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Coercivity
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<h2 id="definitions">Definitions</h2> <p>Coercivity in a <a href="/facts/Ferromagnet/fH3HFnSl">ferromagnetic material</a> is the intensity of the applied <a href="/facts/Magnetic_field/Ta8Ev588">magnetic field</a> (<i>H</i> field) required to demagnetize that material, after the magnetization of the sample has been driven to <a href="/facts/Saturation_(magnetic)/QvhGEldn">saturation</a> by a strong field. This demagnetizing field is applied opposite to the original saturating field. There are however different definitions of coercivity, depending on what counts as 'demagnetized', thus the bare term "coercivity" may be ambiguous: </p> <ul><li>The <i>normal coercivity</i>, <i>H</i>Cn, is the <i>H</i> field required to reduce the <a href="/facts/Magnetic_flux/jQMVxrnD">magnetic flux</a> (average <i>B</i> field inside the material) to zero.</li> <li>The <i>intrinsic coercivity</i>, <i>H</i>Ci, is the <i>H</i> field required to reduce the <a href="/facts/Magnetization/zxrtXzTN">magnetization</a> (average <i>M</i> field inside the material) to zero.</li> <li>The <i>remanence coercivity</i>, <i>H</i>Cr, is the <i>H</i> field required to reduce the <a href="/facts/Remanence/64q5LcMV">remanence</a> to zero, meaning that when the <i>H</i> field is finally returned to zero, then both <i>B</i> and <i>M</i> also fall to zero (the material reaches the origin in the hysteresis curve).<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a></li></ul> <p>The distinction between the normal and intrinsic coercivity is negligible in soft magnetic materials, however it can be significant in hard magnetic materials.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> The strongest <a href="/facts/Rare-earth_magnet/Y5oKSjA7">rare-earth magnets</a> lose almost none of the magnetization at <i>H</i>Cn. </p> <h2 id="experimental-determination">Experimental determination</h2> Coercivities of some magnetic materials<table><tbody><tr><th>Material</th><th>Coercivity(kA/m)</th></tr><tr><td><a href="/facts/Supermalloy/y3MeMD6F">Supermalloy</a>(16<a href="/facts/Iron/QK1JYy8E">Fe</a>:79<a href="/facts/Nickel/KwMCHYRP">Ni</a>:5<a href="/facts/Molybdenum/RX6vp2bF">Mo</a>)</td><td>0.0002<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>: 131, 133 </td></tr><tr><td><a href="/facts/Permalloy/FkJSmCnY">Permalloy</a> (<a href="/facts/Iron/QK1JYy8E">Fe</a>:4<a href="/facts/Nickel/KwMCHYRP">Ni</a>)</td><td>0.0008–0.08<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a></td></tr><tr><td><a href="/facts/Iron_filings/Jmktu6da">Iron filings</a> (0.9995 <a href="/facts/Mass_fraction_(chemistry)/YMIH9egn">wt</a>)</td><td>0.004–37.4<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a></td></tr><tr><td><a href="/facts/Electrical_steel/K8oyIxsb">Electrical steel</a> (11Fe:Si)</td><td>0.032–0.072<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a></td></tr><tr><td><a href="/facts/Wrought_iron/zynpjrIv">Raw iron</a> (1896)</td><td>0.16<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a></td></tr><tr><td><a href="/facts/Nickel/KwMCHYRP">Nickel</a> (0.99 wt)</td><td>0.056–23<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a><a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a></td></tr><tr><td><a href="/facts/Ferrite_(magnet)/kBTM7Dqk">Ferrite</a> magnet(ZnxFeNi1−xO3)</td><td>1.2–16<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a></td></tr><tr><td>2Fe:Co,<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> iron pole</td><td>19<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a></td></tr><tr><td><a href="/facts/Cobalt/gqhScEw4">Cobalt</a> (0.99 wt)</td><td>0.8–72<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a></td></tr><tr><td><a href="/facts/Alnico/gEW0Itz3">Alnico</a></td><td>30–150<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a></td></tr><tr><td>Disk drive recording medium (<a href="/facts/Chromium/6sVk6Uu7">Cr</a>:<a href="/facts/Cobalt/gqhScEw4">Co</a>:<a href="/facts/Platinum/qJC6lQf7">Pt</a>)</td><td>140<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a></td></tr><tr><td><a href="/facts/Neodymium_magnet/1LApJ5Xq">Neodymium magnet</a> (NdFeB)</td><td>800–950<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a><a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a></td></tr><tr><td>12<a href="/facts/Iron/QK1JYy8E">Fe</a>:13<a href="/facts/Platinum/qJC6lQf7">Pt</a> (Fe48Pt52)</td><td>≥980<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a></td></tr><tr><td>?