• Infrared and Laser Engineering
  • Vol. 51, Issue 4, 20210198 (2022)
Bo Chong, Boyang Chen*, Changcheng Chen, and Dongping Tian
Author Affiliations
  • School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China
  • show less
    DOI: 10.3788/IRLA20210198 Cite this Article
    Bo Chong, Boyang Chen, Changcheng Chen, Dongping Tian. Design of double-arm micro-cantilever beam of two-dimensional nanomaterial magnetic detection[J]. Infrared and Laser Engineering, 2022, 51(4): 20210198 Copy Citation Text show less

    Abstract

    Magnetic resonance weak force microscopy (MRWFM) can achieve non-destructive high-precision structural information detection of substances. This advantage makes MRWFM be widely applied in fields of physics, biology, medicine, and so on. The super-sensitive cantilever beam is one of core composition to realize weak force detection in this technology. In recent years, two-dimensional nanomaterials have attracted more and more attention due to their unique physical properties. In order to achieve the detection of the magnetism of two-dimensional nanomaterials, the design of double-arm micro-cantilever beams with differential amplification based on single arm micro-cantilever beam model was proposed. Then the magnetic field distributions inside and outside of the scan balls fastened on the double-arm micro-cantilever beams were analyzed. Finally, the numerical simulation of the cantilever beam was completed, taking the single-crystal silicon cantilever beams and CoSm magnetic ball probe as examples. It is found that the scheme can improve detection sensitivity of cantilever beam significantly.
    $\left\{ \begin{array}{l} {\nabla ^2}{\varphi _{m1}} = 0,R > {R_0} \\ {\nabla ^2}{\varphi _{m2}} = 0,R < {R_0} \\ {\left. {{\varphi _{m1}}} \right|_{R \to \infty }} = 0 \\ {\left. {{\varphi _{m2}}} \right|_{R = 0}} < \infty \\ {\left. {{\varphi _{m1}}} \right|_S} = {\left. {{\varphi _{m2}}} \right|_S} \\ {\mu _0}{\left. {\dfrac{{\partial {\varphi _{m1}}}}{{\partial n}}} \right|_S} = {\mu _0}\left({\left. {\dfrac{{\partial {\varphi _{m2}}}}{{\partial n}}} \right|_S} + {\overrightarrow M _{OR}}\right) \\ \end{array} \right.$(1)

    View in Article

    $\left\{ \begin{array}{l} {\varphi _{{{m1}}}} = \displaystyle\mathop \sum \limits_n [{a_n}{R^n} + {b_n}{R^{ - (n + 1)}}]{P_n}(\cos \theta ) \\ {\varphi _{{{m2}}}} = \displaystyle\mathop \sum \limits_n [{c_n}{R^n} + {d_n}{R^{ - (n + 1)}}]{P_n}(\cos \theta ) \end{array} \right.$(2)

    View in Article

    $ \begin{split} {\overrightarrow{H}}_{1}=&-\left(\dfrac{\partial }{\partial R}\overrightarrow{{\rm e}_{R}}+\dfrac{1}{R}\dfrac{\partial }{\partial \theta }\overrightarrow{{\rm e}_{\theta }}+\dfrac{1}{R\mathrm{sin}\theta }\dfrac{\partial }{\partial \varphi }\overrightarrow{{\rm e}_{\varphi }}\right)\dfrac{{R}_{0}{}^{3}{M}_{0}\mathrm{cos}\theta }{3{R}^{2}}=\\ &\dfrac{1}{4\pi }\left[\dfrac{3(\overrightarrow{m\cdot }\overrightarrow{R})\overrightarrow{R}}{{R}^{5}}-\dfrac{\overrightarrow{m}}{{R}^{3}}\right] \end{split}$(3)

    View in Article

    ${\overrightarrow B _1} = {\mu _0}{\overrightarrow H _1} = \frac{{{\mu _0}}}{{4\pi }}\left[\frac{{3(\overrightarrow {m \cdot } \overrightarrow R )\overrightarrow R }}{{{R^5}}} - \frac{{\overrightarrow m }}{{{R^3}}}\right]$(4)

    View in Article

    $ \begin{split} \overrightarrow{{H}_{2}}=&-\nabla {\varphi }_{\rm{m2}}=-\left(\frac{\partial }{\partial R}\overrightarrow{{\rm e}_{R}}+\frac{1}{R}\frac{\partial }{\partial \theta }\overrightarrow{{\rm e}_{\theta }}+\frac{1}{R\mathrm{sin}\theta }\frac{\partial }{\partial \varphi }\overrightarrow{{\rm e}_{\varphi }}\right)\cdot\\ &\frac{R{M}_{0}\mathrm{cos}\theta }{3}=-\frac{1}{3}{M}_{0}\overrightarrow{{\rm e}_{{\textit{z}}}} \end{split}$(5)

    View in Article

    $\overrightarrow {{B_2}} = {\mu _0}({\overrightarrow H _2} + {\overrightarrow M _2}) = {\mu _0}\left( - \frac{1}{3}\overrightarrow {{M_0}} + \overrightarrow {{M_0}} \right) = \frac{2}{3}{\mu _0}\overrightarrow {{M_0}} $(6)

    View in Article

    $ \overrightarrow {{B_{a{\textit{z}}}}} = - \frac{{4{\mu _0}{R_0}^3{M_0}}}{{3{R^3}}}\overrightarrow {{{\rm e}_{\textit{z}}}} ,\;\overrightarrow {{B_{b{\textit{z}}}}} = \frac{{2{\mu _0}}}{3}\frac{{{R_0}^3{M_0}}}{{{{(d - R)}^3}}}\overrightarrow {{{\rm e}_{\textit{z}}}} $(7)

    View in Article

    $\overrightarrow {{B_{\textit{z}}}} = \overrightarrow {{B_{a{\textit{z}}}}} + \overrightarrow {{B_{b{\textit{z}}}}} + \overrightarrow {{B_0}}$(8)

    View in Article

    ${m_{can}} = \frac{1}{4}\rho wlt = 1.354 \times {10^{ - 12}}\;{\rm{kg}}$(9)

    View in Article

    $k = \frac{1}{4}Ew{\left(\frac{t}{l}\right)^3} = 5.221 \times {10^{ - 4}}\;{\rm{N/m}}$(10)

    View in Article

    ${f_0} = \frac{1}{{2\pi }}\sqrt {\frac{k}{{{m_{can}}}}} = 3\;125\;{\rm{Hz}}$(11)

    View in Article

    ${F_{\min }} = t{\left(\frac{w}{{lQ}}\right)^{1/2}}{(E\rho )^{1/4}}{({k_B}TB)^{1/2}} = 7.382 \;{\rm aN}$(12)

    View in Article

    $f = \sqrt {\frac{1}{{7.561 \times (\Delta m + 5.498 \times {{10}^{ - 13}}) \times {{10}^4} + \dfrac{1}{{{{3\;125}^2}}}}}} $(13)

    View in Article

    ${F_{\min }}' = 6.527\;{\rm aN}$(14)

    View in Article

    Bo Chong, Boyang Chen, Changcheng Chen, Dongping Tian. Design of double-arm micro-cantilever beam of two-dimensional nanomaterial magnetic detection[J]. Infrared and Laser Engineering, 2022, 51(4): 20210198
    Download Citation