  Understanding the role of the Dzyaloshinskii-Moriya interaction (DMI) for the
formation of helimagnetic order, as well as the emergence of skyrmions in
magnetic systems that lack inversion symmetry, has found increasing interest
due to the significant potential for novel spin based technologies. Candidate
materials to host skyrmions include those belonging to the B20 group such as
FeGe, known for stabilising Bloch-like skyrmions, interfacial systems such as
cobalt multilayers or Pd/Fe bilayers on top of Ir(111), known for stabilising
N\'eel-like skyrmions, and, recently, alloys with a crystallographic symmetry
where anti-skyrmions are stabilised. Micromagnetic simulations have become a
standard approach to aid the design and optimisation of spintronic and magnetic
nanodevices and are also applied to the modelling of device applications which
make use of skyrmions. Several public domain micromagnetic simulation packages
such as OOMMF, MuMax3 and Fidimag already offer implementations of different
DMI terms. It is therefore highly desirable to propose a so-called
micromagnetic standard problem that would allow one to benchmark and test the
different software packages in a similar way as is done for ferromagnetic
materials without DMI. Here, we provide a sequence of well-defined and
increasingly complex computational problems for magnetic materials with DMI.
Our test problems include 1D, 2D and 3D domains, spin wave dynamics in the
presence of DMI, and validation of the analytical and numerical solutions
including uniform magnetisation, edge tilting, spin waves and skyrmion
formation. This set of problems can be used by developers and users of new
micromagnetic simulation codes for testing and validation and hence
establishing scientific credibility.
