Resistivity anomalies arising from spin correlations in magnetic metals

Some magnetic materials exhibit a pronounced peak or upturn in resistivity upon cooling through the ordering transition, while others do not. To explain and quantify this phenomenon, we develop a simple model in which the carrier lifetime is calculated from the scattering of conduction electrons by local magnetic moments. Within this framework, we derive a general formula for the electron scattering rate, applicable to arbitrary energy dispersions and magnetic structure factors. Using ferromagnets as an example, we show that a resistivity anomaly occurs at <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>T</a:mi> <a:mi>c</a:mi> </a:msub> </a:math> , arising from the rapid increase in the magnetic correlation length <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>ξ</b:mi> </b:math> . We find that this behavior is robust across dimensionality <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>d</c:mi> </c:math> and persists in anisotropic systems. The maximum resistivity is reached when <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mn>1</d:mn> <d:mo>/</d:mo> <d:mi>ξ</d:mi> </d:mrow> </d:math> is comparable to the Fermi momentum <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi mathvariant="normal">k</e:mi> <e:mi mathvariant="normal">F</e:mi> </e:msub> </e:math> , and the peak height scales inversely with <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msubsup> <h:mi mathvariant="normal">k</h:mi> <h:mi mathvariant="normal">F</h:mi> <h:mrow> <h:mi>d</h:mi> <h:mo>+</h:mo> <h:mn>2</h:mn> </h:mrow> </h:msubsup> </h:math> . As a result, the effect is most pronounced for smaller Fermi surfaces, where the anomaly can dominate over other resistivity contributions such as electron-phonon or electron-impurity scattering.