Collective dynamics of domain walls: An antiferromagnetic spin texture in an optical cavity

Spin canting and complex spin textures in antiferromagnetic materials can be described in terms of Dzyaloshinskii-Moriya interactions (DMI). Values for DMI parameters are not easily measurable directly, and often inferred from other quantities. In this work, we examine how domain wall dynamics in an antiferromagnetic optomagnonic system can display unique features directly related to the existence of DMI. Our results indicate that the presence of DMI enables spin interactions with cavity photons in a geometry which otherwise allows no magneto-optical coupling, and on the other hand modulates frequencies in a geometry where coupling is already realized in the absence of DMI. This result may be used to measure the DMI constant in optomagnonic experiments by comparing resonances obtained with different polarizations of the exciting field.

Figure 1

(a) Schematic illustration of the geometry where the effective magnetic field of the light along $\widehat{x}$ interacts with the domain wall with width $\lambda$ and axis along $\widehat{z}$ in the presence of DMI along $\widehat{y}$. (b) Hybridized frequency of the cavity modes and magnon modes of the antiferromagnetic domain wall as a function of the detuning parameter in the absence of DMI. In the absence of DMI, there is no coupling achieved as indicated by the dotted lines. The thick lines represent what happens in the presence of DMI when the magnon modes couple to the cavity modes. The real part of the two modes attract in the region of negative detuning and repulsion is observed in the region of positive detuning.

Figure 2

(a) Frequency gap in the presence of DMI of strength $0.06J$ as a function of the negative detuning around the point of attraction for different coupling strengths: $g=0.10$ MHz, $g=0.12$ MHz, and $g=0.14$ MHz represented by the purple dotted, orange dashed, and green solid lines, respectively. Around the exceptional point, attraction dominates a wider range for larger coupling strengths and decreases for lower coupling strengths. (b) Frequency gap in the presence of DMI of strength $0.06J$ as a function of the positive detuning. For the same value of detuning, larger frequency gaps are observed for larger coupling. In all cases, the gap is minimum at resonance and increases as we move away from resonance. (c) Frequency gap as a function of negative and positive DMI present along the $\widehat{y}$. At $d_y=0$ there is no gap. In the presence of DMI, the frequency gaps increase linearly with increasing magnitude of DMI and the gap is observed to be larger for larger coupling strengths.

Figure 3

(a) Schematic illustrating the geometry where the effective magnetic field of the light along $\widehat{y}$ interacts with the domain wall of width, $\lambda$ with axis along $\widehat{z}$ in the presence of DMI along $\widehat{x}$. (b) Hybridized frequency of the cavity modes and magnon modes of the antiferromagnetic domain wall as a function of the detuning parameter in the absence of DMI. The red and blue thick lines indicate coupling between the magnonic and photonic modes in the absence of DMI. The real part of the two modes attract in the region of negative detuning and repulsion is observed in the region of positive detuning. As the magnitude of DMI increases, coupling between modes reduces until no coupling is achieved. The black dotted lines show that there is no coupling at the saturated value of DMI.

Figure 4

Effect of DMI of strength $0.06J$ on the frequency gaps as (a) a function of the negative detuning around the point of attraction for different coupling strengths: $g=0.10$ MHz, $g=0.12$ MHz, and $g=0.14$ MHz represented by the purple dotted, orange dashed, and green solid lines, respectively. Around the exceptional point, attraction dominates a wider range for larger coupling strengths and decreases for lower coupling strengths. (b) Frequency gap in the presence of DMI of strength $0.06J$ as a function of the positive detuning. For the same value of detuning, larger frequency gaps are observed for larger coupling. In all cases, the gap is minimum at resonance and increases as we move away from resonance. (c) Frequency gap as a function of negative and positive DMI present along the $\widehat{y}$. The values of the coupling strength $g$ become more important as $d_x$ approaches zero. The frequency gap reduces for increasing magnitude of the DMI and vanishes as the saturated value of DMI is reached.