(<a href="/facts/Dysprosium/eMev6zGS">Dy</a>,<a href="/facts/Niobium/3zNI8AKp">Nb</a>,<a href="/facts/Gallium/EucevDs9">Ga</a>(<a href="/facts/Cobalt/gqhScEw4">Co</a>):2<a href="/facts/Neodymium/GzDkTIoI">Nd</a>:14<a href="/facts/Iron/QK1JYy8E">Fe</a>:<a href="/facts/Boron/Pmwgd7Mf">B</a>)</td><td>2040–2090<a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a><a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a></td></tr><tr><td>Samarium-cobalt magnet (2<a href="/facts/Samarium/09K3kl93">Sm</a>:17<a href="/facts/Iron/QK1JYy8E">Fe</a>:3<a href="/facts/Nitrogen/Nf1QpGDz">N</a>; 10 <a href="/facts/Kelvin/E3trzC4C">K</a>)</td><td><40–2800<a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a><a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a></td></tr><tr><td><a href="/facts/Samarium%E2%80%93cobalt_magnet/Qcr5aIBr">Samarium-cobalt magnet</a></td><td>3200<a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a></td></tr></tbody></table> <p>Typically the coercivity of a magnetic material is determined by measurement of the <a href="/facts/Magnetic_hysteresis/KchYJC1p">magnetic hysteresis</a> loop, also called the <i>magnetization curve</i>, as illustrated in the figure above. The apparatus used to acquire the data is typically a <a href="/facts/Vibrating-sample_magnetometer/VMGX2pFI">vibrating-sample</a> or alternating-gradient <a href="/facts/Magnetometer/dqX9g1og">magnetometer</a>. The applied field where the data line crosses zero is the coercivity. If an <a href="/facts/Antiferromagnet/aQ124Kh7">antiferromagnet</a> is present in the sample, the coercivities measured in increasing and decreasing fields may be unequal as a result of the <a href="/facts/Exchange_bias/aTlT5GLu">exchange bias</a> effect. </p><p>The coercivity of a material depends on the time scale over which a magnetization curve is measured. The magnetization of a material measured at an applied reversed field which is nominally smaller than the coercivity may, over a long time scale, slowly <a href="/facts/Relaxation_(physics)/IhdVkDQ4">relax</a> to zero. Relaxation occurs when reversal of magnetization by domain wall motion is <a href="/facts/Arrhenius_equation/TdAeo3Lf">thermally activated</a> and is dominated by <a href="/facts/Magnetic_viscosity/JxaIscUY">magnetic viscosity</a>.<a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a> The increasing value of coercivity at high frequencies is a serious obstacle to the increase of <a href="/facts/Bit_rate/ppUNMmVd">data rates</a> in high-<a href="/facts/Bandwidth_(computing)/lY6Tb4gX">bandwidth</a> magnetic recording, compounded by the fact that increased storage density typically requires a higher coercivity in the media. </p> <h2 id="theory">Theory</h2> <p>At the coercive field, the <a href="/facts/Vector_(geometry)/bCLrdksy">vector component</a> of the magnetization of a ferromagnet measured along the applied field direction is zero. There are two primary modes of <a href="/facts/Magnetization_reversal/zxrtXzTN">magnetization reversal</a>: <a href="/facts/Single_domain_(magnetic)/0LLtyIbC">single-domain</a> rotation and <a href="/facts/Domain_wall_(magnetism)/4f76pEXb">domain wall</a> motion. When the magnetization of a material reverses by rotation, the magnetization component along the applied field is zero because the vector points in a direction orthogonal to the applied field. When the magnetization reverses by domain wall motion, the net magnetization is small in every vector direction because the moments of all the individual domains sum to zero. Magnetization curves dominated by rotation and <a href="/facts/Magnetocrystalline_anisotropy/AqMyac3R">magnetocrystalline anisotropy</a> are found in relatively perfect magnetic materials used in fundamental research.