New model to predict thermomagnetic properties of nanostructured magnetic compounds

Abstract The development of new materials showing the magneto-caloric effect (MCE) requires fast and reliable characterization methods. For this purpose, a phenomenological model developed by M. A. Hamad has proven to be a useful tool to predict the magnetocaloric properties (the isothermal magnetic entropy change, $$\Delta S_\textrm{M}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:msub> <mml:mi>S</mml:mi> <mml:mtext>M</mml:mtext> </mml:msub> </mml:mrow> </mml:math> , the magnetization-related change of the specific heat, $$\Delta C_{P,H}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>P</mml:mi> <mml:mo>,</mml:mo> <mml:mi>H</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , and the relative cooling power, RCP) via calculation from magnetization measurements as a function of temperature, M ( T ). However, fitting the M ( T ) data is difficult for broad, smoothed-out transition curves which are often observed for material systems such as core-shell nanoparticles, nanowires, nanowire fabrics or nanoparticle hybrid materials. Thus, in this contribution we present a different approach enabling proper fitting of such magnetization data via the use of an asymmetric Boltzmann sigmoid function, which provides a clear physical background and enables to properly describe the broad and smoothed out transitions of nanomaterials. As examples for our procedure, we present fits to M ( T ) curves of polycrystalline, bulk $$\hbox {La}_{0.67}\hbox {Ba}_{0.33}\hbox {MnO}_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mtext>La</mml:mtext> <mml:mrow> <mml:mn>0.67</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>Ba</mml:mtext> <mml:mrow> <mml:mn>0.33</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>MnO</mml:mtext> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> as well as $$\hbox {La}_{1-x}\hbox {Sr}_{x}\hbox {MnO}_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mtext>La</mml:mtext> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>Sr</mml:mtext> <mml:mi>x</mml:mi> </mml:msub> <mml:msub> <mml:mtext>MnO</mml:mtext> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> ( $$x=$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 0.2, 0.3, 0.4) and $$\hbox {La}_{0.7}\hbox {Ca}_{0.3}\hbox {MnO}_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mtext>La</mml:mtext> <mml:mrow> <mml:mn>0.7</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>Ca</mml:mtext> <mml:mrow> <mml:mn>0.3</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mtext>MnO</mml:mtext> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> nanostructured materials from various authors.