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   "source": [
    "# Spatially dependent uniaxial anisotropy\n",
    "\n",
    "In this notebook, an example is given for a spatially varying uniaxial anisotropy. To demonstrate it, we will use a nanotube (with R=30 nm and r=20 nm outer and inner radii) and set a radial uniaxial anisotropy with constant magnitude. Any other material parametes can be made spatially dependent, it isn't restricted to the uniaxial anisotropy."
   ]
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   "id": "a0ea9478",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                                                                                                                               "
     ]
    }
   ],
   "source": [
    "import tetrax as tx\n",
    "\n",
    "sample = tx.Sample(\n",
    "    tx.geometries.waveguide.tube(20, 30, 3),\n",
    "    name='tube_radial_uanis'\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd7bbdd8",
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   "source": [
    "In the following we set a radial uniaxial anisotropy using the ```tx.vectorfields.radial(sample.xyz,1)``` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "53b30d39",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/attilak/micromag/tetrax-tests/fresh_environement_test/venv/lib/python3.13/site-packages/traittypes/traittypes.py:97: UserWarning: Given trait value dtype \"float32\" does not match required type \"float32\". A coerced copy has been created.\n",
      "  warnings.warn(\n"
     ]
    },
    {
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      },
      "text/plain": [
       "Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, axes_helper_colors=[16711680, 65280, 255], background…"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample.material[\"Ku1\"] = 1e6 #J/m^3\n",
    "sample.material[\"e_u\"]  = tx.vectorfields.radial(sample.xyz,1)\n",
    "\n",
    "sample.show(sample.material[\"e_u\"].value)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb1a08a1",
   "metadata": {},
   "source": [
    "![spatially dependent anisotropy](uanis_sp_dep.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "124484f3-f8e7-43a5-b7ff-6644ac64348e",
   "metadata": {},
   "source": [
    "By initializing the tube in a transversally magnetized state, one will observe the stabilization of a two-domain state, by the radial anisotropy, with radial domains and Néel walls between them.\n",
    "This example is a perfect example for the usage of the LLG based dynamic relaxation, which will follow the preliminary nergy minimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c14f7e63",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimizing energy in using 'L-BFGS-B' (tolerance 1e-11) ...\n",
      "energy length density: -8.604699660646469e-10 J/m, <mag.x> = 0.15, <mag.y> = 0.77, <mag.z> = -0.00\n",
      "Failure. Returning last iteration step.\n",
      "Minimizing torque with over-damped LLG (alpha=1, tolerance=1e-10) ...\n",
      "t = 4.0205874505712437e-10 (s), dm/dt = 1330852.6056958192 [Hz], <mag.x> = 0.16, <mag.y> = 0.77, <mag.z> = 0.000\n",
      "Success!\n",
      "\n"
     ]
    }
   ],
   "source": [
    "sample.mag = (0, 1, .1)\n",
    "\n",
    "relaxation = tx.experiments.relax(sample, \n",
    "                                  set_initial_on_failure=False,\n",
    "                                  tolerance=1e-11)\n",
    "\n",
    "if relaxation.was_success is False:\n",
    "    relax_dyn = tx.experiments.relax_dynamic(sample, tolerance=1e-10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "72b573d5",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/attilak/micromag/tetrax-tests/fresh_environement_test/venv/lib/python3.13/site-packages/traittypes/traittypes.py:97: UserWarning: Given trait value dtype \"float32\" does not match required type \"float32\". A coerced copy has been created.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9573390ad0264d94b38e61b05ca954ec",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, axes_helper_colors=[16711680, 65280, 255], background…"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56a1a596",
   "metadata": {},
   "source": [
    "![Magnetic state sp_dep_anis](mag_uanis_sp_dep.png)"
   ]
  }
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