and [110] crystal axes.

Figure 7

The optimized structures of different Fe cationic dimer arrangements into the (001) InAs surface. Panels (a) and (b) present optimized structures of the Fe pair along the (a) [110] and (b) $\left[1\overline{1}0\right]$ crystallographic directions, respectively. The top pictures present the side views of the slab, whereas the bottom ones are the top views of the surface. The pink plane is presented only for the visibility of the Fe pair in the slab.

Figure 8

The optimized structures of different Fe cationic dimer arrangements into the (001) InAs surface. The (a) and (b) denote positions of Fe cation dimers pointing inside the slab, along the $\left[01\overline{1}\right]$ and $\left[30\overline{1}\right]$ directions, respectively. The top pictures present the side views of the slab, whereas the bottom ones are the top views of the surface. The pink plane is presented only for the visibility of the Fe pair in the slab. The optimized structures of the Fe pair along the [110] and $\left[1\overline{1}0\right]$ crystallographic directions are shown in Fig. 7.

Figure 9

Definitions of the angles.

Figure 10

Polar plots of the longitudinal anisotropic magnetoresistance as a function of the angle $\alpha$ defined in the insets: current parallel to (a) [110] and (b) $\left[\overline{1}10\right]$ crystallographic directions. Red dots are experimental data for (In,Fe)As:Be taken from Ref. [11]. Solid black lines are fitted curves with the parameters given in the text.

Figure 11

Polar plots of the planar Hall effect as a function of the angle $\theta$ (defined in the insets) for current parallel to (a) [110] and (b) $\left[\overline{1}10\right]$ crystallographic directions. Red dots are experimental data for (In,Fe)As:Be taken from Ref. [11], whereas solid black lines are fitted curves with the parameters given in the text.