Capturing first- and second-order behavior in magnetocaloric ${\text{CoMnSi}}_{0.92}{\text{Ge}}_{0.08}$

Capturing first- and second-order behavior in magnetocaloric ${CoMnSi}_{0.92} {Ge}_{0.08}$

K. Morrison, J. D. Moore, K. G. Sandeman, A. D. Caplin, and L. F. Cohen

Phys. Rev. B 79, 134408 – Published 6 April 2009

Abstract

Here we examine the constituent components that make a magnetocaloric material attractive for application. The field-temperature phase diagram is studied and using calorimetry, the first-order and second-order components of the magnetic field-driven magneto-structural phase transition in ${CoMnSi}_{0.92} {Ge}_{0.08}$ are extracted. It is demonstrated that below 262 K the transition shows a latent heat component associated with first-order behavior when the material changes from antiferromagnetic to ferromagnetic order. Such a transition is known as a metamagnetic transition. We identify 262 K as a tricritical point and above this temperature $T_{crit}$ the transition shows only continuous, second-order characteristics. Hall-probe imaging that has a five micron pixel resolution is then used to study the striking differences in the spatial evolution of the transition above and below $T_{crit}$ . We demonstrate that the hysteresis of the transition is linearly related to the magnitude of the latent heat; an observation that has important implications for the use of this and other first-order systems for application as magnetic refrigerants.

Received 15 January 2009

DOI:https://doi.org/10.1103/PhysRevB.79.134408

Authors & Affiliations

K. Morrison¹, J. D. Moore¹, K. G. Sandeman², A. D. Caplin¹, and L. F. Cohen¹

¹The Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom
²Department of Material Science and Metallurgy, University of Cambridge, Cambridge CB2 3QZ, United Kingdom

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Vol. 79, Iss. 13 — 1 April 2009

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Figure 1
Magnetic behavior of bulk and micrometer sized fragments of ${CoMnSi}_{0.92} {Ge}_{0.08}$ at 230 K. (a) $M − H$ loop of a $\sim 1 {mm}^{3}$ bulk sample—see the text for definitions and (b) $M − H$ loop of a $\sim 200 − μ m^{3}$ -sized fragment suggesting the presence of two crystallites with individual critical fields $H_{c}^{↑, ↓}$ . Lower inset: Angular variation of $H_{c}^{↑} (θ)$ , defined as the mid-point of the transition of each crystallite, 1 (▲) and 2 (○), identified in the fragment, as a function of angle with respect to the applied field. The shaded region indicates $H_{width}$ of the bulk material. Upper inset: Angular variation of the hysteresis width associated with the crystallite, $Δ H_{1}$ (▲) and $Δ H_{2}$ (○), as a function of angle; the dotted line indicates the hysteresis width observed in the bulk, which is, as expected, independent of field angle.Reuse & Permissions
Figure 2
(Color online) Temperature dependence of the entropy change. (a) Total entropy change (for a field change of 0–8 T) calculated from calorimetry, $Δ S_{Total}$ (-◼-), of a $100 μ m$ fragment, compared to results from bulk magnetization measurements, $Δ S_{Maxwell}$ (-). $Δ S_{Total}$ consists of latent heat, $Δ S_{LH}$ (-●-), and heat capacity, $Δ S_{C}$ (-△-), contributions. Error bars at 180 K are indicative of the errors at all temperatures. Inset shows latent heat data taken from the fragment at 180 K where there is a single spike associated with the transition in each field direction. (b) $H_{c} − T$ schematic constructed from bulk magnetometry (-) and latent heat (- - -) measurements, where the lower line corresponds to $H_{c}^{↓}$ and the upper line $H_{c}^{↑}$ . We identify the tricritical point, $T_{crit}$ , as the temperature at which $Δ H$ and the latent heat reach zero, below which phase coexistence occurs (gray shaded area).Reuse & Permissions
Figure 3
(Color online) Hall-probe imaging of ${CoMnSi}_{0.92} {Ge}_{0.08}$ across the field-driven magnetic transition: (a) first-order transition at 230 K, (b) second-order transition at 296 K. Left: The $M − H$ loops constructed from a single pixel (-○-) of a series of images are shown at these temperatures alongside bulk measurements (−). Right: Equivalent up-field and down-field images are shown to highlight reversibility of this sample. Each image is 1 mm across. The color scale is set to black at 10% of saturation (AFM state), and white (yellow online) at 90% saturation (FM state). Dark areas in the magnetically saturated images indicate the presence of cracks in the sample surface or the sample edge (top left corner), which were used as location markers.Reuse & Permissions
Figure 4
(Color online) Relationship between hysteresis and entropy change. Main figure: Hysteresis associated with a single latent heat spike (identified in upper inset by the arrows; $Δ H = H^{↑} − H^{↓}$ ) plotted as a function of latent heat, $Δ Q$ . Upper inset: Example of how the transition “breaks up” into multiple latent heat spikes at high temperatures. Note that $Δ S_{LH}$ is determined as the sum of these spikes. Lower inset: Hysteresis, $Δ H$ , of bulk (◼) and fragment (△) plotted as a function of total entropy change calculated using the Maxwell relation (see methods section for details). The lines are guides for the eye and the error scale has been indicated on one of the points. In this case we have estimated $Δ H$ using the average over multiple latent heat spikes that appear as the temperature is increased.Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Capturing first- and second-order behavior in magnetocaloric ${CoMnSi}_{0.92} {Ge}_{0.08}$

K. Morrison, J. D. Moore, K. G. Sandeman, A. D. Caplin, and L. F. Cohen

Phys. Rev. B 79, 134408 – Published 6 April 2009

Abstract

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Physical Review B

covering condensed matter and materials physics

Capturing first- and second-order behavior in magnetocaloric CoMnSi0.92Ge0.08

K. Morrison, J. D. Moore, K. G. Sandeman, A. D. Caplin, and L. F. Cohen

Phys. Rev. B 79, 134408 – Published 6 April 2009

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Capturing first- and second-order behavior in magnetocaloric ${CoMnSi}_{0.92} {Ge}_{0.08}$