Presence of X-Ray Magnetic Circular Dichroism Signal for Zero-Magnetization Antiferromagnetic State

X-ray magnetic circular dichroism (XMCD) is generally not observed for antiferromagnetic (AFM) states because XMCD signals from the antiparallelly coupled spins cancel each other. In this Letter, we theoretically show the presence of an XMCD signal from compensated two-dimensional triangle AFM structures on a Kagome lattice. The calculation reveals the complete correspondence between the XMCD spectra and the sign of the spin chirality: the XMCD signal only appears when the spin chirality is negative. This XMCD signal originates from the different absorption coefficients of the three sublattices reflecting different charge density anisotropies and directions of spin and orbital magnetic moments.

Figure 1

Fe $2p\mathrm{XAS}$ and XMCD calculation for the AFM state of the triangular structure considering ${\mathrm{Fe}}^{2+}$. The direction of the incident x ray is parallel to the $z$ axis. The triangular structure is located in the xz plane. (a) The spin direction of the red target is parallel to the $z$ axis, and the blue and orange targets are rotated 120° and 240° clockwise from the red, respectively. (b) The spin direction of the red target is parallel to the $x$ axis, and the blue and orange targets are rotated 240° and 120° clockwise from the red, respectively. (c) The spin direction of the red target is parallel to the $z$ axis, and the blue and orange targets are 240° and 120° rotated clockwise from the red, respectively.

Figure 2

Fe $2p\mathrm{XAS}$ and XMCD calculation for the AFM state of the triangular structure considering ${\mathrm{Fe}}^{2+}$. The direction of the incident x ray is parallel to the $x$ axis. The triangular structure is located in the xz plane. (a) The spin direction of the red target is parallel to the $z$ axis, and the blue and orange targets are rotated 120° and 240° clockwise from the red, respectively. (b) The spin direction of the red target is parallel to the $x$ axis, and the blue and orange targets are 240° and 120° rotated clockwise from the red, respectively. (c) The spin direction of the red target is parallel to the $z$ axis, and the blue and orange targets are 240° and 120° rotated clockwise from the red, respectively.

Figure 3

Mn $2p\mathrm{XAS}$ and XMCD calculation for the AFM state of the triangular structure considering ${\mathrm{Mn}}^{2+}$. The triangular structure is located in the xz plane. (a) The spin direction of the red target is parallel to the $z$ axis, and the blue and orange targets are rotated 240° and 120° clockwise from the red, respectively. The direction of incident x ray is parallel to the $z$ axis. (b) The spin direction of the red target is parallel to the $x$ axis, and the rotations of the blue and orange targets are same as in Fig. 3. The direction of the incident x ray is parallel to the $x$ axis. (c) Spin-orbit interaction (SOI) effect; the spin ordered state and incident photon settings are the same as in Fig. 3. The black solid line shows XMCD calculation considering that spin-orbit coupling constant for the $3d$ orbital is zero [21], and the green dotted line is the difference of the XMCD signal (black line) in Figs. 3 and 3.

Figure 4

(a) A state of positive chirality (left) and negative chirality (right) of the triangular geometry in the upper half. When one target is transferred clockwise to the neighbor position, the spin and charge distribution changes by 120° following the spin and orbital rotation directions, respectively. In the bottom half, the spin and charge distributions are arranged by considering one quantization axis (QA). (b) The geometry between the incident x-ray direction and triangular structure is described in the left side; the solid arrow corresponds to Figs. 1 and Fig. 3 and the dotted arrow corresponds to Figs. 2 and Fig. 3. By arranging the incident x-ray direction using the above QA, the incident x-ray direction of each target is shown in the right side.