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We have investigated the magnetic and charge transport properties of singlecrystals of Nowotney Chimney Ladder compound Cr$_{11}$Ge$_{19}$ and mapped outa comprehensive phase diagram reflecting the complicated interplay between theDzyaloshinskii-Moriya (DM) interaction, the dipolar interaction, and themagnetic anisotropy. We have identified a set of interesting magnetic phasesand attributed a finite topological Hall effect to the recently discoveredbi-skyrmion phase. These data also suggest the existence of an anti-skyrmionstate at finite fields for temperatures just below the magnetic orderingtemperature, $T_c$, as indicated by a distinct change in sign of thetopological Hall effect. Above $T_c$, we discovered a region of enhancedmagnetic response corresponding to a disordered phase likely existing near theferromagnetic critical point under small magnetic fields. Strong spin chiralityfluctuations are demonstrated by the large value of the topological Hallresistivity persisting up to 1 T which is most likely due to the existence ofthe DM interaction. We argue that changes to the topological Hall effectcorrespond to different topological spin textures that are controlled bymagnetic dipolar and DM interactions that vary in importance with temperature.

Topological Hall effect and the magnetic states of Nowotney chimney ladder compound Cr$_{11}$Ge$_{19}$}