### Magnetic Properties of Skyrmion Lattices:

Under pressure, MnSi a metal with a tendency to form helical magnetic structures, undergoes a transition into an unusual phase that shows "partial order" and non-Fermi liquid electrical transport. We have developed a theory of helical magnetic crystals - a coherent multi-spiral state (depicted in the figure), that agrees well with existing data on the magnetic structure. Moreover, it makes several predictions for unusual electrical transport arising from the presence of non-trivial magnetic structures [3]. The presence of field induced skyrmions was verified in Mn Si, while spin crystals also occur in the absence of a magnetic field in materials such as MnGe.

[1] B. Binz, A. Vishwanath, V. Aji, "Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi," *Phys. Rev. Lett.* 96, 207202 (2006).

[2] B. Binz and A. Vishwanath, "Theory of helical spin crystals: Phases, textures, and properties," *Phys. Rev. B *74: 214408 (2006).

[3] B. Binz and A. Vishwanath, "Theoretical proposal predicting anomalous magnetoresistance and quadratic Hall effect in the partially ordered state of MnSi." In *Proceedings of the 17th International Conference on Magnetism. JMMM* v.310:no.2:pt.2, pp. 1062–1064 (2007).

TALK: MnSi-Theory of the Helical Spin Cystal

### Anomalous Hall Effect and Transport in Skyrmion Lattices:

In the paper below we showed that skyrmion lattices display a characteristic topological Hall effect, distinct from the anomalous Hall effect, and discussed fingerprints of the magnetic order in the evolution of the hall coefficient in a field. This was later used to verify the existence of skyrmion lattics in a variety of materials including MnSi (and MnGe by Kanazawa et al.).

[1] B. Binz and A. Vishwanath, "Chirality induced anomalous-Hall effect in helical spin crystals Physica B: Condensed Matter 1336 (2008)

In the paper below we discuss possible explanations for the anomalous temperature dependence of resistivity from coupling of electrons to goldstone modes of the skyrmion lattice. This also inspired the following work, that explored fundamental properties of Goldstone's theorem in the context of a metal.

[2] Haruki Watanabe, S. A. Parameswaran, S. Raghu, and Ashvin Vishwanath, "Anomalous Fermi-liquid phase in metallic skyrmion crystals," *Phys. Rev. B* 90: 045145 (2014).

Goldstone's theorem guarantees long lived gapless excitations when a continuous symmetry is spontaneously broken. Does this remains true if the symmetry breaking occurs inside a metal, where gapless Fermi liquid excitations are also present? We found a simple criterion which determines if the coupling between these two kinds of excitations is relevant or irrelevant. In the latter case the Goldstone modes are long lived. In most cases the coupling is irrelevant. But we found two, and only two cases where the coupling is relevant - which implies that something interesting must happen, eg. non-Fermi liquid physics. One case was previously known (nematic order), but we also found an entirely new pattern of symmetry breaking (breaking magnetic translations) that could be a new route to realizing non Fermi liquids. |

[3] Haruki Watanabe and Ashvin Vishwanath, "Criterion for non-Fermi liquid phases via interactions with Goldstone bosons," PNAS 2 2014. (arXiv:1404.3728).

(Featured in Journal Club for Condensed Matter Article by Jörg Schmalian).