Kayla Nguyen1,Yi Jiang2,Michael Cao3,Prafull Purohit4,Pablo Garcia-Fernandez5,Mark Tate4,Celesta Chang6,Pablo Aguado-Puente7,Jorge Iniguez8,Fernando Gomez-Ortiz5,Sol Gruner4,Javier Junquera5,Lane Martin9,Ramamoorthy Ramesh9,David Muller4
University of Illinois at Urbana-Champaign1,Argonne National Laboratory2,Rice University3,Cornell University4,Universidad de Cantabria5,Massachusetts Institute of Technology6,Queen\'s University Belfast7,Luxembourg Institute of Science and Technology8,University of California, Berkeley9
Kayla Nguyen1,Yi Jiang2,Michael Cao3,Prafull Purohit4,Pablo Garcia-Fernandez5,Mark Tate4,Celesta Chang6,Pablo Aguado-Puente7,Jorge Iniguez8,Fernando Gomez-Ortiz5,Sol Gruner4,Javier Junquera5,Lane Martin9,Ramamoorthy Ramesh9,David Muller4
University of Illinois at Urbana-Champaign1,Argonne National Laboratory2,Rice University3,Cornell University4,Universidad de Cantabria5,Massachusetts Institute of Technology6,Queen\'s University Belfast7,Luxembourg Institute of Science and Technology8,University of California, Berkeley9
Orbital angular momentum (OAM) and torque transfer play central roles in a wide range of physical processes and devices ranging from skyrmions to spin torque transfer electronics. For ferroelectrics, recent experimental realization of polarization vortex arrays offers analogous roles for topological structures encoded in polarization fields [1-3]. Here, we demonstrate a new phase-sensitive detection method for measuring the OAM of an electron beam where its shape and resolution are not compromised. Furthermore, we recover the chirality of the structure and identify regions of right and left handedness [4,5]. The starting point is a new generation of high-speed, momentum-resolved electron microscope detectors; from which, we highlight the electron microscope pixel array detector (EMPAD) [6]. The EMPAD’s high dynamic range makes it possible to record the complete angular distribution of all transmitted electrons from a focused electron beam at every scanned position, building up a 4-dimensional phase space. Our measurements extracted from this method can range over five orders of magnitude in length scales, making it well suited for measuring polarization fields, chirality and torque transfer in complex, extended patterns. This imaging method should work equally well for electric and magnetic structures, in our case, it is uniquely well suited for imaging the toroidal order parameter of ferroelectric polarization vortex arrays.<br/><br/><br/>[1] Yadav, AK et al.,<i> Nature</i>, 530, (2016) 198-201.<br/>[2] Yadav, AK, Nguyen, KX et al.,<i> Nature</i>, 565, (2019) 468-471.<br/>[3] Das, S et al., <i>Nature, </i>568, (2019) 368-372.<br/>[4] Nguyen, KX, et al.,<i> </i>arXiv:2012.04134.<br/>[5] Behara, P, et al., arXiv:2105.14109.<br/>[6] Tate W. M. et al., <i>Microscopy and Microanalysis. </i>22 (2016) 237-249.<br/>[7] Supported by NSF MRSEC program (DMR-1719875), Kavli Institute at Cornell.