Terahertz time-domain signatures of the inverse Edelstein effect in topological-insulator/ferromagnet heterostructures

Three-dimensional topological insulators possess topologically protected surface states with spin-momentum locking, which enable spin-charge-current interconversion (SCI) by the inverse Edelstein effect (IEE). However, it remains experimentally challenging to separate the surface-related IEE from the bulk-type inverse spin Hall effect (ISHE). Here we search for distinct time-domain signatures of the two SCI phenomena in an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi mathvariant="script">F</a:mi> </a:mrow> </a:math> /TI model stack of a ferromagnetic-metal layer <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mrow> <d:mi mathvariant="script">F</d:mi> </d:mrow> </d:math> ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>Co</g:mi> </g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>Fe</i:mi> </i:math> ) and a topological-insulator (TI) layer ( <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>Bi</k:mi> <k:mn>2</k:mn> </k:msub> <k:msub> <k:mi>Te</k:mi> <k:mn>3</k:mn> </k:msub> </k:math> , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mrow> <m:mi>Sn</m:mi> <m:mi>Bi</m:mi> </m:mrow> <m:mn>2</m:mn> </m:msub> <m:msub> <m:mi>Te</m:mi> <m:mn>4</m:mn> </m:msub> </m:math> , and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>Bi</o:mi> <o:mrow> <o:mn>1</o:mn> <o:mo>−</o:mo> <o:mi>x</o:mi> </o:mrow> </o:msub> <o:msub> <o:mi>Sb</o:mi> <o:mi>x</o:mi> </o:msub> </o:math> with = 0.15 and = 0.3), where the focus is on <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>Bi</q:mi> <q:mn>2</q:mn> </q:msub> <q:msub> <q:mi>Te</q:mi> <q:mn>3</q:mn> </q:msub> </q:math> . A femtosecond laser pulse serves to induce a transient spin voltage <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msubsup> <s:mi>μ</s:mi> <s:mrow> <s:mi mathvariant="normal">s</s:mi> </s:mrow> <s:mrow> <s:mrow> <s:mi mathvariant="script">F</s:mi> </s:mrow> </s:mrow> </s:msubsup> </s:math> in <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mrow> <w:mi mathvariant="script">F</w:mi> </w:mrow> </w:math> and, thus, drive an ultrafast spin current out of <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mrow> <z:mi mathvariant="script">F</z:mi> </z:mrow> </z:math> . SCI results in a transverse charge current with a sheet density <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msub> <cb:mi>I</cb:mi> <cb:mrow> <cb:mi mathvariant="normal">c</cb:mi> </cb:mrow> </cb:msub> </cb:math> that is detected by sampling of the emitted terahertz electric field. Analysis of the dynamics of <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:msub> <fb:mi>I</fb:mi> <fb:mrow> <fb:mi mathvariant="normal">c</fb:mi> </fb:mrow> </fb:msub> </fb:math> () vs time relative to <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:msubsup> <ib:mi>μ</ib:mi> <ib:mrow> <ib:mi mathvariant="normal">s</ib:mi> </ib:mrow> <ib:mrow> <ib:mrow> <ib:mi mathvariant="script">F</ib:mi> </ib:mrow> </ib:mrow> </ib:msubsup> <ib:mo stretchy="false">(</ib:mo> <ib:mi>t</ib:mi> <ib:mo stretchy="false">)</ib:mo> </ib:math> reveals two components with distinct timescales: (1) a quasi-instantaneous response and (2) a longer-lived response with a relaxation time of 270 fs, which is independent of the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:mrow> <ob:mi mathvariant="script">F</ob:mi> </ob:mrow> </ob:math> material chosen. Component (1) is consistently ascribed to the ISHE. In contrast, we interpret component (2) as a signature of interfacial spin accumulation and the IEE at the <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"> <rb:mrow> <rb:mi mathvariant="script">F</rb:mi> </rb:mrow> </rb:math> / <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"> <ub:msub> <ub:mi>Bi</ub:mi> <ub:mn>2</ub:mn> </ub:msub> <ub:msub> <ub:mi>Te</ub:mi> <ub:mn>3</ub:mn> </ub:msub> </ub:math> interface, with a fraction of less than <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"> <wb:msup> <wb:mn>10</wb:mn> <wb:mrow> <wb:mo>−</wb:mo> <wb:mn>2</wb:mn> </wb:mrow> </wb:msup> </wb:math> of the incident spins participating. This assignment is fully consistent with respect to its dynamics and magnitude. We rate other possible signal contributions, such as spin trapping in intermediate states, as less likely. Our results show that the femtosecond dynamics of photocurrents allow us to differentiate the ISHE and the IEE and, more generally, provide important insights into the mechanisms of spin transport and SCI in <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:mrow> <yb:mi mathvariant="script">F</yb:mi> </yb:mrow> </yb:math> /TI stacks.