Domain wall dynamics in tungsten trioxide: Evidence for polar domain walls

Domain walls have distinct properties from the bulk, and tailoring them to suit the needs for device applications is critical. Tungsten trioxide, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>WO</a:mi><a:mn>3</a:mn></a:msub></a:math>, is of great interest for device applications that make use of domain wall properties; it exhibits a phenomenologically rich sequence of phase transitions, virtually all of which are ferroelastic in character, resulting in many sets of domain walls at low temperatures, each with their own unique properties. Domain wall motion and its contribution to the piezoelectric response have been investigated in <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>WO</b:mi><b:mn>3</b:mn></b:msub></b:math> from 300 to 180 K using resonant ultrasound spectroscopy (RUS) and resonant piezoelectric spectroscopy (RPS), which showed that the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>P</c:mi><c:msub><c:mn>2</c:mn><c:mn>1</c:mn></c:msub><c:mo>/</c:mo><c:mi>n</c:mi><c:mo>,</c:mo><c:mi>P</c:mi><c:mover accent="true"><c:mn>1</c:mn><c:mo>¯</c:mo></c:mover></c:mrow></c:math>, and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>P</e:mi><e:msub><e:mn>2</e:mn><e:mn>1</e:mn></e:msub><e:mo>/</e:mo><e:mi>c</e:mi></e:mrow></e:math> phases give a piezoelectric response despite the bulk being nominally centrosymmetric. Second harmonic generation (SHG) confirmed that polarity was strongest within the domain walls, and additional weak signals were found in the domains. Domain wall mobility was investigated in the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi>P</f:mi><f:mi>b</f:mi><f:mi>c</f:mi><f:mi>n</f:mi><f:mo>,</f:mo><f:mi>P</f:mi><f:msub><f:mn>2</f:mn><f:mn>1</f:mn></f:msub><f:mo>/</f:mo><f:mi>n</f:mi></f:mrow></f:math>, and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>P</g:mi><g:msub><g:mn>2</g:mn><g:mn>1</g:mn></g:msub><g:mo>/</g:mo><g:mi>c</g:mi></g:mrow></g:math> phases from 685 to 5 K. Domain walls in the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi>P</h:mi><h:msub><h:mn>2</h:mn><h:mn>1</h:mn></h:msub><h:mo>/</h:mo><h:mi>n</h:mi></h:mrow></h:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi>P</i:mi><i:mover accent="true"><i:mn>1</i:mn><i:mo>¯</i:mo></i:mover></i:mrow></i:math> were more mobile than those in the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi>P</k:mi><k:mi>b</k:mi><k:mi>c</k:mi><k:mi>n</k:mi></k:mrow></k:math> and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:mi>P</l:mi><l:msub><l:mn>2</l:mn><l:mn>1</l:mn></l:msub><l:mo>/</l:mo><l:mi>c</l:mi></l:mrow></l:math> structures, and soon after the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>P</m:mi><m:mover accent="true"><m:mn>1</m:mn><m:mo>¯</m:mo></m:mover><m:mo>→</m:mo><m:mi>P</m:mi><m:msub><m:mn>2</m:mn><m:mn>1</m:mn></m:msub><m:mo>/</m:mo><m:mi>c</m:mi></m:mrow></m:math> transition the walls become pinned at <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:mrow><o:mo>∼</o:mo><o:mn>140</o:mn><o:mspace width="0.16em"/><o:mi mathvariant="normal">K</o:mi></o:mrow></o:math>.