<p>Theoretical understanding of spin dynamics in ferromagnets is a crucial question in spintronics. A recent work considered the dynamical equations for ferromagnets using Onsager’s irreversible thermodynamics with fundamental variables magnetization <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\vec {M}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </math></EquationSource> </InlineEquation> and spin current <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\vec {J}_{i}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mi>J</mi> <mo stretchy="false">→</mo> </mover> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation>. The resulting equations have the same structure as Leggett’s Fermi liquid theory for the nuclear paramagnet <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$^{3}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>He. Specifically, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\partial _{t}\vec {J}_{i}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>∂</mi> <mi>t</mi> </msub> <msub> <mover accent="true"> <mi>J</mi> <mo stretchy="false">→</mo> </mover> <mi>i</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> contains a term varying as <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\partial _{i}\vec {M}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>∂</mi> <mi>i</mi> </msub> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mrow> </math></EquationSource> </InlineEquation> that we interpret as associated with a vector spin pressure and a term giving a mean-field along <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\vec {M}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </math></EquationSource> </InlineEquation>, about which <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\vec {J}_{i}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mi>J</mi> <mo stretchy="false">→</mo> </mover> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> precesses. (There is also a decay term in <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\partial _{t}\vec {M}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>∂</mi> <mi>t</mi> </msub> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mrow> </math></EquationSource> </InlineEquation> not normally present in the Leggett equations, which are intended for shorter-time spin-echo experiments.) The present work applies Fermi liquid theory to <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$\vec {J}_{i}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mi>J</mi> <mo stretchy="false">→</mo> </mover> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> of ferromagnets. The resulting dynamical equation for <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$\vec {J}_i$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mi>J</mi> <mo stretchy="false">→</mo> </mover> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> confirms the form of <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$\vec {J}_i$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mi>J</mi> <mo stretchy="false">→</mo> </mover> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> found earlier using irreversible thermodynamics, but now the previously unknown exchange constant is given in terms of the quasiparticle interaction parameters of Fermi liquid theory. Our results indicate that study of spin currents in ferromagnets can yield information about the Fermi liquid coefficients.</p>

Fermi Liquid Theory for Spin Current Dynamics of a Ferromagnet

期刊论文
发表日期：

2026年2月16日

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Chen Sun,
Wayne Saslow

摘要

Theoretical understanding of spin dynamics in ferromagnets is a crucial question in spintronics. A recent work considered the dynamical equations for ferromagnets using Onsager’s irreversible thermodynamics with fundamental variables magnetization $\vec {M}$ $\vec{M}$ and spin current $\vec {J}_{i}$ ${\vec{J}}_{i}$ . The resulting equations have the same structure as Leggett’s Fermi liquid theory for the nuclear paramagnet $^{3}$ $^{3}$ He. Specifically, $\partial _{t}\vec {J}_{i}$ $\partial_{t} {\vec{J}}_{i}$ contains a term varying as $\partial _{i}\vec {M}$ $\partial_{i} \vec{M}$ that we interpret as associated with a vector spin pressure and a term giving a mean-field along $\vec {M}$ $\vec{M}$ , about which $\vec {J}_{i}$ ${\vec{J}}_{i}$ precesses. (There is also a decay term in $\partial _{t}\vec {M}$ $\partial_{t} \vec{M}$ not normally present in the Leggett equations, which are intended for shorter-time spin-echo experiments.) The present work applies Fermi liquid theory to $\vec {J}_{i}$ ${\vec{J}}_{i}$ of ferromagnets. The resulting dynamical equation for $\vec {J}_i$ ${\vec{J}}_{i}$ confirms the form of $\vec {J}_i$ ${\vec{J}}_{i}$ found earlier using irreversible thermodynamics, but now the previously unknown exchange constant is given in terms of the quasiparticle interaction parameters of Fermi liquid theory. Our results indicate that study of spin currents in ferromagnets can yield information about the Fermi liquid coefficients.