Recent advances in mechanical torque studies of small-scale magnetism

Abstract

There is a storied scientific history in the role of mechanical instruments for the measurement of fundamental physical interactions. Among these include the detection of magnetic torques via a displacement of a compliant mechanical sensor as a result of angular momentum transfer. Modern nanofabrication methods have enabled the coupling of mechanical structures to single, miniature magnetic specimens. This has allowed for strikingly sensitive detection of magnetic hysteresis and other quasi-static effects, as well as spin resonances, in materials confined to nanoscale geometries. The extraordinary sensitivities achieved in mechanical transduction through recent breakthroughs in cavity optomechanics, where a high-finesse optical cavity is used for readout of motion, are now being harnessed for torque magnetometry. In this article, we review the recent progress in mechanical detection of magnetic torques, highlight current applications, and speculate on possible future developments in the technology and science. Guidelines for designing and implementing the measurements are also included. Acknowledgements 21 Appendix: Designer's guide 22 A feel for the numbers 22 Underlying scaling behaviour as a function of torque sensor/specimen linear size 22 Readout sensitivity 23 Low finesse interferometer 23 High finesse optical cavity 24 References 25 arXiv:1806.06288v1 [cond-mat.mes-hall]

Ultrasensitive torque detection with an optically levitated nanorotor

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Torque sensors such as the torsion balance enabled the first determination of the gravitational constant by Cavendish [1] and the discovery of Coulomb's law. Torque sensors are also widely used in studying small-scale magnetism [2,3], the Casimir effect [4], and other applications [5]. Great effort has been made to improve the torque detection sensitivity by nanofabrication and cryogenic cooling.

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“…Our calculations show that this system will be able to detect the long-sought vacuum friction [7-10] near a surface under realistic conditions. The optically levitated nanorotor will also have applications in studying nanoscale magnetism [2,3] and quantum geometric phase [11].…”

Sub-Kelvin Feedback Cooling and Heating Dynamics of an Optically Levitated Librator

“…Furthermore, our work is of significance for the development of torque sensors based on levitated nanoparticles [21] with potential applications for the characterization of materials at the nanoscale [49][50][51] and for the detection of angular momentum states of light [52]. Our experiments constitute an important step toward operating those sensors at the standard quantum limit, which requires careful balancing of measurement backaction with intrinsic damping [14].…”

Initiating revolutions for optical manipulation: the origins and applications of rotational dynamics of trapped particles

“…The original Cavendish experiment measured a torque of about 10 À 7 N m caused by gravitational attraction. Modern cavity-optomechanical torque sensors have a torque sensitivity as low as 3 � 10 À 24 N m Hz À 1=2 [258] after cryogenic cooling and can be used to probe small-scale magnetism [259] and Casimir forces [260]. Recently, a 10 mg-mass torsion pendulum was demonstrated with 20 aN m Hz À 1=2 sensitivity.…”