Separating spin dynamics modes in iron oxide nanoparticles

The different modes of the spin dynamics in ferrimagnetic magnetite iron oxide nanoparticles (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi mathvariant="normal">Fe</a:mi><a:mn>3</a:mn></a:msub><a:msub><a:mi mathvariant="normal">O</a:mi><a:mn>4</a:mn></a:msub></a:mrow></a:math>) have been addressed by µeV neutron spectroscopy for particles with a diameter of 75 ± 18 Å. In an approach building on intensity considerations over a wide range of wave vectors <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>Q</d:mi></d:mrow></d:math> in combination with diffusion dynamics, we identify three magnetic modes prevailing in distinct <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>Q</e:mi></e:mrow></e:math> regimes up to 1.7 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msup><f:mrow><f:mi>Å</f:mi></f:mrow><f:mrow><f:mo>−</f:mo><f:mn>1</f:mn></f:mrow></f:msup></f:math>: (i) Evaluating the structure factor of quasielastic magnetic intensity enables to identify uniquely longitudinal superparamagnetic spin fluctuations in the small <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>Q</g:mi></g:mrow></g:math> regime <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mo>&lt;</h:mo><h:mn>0.5</h:mn><h:msup><h:mrow><h:mrow><h:mspace width="4.pt"/><h:mtext>Å</h:mtext></h:mrow></h:mrow><h:mrow><h:mo>−</h:mo><h:mn>1</h:mn></h:mrow></h:msup></h:mrow></h:math>, (ii) individual spin relaxation with quasielastic intensity albeit of low intensity is present in two <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mi>Q</j:mi></j:mrow></j:math> ranges of 0.5 <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:msup><k:mrow><k:mrow><k:mspace width="4.pt"/><k:mtext>Å</k:mtext></k:mrow></k:mrow><k:mrow><k:mo>−</k:mo><k:mn>1</k:mn></k:mrow></k:msup><k:mo>&lt;</k:mo><k:mi>Q</k:mi><k:mo>&lt;</k:mo><k:mn>1.0</k:mn><k:msup><k:mrow><k:mrow><k:mspace width="4.pt"/><k:mtext>Å</k:mtext></k:mrow></k:mrow><k:mrow><k:mo>−</k:mo><k:mn>1</k:mn></k:mrow></k:msup></k:mrow></k:math> and 1.5 <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:mrow><n:msup><n:mrow><n:mrow><n:mspace width="4.pt"/><n:mtext>Å</n:mtext></n:mrow></n:mrow><n:mrow><n:mo>−</n:mo><n:mn>1</n:mn></n:mrow></n:msup><n:mo>&lt;</n:mo><n:mi>Q</n:mi><n:mo>&lt;</n:mo><n:mn>1.7</n:mn><n:msup><n:mrow><n:mrow><n:mspace width="4.pt"/><n:mtext>Å</n:mtext></n:mrow></n:mrow><n:mrow><n:mo>−</n:mo><n:mn>1</n:mn></n:mrow></n:msup></n:mrow></n:math>, and (iii) a surprisingly low-energy inelastic spin excitation of 23.2 µeV in magnetite IONPs is found at 150 K in the magnetic Bragg region between 1.1 <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"><q:mrow><q:msup><q:mrow><q:mi>Å</q:mi></q:mrow><q:mrow><q:mo>−</q:mo><q:mn>1</q:mn></q:mrow></q:msup><q:mo>&lt;</q:mo><q:mi>Q</q:mi><q:mo>&lt;</q:mo><q:mn>1.4</q:mn><q:msup><q:mrow><q:mrow><q:mspace width="4.pt"/><q:mtext>Å</q:mtext></q:mrow></q:mrow><q:mrow><q:mo>−</q:mo><q:mn>1</q:mn></q:mrow></q:msup></q:mrow></q:math>. Its temperature dependence suggests a collapse of the coherent transverse magnetic fluctuations and a transition into a generalized diffusive mode at about 500 K.