# Generation of DC, AC, and Second-Harmonic Spin Currents by Electromagnetic Fields in an Inversion-Asymmetric Antiferromagnet

## Abstract

**:**

## 1. Introduction

## 2. Formulation of the Problem

#### 2.1. Time-Independent Hamiltonian

#### 2.2. Coupling to AC Electric Field: Difference- and Sum-Frequency Mechanisms

#### 2.3. Total Hamiltonian and Spin Current

## 3. Results

#### 3.1. DC and Second-Harmonic Spin Currents

#### 3.2. Direction of DC Spin Current

#### 3.3. Mechanism of Spin Current Generation

#### 3.4. DC Spin Current Generation by External Magnetic Field

## 4. Discussion and Conclusions

## 5. Materials and Methods

#### 5.1. Fermionization

#### 5.2. Quantum Master Equation

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic illustration of our model (Equation (1)).The thick and thin bonds represent the exchange couplings $J(1+{\eta}_{\mathrm{stag}})$ and $J(1-{\eta}_{\mathrm{stag}})$, respectively, and the red and blue sites represent the local magnetic fields ${H}_{\mathrm{stag}}$ and $-{H}_{\mathrm{stag}}$, respectively.

**Figure 2.**(

**a**) Form of oscillating exchange interaction ${J}_{\mathrm{pulse}}^{\prime}$ (12). (

**b**) Time profile of spin current ${J}_{\mathrm{spin}}\left(t\right)$ for $({\eta}_{\mathrm{stag}},{H}_{\mathrm{stag}}/J)=(0.1,0.03)$ and $\Omega =5\times {10}^{-2}J$ and $\alpha =0.1$. (

**c**) Amplitude of the corresponding Fourier transform. (

**d**) Amplitudes of the dc and harmonic spin currents, $|{J}_{\mathrm{spin}}(n\Omega )|$ ($n=0,2$, and 4), plotted against the exchange-interaction-modulation amplitude $\alpha $. The solid (dashed) line shows the slope 1 (2) for the guide to the eye.

**Figure 3.**Rescaled dc spin current calculated in the pulse dynamics over the $({\eta}_{\mathrm{stag}},{H}_{\mathrm{stag}})$-plane. The other parameters are set as ${T}_{\mathrm{FWHM}}=10\pi /\Omega $, $\Omega =5\times {10}^{-2}J$ and $\alpha =0.1$.

**Figure 4.**(

**a**) Schematic illustration of our model (1) for ${\eta}_{\mathrm{stag}}=1$ (top) and ${\eta}_{\mathrm{stag}}=-1$ (bottom). The missing bonds show that the exchange couplings vanish on them. (

**b**) Isolated dimer in Equation (14) for ${H}_{\mathrm{stag}}>0$, where the red (blue) site shows the positive (negative) local magnetic field. The green arrows represent the local magnetization on each site in the ground state in Equation (16). The top (bottom) plot shows the dimer for the weaker (stronger) exchange interaction. (

**c**) Mechanism of spin current generation by exchange-interaction modulation. As the exchange interaction increases, the local magnetization flows from right to left when ${H}_{\mathrm{stag}}>0$.

**Figure 5.**(

**a**) Form of external magnetic field for the dc (blue) and ac (orange) cases. (

**b**) Time profile of spin current ${J}_{\mathrm{spin}}\left(t\right)$ for the dc (blue) and ac (orange) cases. The parameters are $({\eta}_{\mathrm{stag}},{H}_{\mathrm{stag}}/J)=(0.1,0.03)$, $\Omega =5\times {10}^{-2}J$, and $\beta =0.1$. (

**c**) Amplitude of the corresponding Fourier transform for the dc (blue) and ac (orange) cases. The amplitude is normalized so that that $|{J}_{\mathrm{spin}}(\omega =0)|=1$ for the dc case. (

**d**) Amplitudes of the dc and harmonic spin currents plotted against the magnetic-field amplitude $\beta $. The blue show the dc spin current $|{J}_{\mathrm{spin}}\left(0\right)|$, and the orange, green, and red show $|{J}_{\mathrm{spin}}(n\Omega )|$ with $n=1,0$, and 2), respectively. The solid (dashed) line shows the slope 1 (2) for the guide to the eye.

**Figure 6.**Energy bands for four choices of the staggered exchange interaction ${\eta}_{\mathrm{stag}}$ in the absence (

**a**) and presence (

**b**) of the staggered magnetic field ${H}_{\mathrm{stag}}$. Each parameter is shown in the figure, and J is set to unity.

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**MDPI and ACS Style**

Ikeda, T.N.
Generation of DC, AC, and Second-Harmonic Spin Currents by Electromagnetic Fields in an Inversion-Asymmetric Antiferromagnet. *Condens. Matter* **2019**, *4*, 92.
https://doi.org/10.3390/condmat4040092

**AMA Style**

Ikeda TN.
Generation of DC, AC, and Second-Harmonic Spin Currents by Electromagnetic Fields in an Inversion-Asymmetric Antiferromagnet. *Condensed Matter*. 2019; 4(4):92.
https://doi.org/10.3390/condmat4040092

**Chicago/Turabian Style**

Ikeda, Tatsuhiko N.
2019. "Generation of DC, AC, and Second-Harmonic Spin Currents by Electromagnetic Fields in an Inversion-Asymmetric Antiferromagnet" *Condensed Matter* 4, no. 4: 92.
https://doi.org/10.3390/condmat4040092