Spin-orbit-torque-enabled three-dimensional magnetic field sensor with low offset and high sensitivity

In this work we demonstrate a spin-orbit-torque (SOT) magnetic field sensor, designed as a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>Ta</a:mi> </a:math> / <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mi>Co</c:mi> <c:mi>Fe</c:mi> <c:mi mathvariant="normal">B</c:mi> </c:mrow> </c:math> / <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:mi>Mg</f:mi> <f:mi mathvariant="normal">O</f:mi> </f:mrow> </f:math> structure, with high sensitivity and capable of active offset compensation in all three spatial directions. This is described and verified in experiment and simulation. The measurements of magnetic fields showed an offset of 35, 42, and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mn>3</i:mn> <i:mspace width="0.1em"/> <i:mtext fontfamily="times">μ</i:mtext> <i:mrow> <i:mi mathvariant="normal">T</i:mi> </i:mrow> </i:math> for <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>x</n:mi> </n:math> -, <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mi>y</p:mi> </p:math> -, and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>z</r:mi> </r:math> -fields respectively. Furthermore, the sensitivities of these measurements had values of 590, 580, and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mn>490</t:mn> <t:mspace width="0.1em"/> <t:msup> <t:mrow> <t:mi mathvariant="normal">V</t:mi> <t:mspace width="0.1em"/> <t:mi mathvariant="normal">A</t:mi> </t:mrow> <t:mrow> <t:mo>−</t:mo> <t:mn>1</t:mn> </t:mrow> </t:msup> <t:mspace width="0.1em"/> <t:msup> <t:mrow> <t:mi mathvariant="normal">T</t:mi> </t:mrow> <t:mrow> <t:mo>−</t:mo> <t:mn>1</t:mn> </t:mrow> </t:msup> </t:math> in the <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi>x</bb:mi> </bb:math> -, <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:mi>y</db:mi> </db:math> -, and <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mi>z</fb:mi> </fb:math> -direction, respectively. In addition, the robustness to bias fields is demonstrated via experiments and single-spin simulations by applying bias fields in the <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:mi>y</hb:mi> </hb:math> -direction. Cross sensitivities were further analyzed via single-spin simulations, performing a parameter sweep of different bias fields in the <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:mi>y</jb:mi> </jb:math> - and <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:mi>z</lb:mi> </lb:math> -direction up to <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"> <nb:mo>±</nb:mo> <nb:mn>1</nb:mn> <nb:mspace width="0.1em"/> <nb:mi>mT</nb:mi> </nb:math> . The extraction of the SOT parameters <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:msub> <qb:mi>η</qb:mi> <qb:mi>DL</qb:mi> </qb:msub> </qb:math> and <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"> <sb:msub> <sb:mi>η</sb:mi> <sb:mi>FL</sb:mi> </sb:msub> </sb:math> is shown via an optimization of a single-spin curve to the experimental measurements.