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 bias2,3, 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 order7,8. 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 crystal11,12 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.