Larmor Precession and Debye Relaxation of Single-Domain Magnetic Nanoparticles

<table>(colour online) The dependence of <svg height="11.4625" id="M168" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.5875 11.4625" width="12.5875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>  <i>∝</i>  <svg height="11.175" id="M169" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 10.8625 11.175" width="10.8625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M609 650l-19 -162l-30 -2q2 69 -14 94q-9 18 -28.5 26t-74.5 8h-88q-30 0 -37 -6.5t-12 -36.5l-41 -212h103q48 0 69 5.5t32 19t26 50.5h29l-40 -198h-30q2 58 -11.5 70.5t-85.5 12.5h-99l-30 -167q-17 -87 3 -101q18 -15 111 -15q59 0 89 7t54 27q8 7 15.5 16t16 21.5
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</svg>, the energy loss, on <svg height="8.125" id="M170" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 19.174999 8.125" width="19.174999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.863)"><path d="M615 290q0 -148 -114 -245q-65 -57 -125 -57q-39 0 -62 27t-29 70q-31 -41 -72 -69t-74 -28q-49 0 -82.5 43t-33.5 124q0 97 55 174.5t148 124.5l15 -24q-59 -45 -94 -113t-35 -146q0 -58 19.5 -88.5t48.5 -30.5q33 0 62 34.5t45 101.5q16 73 20 135l80 17l5 -6
q-11 -37 -23.5 -100t-12.5 -92q0 -47 16.5 -71.5t44.5 -24.5q62 0 95.5 67t33.5 160q0 107 -63 152l1 9q14 14 45 14q29 0 57.5 -44t28.5 -114z" id="x1D714"></path></g><g transform="matrix(.017,-0,0,-.017,10.908,7.863)"><path d="M471 456q-22 -60 -37 -85q-20 -3 -84 -3q-9 0 -29 2t-29 2q-38 -145 -54 -234q-15 -80 14 -80q23 0 68 38l14 -25q-78 -83 -137 -83q-50 0 -50 64q0 25 7 57l67 266q-57 4 -98 -9t-80 -49l-20 21q14 18 27 31t36.5 30t56.5 26t73 9q26 0 82.5 -2t89.5 -2q21 0 32 5t24 24
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</svg> for various <svg height="16.15" id="M171" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 36.237499 16.15" width="36.237499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M615 290q0 -148 -114 -245q-65 -57 -125 -57q-39 0 -62 27t-29 70q-31 -41 -72 -69t-74 -28q-49 0 -82.5 43t-33.5 124q0 97 55 174.5t148 124.5l15 -24q-59 -45 -94 -113t-35 -146q0 -58 19.5 -88.5t48.5 -30.5q33 0 62 34.5t45 101.5q16 73 20 135l80 17l5 -6
q-11 -37 -23.5 -100t-12.5 -92q0 -47 16.5 -71.5t44.5 -24.5q62 0 95.5 67t33.5 160q0 107 -63 152l1 9q14 14 45 14q29 0 57.5 -44t28.5 -114z" id="x1D714"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.912,16.087)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g>
<g transform="matrix(.017,-0,0,-.017,18.325,12.012)"><path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path></g><g transform="matrix(.017,-0,0,-.017,25.328,12.012)"><path d="M615 290q0 -148 -114 -245q-65 -57 -125 -57q-39 0 -62 27t-29 70q-31 -41 -72 -69t-74 -28q-49 0 -82.5 43t-33.5 124q0 97 55 174.5t148 124.5l15 -24q-59 -45 -94 -113t-35 -146q0 -58 19.5 -88.5t48.5 -30.5q33 0 62 34.5t45 101.5q16 73 20 135l80 17l5 -6
q-11 -37 -23.5 -100t-12.5 -92q0 -47 16.5 -71.5t44.5 -24.5q62 0 95.5 67t33.5 160q0 107 -63 152l1 9q14 14 45 14q29 0 57.5 -44t28.5 -114z" id="x1D714"></path></g>
</svg> ratios from <svg height="11.125" id="M172" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.2875004 11.125" width="8.2875004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg> to <svg height="10.8625" id="M173" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 8.2875004 10.8625" width="8.2875004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.8)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
</svg>. See (<a href="https://static.hindawi.com/articles/acmp/volume-2014/125454/figures/#EEq20">20</a>).</table>

Advances in Condensed Matter Physics

fig3

Figure 3

Figure 3: Larmor Precession and Debye Relaxation of Single-Domain Magnetic Nanoparticles 