Instability in domain wall dynamics in almost-compensated ferrimagnets

Nanoscale self-localized topological spin textures, such as domain walls and skyrmions, are of interest for the fundamental physics of magnets and spintronics applications. Ferrimagnets (FiMs), in the region close to the angular momentum compensation point, are promising materials because of their ultrafast spin dynamics at nonzero magnetization. In this work, we study specific features of the FiM domain wall (DW) dynamics, which are absent in both ferromagnets (FM) and antiferromagnets (AFM). In low-damping FMs and AFMs <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>(</a:mo><a:mi>α</a:mi><a:mo>≪</a:mo><a:mn>1</a:mn><a:mo>)</a:mo></a:mrow></a:math>, the nonstationary forced motion of DWs is characterized by slow <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mo>(</b:mo><b:msub><b:mi mathvariant="italic">t</b:mi><b:mi>diss</b:mi></b:msub><b:mo>∝</b:mo><b:mn>1</b:mn><b:mo>/</b:mo><b:mi>α</b:mi><b:mo>)</b:mo></b:mrow></b:math> changes of the DW's velocity and internal structure for all accepted values of the DW energy <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>E</d:mi></d:math> and its linear momentum <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>P</e:mi></e:math>—a consequence of the stability of DWs for any value of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>P</f:mi></f:math>. In contrast, the dispersion law of FiM DWs has specific points, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>P</g:mi><g:mo>=</g:mo><g:msub><g:mi>P</g:mi><g:mi>cr</g:mi></g:msub></g:mrow></g:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:msub><h:mi>E</h:mi><h:mi>cr</h:mi></h:msub><h:mo>=</h:mo><h:mi>E</h:mi><h:mrow><h:mo>(</h:mo><h:msub><h:mi>P</h:mi><h:mi>cr</h:mi></h:msub><h:mo>)</h:mo></h:mrow></h:mrow></h:math>, such that stable DWs are only present for <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi>P</i:mi><i:mo>&lt;</i:mo><i:msub><i:mi>P</i:mi><i:mi>cr</i:mi></i:msub></i:mrow></i:math>, , <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:msub><j:mi>P</j:mi><j:mi>cr</j:mi></j:msub></j:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:msub><k:mi>E</k:mi><k:mi>cr</k:mi></k:msub></k:math> act as endpoints in the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:mi>E</l:mi><l:mo>(</l:mo><l:mi>P</l:mi><l:mo>)</l:mo></l:mrow></l:math> dependence. We show that when a field-like torque driven DW reaches this endpoint, it falls into a highly-nonequilibrium state with the excitation of fast <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mo>(</m:mo><m:mi>t</m:mi><m:mo>≪</m:mo><m:msub><m:mi mathvariant="italic">t</m:mi><m:mi>diss</m:mi></m:msub><m:mo>)</m:mo></m:mrow></m:math> and highly-nonlinear intrawall magnetization dynamics, covering a wide frequency range up until the frequencies of propagating spin waves. The domain wall finally throws off an “excessive” energy by a short “burst” of the propagating spin waves and returns to the stationary state; the full picture of the forced motion is a periodic repetition of such “explosive” events.