Relationship between orbital moment anisotropy, magnetocrystalline anisotropy, and Dzyaloshinskii-Moriya interaction in W/Co/Pt trilayers

We have studied the Co layer thickness dependences of magnetocrystalline anisotropy (MCA), Dzyaloshinskii-Moriya interaction (DMI), and orbital moment anisotropy (OMA) in W/Co/Pt trilayers, in order to clarify their correlations with each other. We find that the MCA favors magnetization along the film normal and monotonically increases with decreasing effective magnetic layer thickness (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>t</a:mi><a:mi>eff</a:mi></a:msub></a:math>). The magnitude of the Dzyaloshinskii-Moriya exchange constant (<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mo>|</b:mo><b:mi>D</b:mi><b:mo>|</b:mo></b:mrow></b:math>) increases with decreasing <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>t</c:mi><c:mi>eff</c:mi></c:msub></c:math> until <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>t</d:mi><d:mi>eff</d:mi></d:msub><d:mo>∼</d:mo><d:mn>1</d:mn></d:mrow></d:math> nm, below which <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mo>|</e:mo><e:mi>D</e:mi><e:mo>|</e:mo></e:mrow></e:math> decreases. The MCA and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mo>|</f:mo><f:mi>D</f:mi><f:mo>|</f:mo></f:mrow></f:math> scale with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mn>1</g:mn><g:mo>/</g:mo><g:msub><g:mi>t</g:mi><g:mi>eff</g:mi></g:msub></g:mrow></g:math> for <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msub><h:mi>t</h:mi><h:mi>eff</h:mi></h:msub></h:math> larger than <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mo>∼</i:mo><i:mn>1</i:mn></i:mrow></i:math> nm, indicating an interfacial origin. The increase of MCA with decreasing <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:msub><j:mi>t</j:mi><j:mi>eff</j:mi></j:msub></j:math> continues below <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:msub><k:mi>t</k:mi><k:mi>eff</k:mi></k:msub><k:mspace width="4pt"/><k:mo>∼</k:mo></k:mrow></k:math> 1 nm, but with a slower rate. To clarify the cause of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub><m:mi>t</m:mi><m:mi>eff</m:mi></m:msub></m:math> dependences of MCA and DMI, the OMA of Co in W/Co/Pt trilayers is studied using x-ray magnetic circular dichroism. We find nonzero OMA when <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:msub><n:mi>t</n:mi><n:mi>eff</n:mi></n:msub></n:math> is smaller than <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:mrow><o:mo>∼</o:mo><o:mn>0.8</o:mn></o:mrow></o:math> nm. The OMA increases with decreasing <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:msub><p:mi>t</p:mi><p:mi>eff</p:mi></p:msub></p:math> more rapidly than what is expected from the MCA, indicating that factors other than OMA contribute to the MCA at small <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"><q:msub><q:mi>t</q:mi><q:mi>eff</q:mi></q:msub></q:math>. The <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"><r:msub><r:mi>t</r:mi><r:mi>eff</r:mi></r:msub></r:math> dependence of the OMA also suggests that <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"><s:mrow><s:mo>|</s:mo><s:mi>D</s:mi><s:mo>|</s:mo></s:mrow></s:math> at <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"><t:msub><t:mi>t</t:mi><t:mi>eff</t:mi></t:msub></t:math> smaller than <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"><u:mrow><u:mo>∼</u:mo><u:mn>1</u:mn></u:mrow></u:math> nm is not related to the OMA at the interface. We propose that the growth of Co on W results in a strain and/or texture that reduces the interfacial DMI, and, to some extent, MCA at small <v:math xmlns:v="http://www.w3.org/1998/Math/MathML"><v:msub><v:mi>t</v:mi><v:mi>eff</v:mi></v:msub></v:math>. Published by the American Physical Society 2024