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449 | 449 | "#### Micromagnetic\n",
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450 | 450 | "The micromagnetic exchange correlation constant $A$ can be related to atomistic exchange using\n",
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451 | 451 | "\\begin{equation}\n",
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452 |
| - "A = \\frac{zJl^2}{12V},\n", |
| 452 | + "A = \\frac{zJL^2}{12V},\n", |
453 | 453 | "\\end{equation}\n",
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454 |
| - "where $J$ is the Heisenberg exchange, $z$ is the number of nearest neighbour atoms, and $l$ is the distance between neighbouring atoms, and $V$ is the crystal volume per magnetic atom." |
| 454 | + "where $J$ is the Heisenberg exchange, $z$ is the number of nearest neighbour atoms, and $L$ is the distance between neighbouring atoms, and $V$ is the crystal volume per magnetic atom." |
455 | 455 | ]
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456 | 456 | },
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457 | 457 | {
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496 | 496 | "source": [
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497 | 497 | "The micromagnetic exchange correlation constant can be obtained directly from $T_c$ using \n",
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498 | 498 | "\\begin{equation}\n",
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499 |
| - "A = \\frac{k_\\text{B}T_\\text{C}l^2}{4\\epsilon V}.\n", |
| 499 | + "A = \\frac{k_\\text{B}T_\\text{C}L^2}{4\\epsilon V}.\n", |
500 | 500 | "\\end{equation}"
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501 | 501 | ]
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502 | 502 | },
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556 | 556 | "#### Micromagentic\n",
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557 | 557 | "The micromagnetic DMI constant $D$ can be related to atomistic DMI using\n",
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558 | 558 | "\\begin{equation}\n",
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559 |
| - "D = \\frac{zdl}{12V},\n", |
| 559 | + "D = \\frac{zdL}{12V},\n", |
560 | 560 | "\\end{equation}\n",
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561 |
| - "where $d$ is the atomistic DMI, $z$ is the number of nearest neighbour atoms, and $l$ is the distance between neighbouring atoms, and $V$ is the crystal volume per magnetic atom." |
| 561 | + "where $d$ is the atomistic DMI, $z$ is the number of nearest neighbour atoms, and $L$ is the distance between neighbouring atoms, and $V$ is the crystal volume per magnetic atom." |
562 | 562 | ]
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563 | 563 | },
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564 | 564 | {
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627 | 627 | "id": "5709f726",
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628 | 628 | "metadata": {},
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629 | 629 | "source": [
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630 |
| - "For a system with a micromagentic exchange of $6\\times 10^{-14}$ Jm$^{-1}$ and a helical period of 20 nm." |
| 630 | + "For a system with a micromagentic exchange of $6\\times 10^{-14}$ Jm $^{-1}$ and a helical period of 20 nm." |
631 | 631 | ]
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632 | 632 | },
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633 | 633 | {
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660 | 660 | "source": [
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661 | 661 | "For atomistic simulations, this can be converted into\n",
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662 | 662 | "\\begin{equation}\n",
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663 |
| - "P = \\frac{4\\pi J l}{|d|},\n", |
| 663 | + "P = \\frac{4\\pi J L}{|d|},\n", |
664 | 664 | "\\end{equation}\n",
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665 |
| - "where $J$ is the Heisenberg exchange, $d$ is the atomistic DMI, and $l$ is the distance between neighbouring atoms." |
| 665 | + "where $J$ is the Heisenberg exchange, $d$ is the atomistic DMI, and $L$ is the distance between neighbouring atoms." |
666 | 666 | ]
|
667 | 667 | },
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668 | 668 | {
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763 | 763 | "source": [
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764 | 764 | "### Anisotropy\n",
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765 | 765 | "#### Micromagnetic\n",
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766 |
| - "Anisotropy can be measured experimentally in a variety of different ways. The results torque magnetometry, for example, can give correct value for the anisotropy in units of Jm$^{-3}$." |
| 766 | + "Anisotropy can be measured experimentally in a variety of different ways. The results torque magnetometry, for example, can give correct value for the anisotropy in units of Jm $^{-3}$." |
767 | 767 | ]
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768 | 768 | },
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769 | 769 | {
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