<a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a> Domain wall motion is a more important reversal mechanism in real engineering materials since defects like <a href="/facts/Grain_boundary/3r6klMTy">grain boundaries</a> and <a href="/facts/Impurity/FfPvIRoB">impurities</a> serve as <a href="/facts/Nucleation/efUVLsLR">nucleation</a> sites for reversed-magnetization domains. The role of domain walls in determining coercivity is complicated since defects may <i>pin</i> domain walls in addition to nucleating them. The dynamics of domain walls in ferromagnets is similar to that of grain boundaries and <a href="/facts/Plasticity_(physics)/2VKo6keA">plasticity</a> in <a href="/facts/Metallurgy/1SANyxX4">metallurgy</a> since both domain walls and grain boundaries are planar defects. </p> <h2 id="significance">Significance</h2> <p>As with any <a href="/facts/Hysteresis/9M2pwR62">hysteretic</a> process, the area inside the magnetization curve during one cycle represents the <a href="/facts/Work_(thermodynamics)/SjChajtw">work</a> that is performed on the material by the external field in reversing the magnetization, and is dissipated as heat. Common dissipative processes in magnetic materials include <a href="/facts/Magnetostriction/hkma4mTU">magnetostriction</a> and domain wall motion. The coercivity is a measure of the degree of magnetic hysteresis and therefore characterizes the lossiness of soft magnetic materials for their common applications. </p><p>The saturation remanence and coercivity are figures of merit for hard magnets, although <a href="/facts/Maximum_energy_product/CwesFEat">maximum energy product</a> is also commonly quoted. The 1980s saw the development of <a href="/facts/Rare-earth_magnet/Y5oKSjA7">rare-earth magnets</a> with high energy products but undesirably low <a href="/facts/Curie_temperature/ygotSuMg">Curie temperatures</a>. Since the 1990s new <a href="/facts/Exchange_spring_magnet/lR8YJ6bI">exchange spring</a> hard magnets with high coercivities have been developed.<a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a> </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Magnetic_susceptibility/hWMbGTjP">Magnetic susceptibility</a></li> <li><a href="/facts/Remanence/64q5LcMV">Remanence</a></li></ul> <ul><li>Chen, Min; Nikles, David E. (2002). "Synthesis, self-assembly, and magnetic properties of Fe<i>x</i>Co<i>y</i>Pt100-<i>x</i>-<i>y</i> nanoparticles". <i><a href="/facts/Nano_Letters/Ec2sQnqI">Nano Letters</a></i>. 2 (3): 211–214. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2002NanoL...2..211C">2002NanoL...2..211C</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1021%2Fnl015649w">10.1021/nl015649w</a>.</li> <li>Gaunt, P. (1986). "Magnetic viscosity and thermal activation energy". <i><a href="/facts/Journal_of_Applied_Physics/Hl94PvsU">Journal of Applied Physics</a></i>. 59 (12): 4129–4132. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1986JAP....59.4129G">1986JAP....59.4129G</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1063%2F1.336671">10.1063/1.336671</a>.</li> <li>Genish, Isaschar; Kats, Yevgeny; Klein, Lior; Reiner, James W.; Beasley, M. R. (2004). "Local measurements of magnetization reversal in thin films of SrRuO3". <i><a href="/facts/Physica_Status_Solidi_C/afWwmqls">Physica Status Solidi C</a></i>. 1 (12): 3440–3442. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2004PSSCR...1.3440G">2004PSSCR...1.3440G</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1002%2Fpssc.200405476">10.1002/pssc.200405476</a>.</li> <li>Kneller, E. F.; Hawig, R. (1991). "The exchange-spring magnet: a new material principle for permanent magnets". <i><a href="/facts/IEEE_Transactions_on_Magnetics/tdrUblx9">IEEE Transactions on Magnetics</a></i>. 27 (4): 3588–3600. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1991ITM....27.3588K">1991ITM....27.3588K</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1109%2F20.102931">10.1109/20.102931</a>.</li> <li>Livingston, J. D. (1981). "A review of coercivity mechanisms". <i><a href="/facts/Journal_of_Applied_Physics/Hl94PvsU">Journal of Applied Physics</a></i>. 52 (3): 2541–2545. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1981JAP....52.2544L">1981JAP....52.2544L</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1063%2F1.328996">10.1063/1.328996</a>.</li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="https://web.archive.org/web/20160303180902/http://www.bama.ua.edu/~tmewes/Java/Reversal/reversal.shtml">Magnetization reversal applet (coherent rotation)</a></li> <li>For a table of coercivities of various magnetic recording media, see "<a href="https://web.archive.org/web/20100714063005/http://www.fujifilmusa.com/shared/bin/Degauss_Data_Tape.pdf">Degaussing Data Storage Tape Magnetic Media</a>" (<a href="/facts/PDF/C9Mn1vYL">PDF</a>), at fujifilmusa.com.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Giorgio Bertotti (21 May 1998). 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