Long-period helical structures and twist-grain boundary phases induced by chemical substitution in the ${\mathrm{Mn}}_{1-x}{(\mathrm{Co},\mathrm{Rh})}_x\mathrm{Ge}$ chiral magnet

We study the evolution of helical magnetism in MnGe chiral magnet upon partial substitution of Mn for $3d$-Co and $4d$-Rh ions. At high doping levels, we observe spin helices with very long periods—more than ten times larger than in the pure compound—and sizable ordered moments. This behavior calls for a change in the energy balance of interactions leading to the stabilization of the observed magnetic structures. Strikingly, neutron scattering unambiguously shows a double periodicity in the observed spectra at $x=0.5$ and >0.2 for Co- and Rh-doping, respectively. In analogy with observations made in smectic liquid crystals, we suggest that it may reveal the presence of magnetic “twist grain boundary” phases, involving a dense short-range correlated network of magnetic screw dislocations. The dislocation cores are here tentatively described as smooth textures, made of nonradial double-core skyrmions.

Figure 1

Evolution of the helimagnetic peak in ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x\mathrm{Ge}$ (a) and ${\mathrm{Mn}}_{1-x}{\mathrm{Rh}}_x\mathrm{Ge}$ (c) upon doping at $T=1.5\text{K}$, as measured by neutron powder diffraction. For each concentration a pattern measured at 300 K was subtracted to eliminate background. For display purposes, patterns were calibrated to the intensity of the (110) nuclear reflection. Small-angle neutron scattering patterns of ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_{\mathrm{x}}\mathrm{Ge}$ (b) and ${\mathrm{Mn}}_{1-x}{\mathrm{Rh}}_{\mathrm{x}}\mathrm{Ge}$ (d) taken at $T=5$ K. One can note (i) the large increase of the helical wavelength as a function of $x$ and (ii) the emergence of a second peak for $x=0.5$ (Co) [see also inset of (b)] and $x>0.2$ (Rh). In all panels, solid lines are fit curves as described in the text.

Figure 2

Doping dependence of the helical wavelength ${\lambda }_{\mathrm{H}}$ (a), the coherence length ${\xi }_{\mathrm{H}}$ (b) and the ordered magnetic moment $m$ (c) in ${\mathrm{Mn}}_{1-x}{(\mathrm{Co},\mathrm{Rh})}_x\mathrm{Ge}$ as determined by powder neutron diffraction and small-angle scattering. In panel (c), results of ab initio calculations of the local Mn moment are shown for comparison. (d) Cubic lattice constant of ${\mathrm{Mn}}_{1-x}{(\mathrm{Co},\mathrm{Rh})}_x\mathrm{Ge}$ versus doping $x$ determined by neutron powder diffraction at $T=1.5$ K. (e) Magnetic phase diagram of ${\mathrm{Mn}}_{1-x}{(\mathrm{Co},\mathrm{Rh})}_x\mathrm{Ge}$ inferred from neutron scattering (Néel temperature, ${\mathrm{T}}_{\mathrm{N}}$). At low temperature, below $x\simeq 0.45$ for Co doping and $x\simeq 0.25$ for Rh doping, a standard helimagnetic (HM) state is stabilized. At higher values of $x$, more complex long-period magnetic structures are observed (LP).

Figure 3

(a) Schematic view of the proposed twist grain boundary (TGB) structure in a chiral helimagnet. (b) Internal structure of a screw dislocation made of stacked double core skyrmions. (c),(d) Cross section of a double core skyrmion: (c) out of plane magnetization component ${\mathrm{M}}_{\mathrm{Z}}$ and (d) projection of the in-plane component, showing a narrowly coupled vortex-antivortex configuration. The ferromagnetic vector $\mathbf{m}$ describes a full sweep over the $4\pi$ surface of the sphere. The projection of $\mathbf{m}$ forms a vortex-antivortex pair in the plane of the cross section perpendicularly to the dislocation line. At the locations of the vortex singularities $\mathbf{m}$ is exactly perpendicular to the plane pointing up and down. Along the dislocation line, the locations of these two extremal values of $\mathbf{m}$ twist in a corkscrew fashion around each other.