Poling of an artificial magneto-toroidal crystal

Although ferromagnetism is known to be of enormous importance, the exploitation of materials with a compensated (for example, antiferromagnetic) arrangement of long-range ordered magnetic moments is still in its infancy. Antiferromagnetism is more robust against external perturbations, exhibits ultrafast responses of the spin system¹ and is key to phenomena such as exchange bias^2,3, magnetically induced ferroelectricity⁴ or certain magnetoresistance phenomena⁵. However, there is no conjugate field for the manipulation of antiferromagnetic order, hindering both its observation and direct manipulation. Only recently, direct poling of a particular antiferromagnet was achieved with spintronic approaches⁶. An interesting alternative to antiferromagnetism is ferrotoroidicity-a recently established fourth form of ferroic order^7,8. This is defined as a vortex-like magnetic state with zero net magnetization, yet with a spontaneously occurring toroidal moment⁹. As a hallmark of ferroic order, there must be a conjugate field that can manipulate the order parameter. For ferrotoroidic materials, this is a toroidal field-a magnetic vortex field violating both space-inversion and time-reversal symmetry analogous to the toroidal moment¹⁰. However, the nature and generation of the toroidal field remain elusive for conventional crystalline systems. Here, we demonstrate the creation of an artificial crystal^11,12 consisting of mesoscopic planar nanomagnets with a magneto-toroidal-ordered ground state. Effective toroidal fields of either sign are applied by scanning a magnetic tip over the crystal. Thus, we achieve local control over the orientation of the toroidal moment despite its zero net magnetization.