Switchable X-Ray Orbital Angular Momentum from an Artificial Spin Ice

Artificial spin ices (ASI) have been widely investigated as magnetic metamaterials with exotic properties governed by their geometries. In parallel, interest in x-ray photon orbital angular momentum (OAM) has been rapidly growing. Here we show that a square ASI with a patterned topological defect, a double edge dislocation, imparts OAM to scattered x rays. Unlike single dislocations, a double dislocation does not introduce magnetic frustration, and the ASI equilibrates to its antiferromagnetic (AFM) ground state. The topological charge of the defect differs with respect to the structural and magnetic order; thus, x-ray diffraction from the ASI produces photons with even and odd OAM quantum numbers at the structural and AFM Bragg conditions, respectively. The magnetic transitions of the ASI allow the AFM OAM beams to be switched on and off by modest variations of temperature and applied magnetic field. These results demonstrate ASIs can serve as metasurfaces for reconfigurable x-ray optics that could enable selective probes of electronic and magnetic properties.

Figure 1

Schematic of x-ray OAM from a topological defect in an artificial spin ice. (a) A square lattice of nanomagnets with a topological defect imparts orbital angular momentum to diffracted x rays. The structural-lattice defect has topological charge 2 and generates even-order OAM in the charge-scattered x-ray beams. The antiferromagnetic ground state defect has topological charge 1 and produces odd-order OAM in the magnetically scattered x-ray beams (four lowest-order beams are shown). The magnetically scattered beams can be manipulated by varying temperature or magnetic field. (b) Structural lattice and AFM lattice. Red arrows show that the magnetic lattice is rotated 45° with respect to the structural lattice. (c) Positions of charge (red) and magnetic (blue) OAM peaks in reciprocal space labeled by OAM quantum number. (d) Schematic of the intensity and phase fronts of beams with OAM quantum number $\ell =0$, 1, 2, and 3. Red and blue represent charge and magnetic scattered beams carrying even- and odd-order OAM, respectively.

Figure 2

Experimental realization of a single-domain AFM ground state in the Z2-ASI and resulting x-ray diffraction. (a) Scanning electron micrograph of a permalloy lattice of nanomagnets with a topological defect consisting of a double edge dislocation. (b) X-ray magnetic circular dichroism PEEM micrograph revealing the AFM ground state order. The blue boxes trace out a Burgers circuit. (c) Off-resonance diffraction produces x-ray vortex beams carrying even order orbital angular momentum at the structural Bragg conditions. (d) Diffraction at the resonance condition dramatically enhances vortex beams at the AFM Bragg conditions (half-integer values of $H$ and $K$) carrying odd-order OAM.

Figure 3

Determination of the AFM OAM quantum number from interference between charge and magnetically scattered x rays. The sum and difference of diffracted intensities (arb. units) from left- ($I_{c+}$) and right- ($I_{c-}$) circularly polarized illumination are plotted for magnetic beams with $\ell =+1$, $\ell =+3$, and $\ell =+5$ OAM quantum numbers. The first column, $I_{c+}+I_{c-}$, shows the vortex structure of the beams. The second column, $I_{c+}-I_{c-}$, reveals the interference pattern between charge and magnetically scattered x rays. Dashed lines serve as a guide and the scale bar applies to all panels. Within the vortex ring, the number of interference fringes corresponds to the OAM quantum number as it would for interference with a plane wave. The third column plots $I_{c+}-I_{c-}/I_{c+}+I_{c-}$ versus azimuthal angle which reveals an approximately sinusoidal oscillation consistent with the OAM phase progression.

Figure 4

Response of the Z2-ASI to temperature and applied magnetic field. (a) Temperature dependent x-ray intensity of the magnetically scattered OAM beam with $\ell =1$. As the sample approaches the antiferromagnetic-to-paramagnetic transition temperature ($T_N\approx 380\mathrm{K}$) of the artificial lattice, the integrated intensity near the AFM Bragg condition decreases. (b) Time dependence of intensity after the beams are switched off using a magnetic field. The field is removed at $t=0$ and the temperature is held at 320 K. The intensity for $t<0$ is labeled in (a). The speckle pattern at early time points indicates that disordered AFM domains form first. Afterwards, the sample further relaxes to its AFM ground state and the OAM vortex beam is restored. Indicated times are in minutes.