Observation of inverse magnetocaloric effect in magnetic-field-induced austenite phase of Heusler alloys ${\mathrm{Ni}}_{50-x}{\mathrm{Co}}_x{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ $(x=9 \mathrm{and} 9.7)$

The magnetocaloric effect (MCE), magnetization, specific heat, and magnetostriction measurements were performed in both pulsed and steady high magnetic fields to investigate the magnetocaloric properties of Heusler alloys ${\mathrm{Ni}}_{50-x}{\mathrm{Co}}_x{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ $(x=9 \mathrm{and} 9.7)$. From direct MCE measurements for ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ up to 56 T, a steep temperature drop was observed for magnetic-field-induced martensitic transformation (MFIMT), designated as inverse MCE. Remarkably, this inverse MCE is apparent not only with MFIMT, but also in the magnetic-field-induced austenite phase. Specific heat measurements under steady high magnetic fields revealed that the magnetic field variation of the electronic entropy plays a dominant role in the unconventional magnetocaloric properties of these materials. First-principles based calculations performed for ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ and ${\mathrm{Ni}}_{45}{\mathrm{Co}}_5{\mathrm{Mn}}_{36.7}{\mathrm{In}}_{13.3}$ revealed that the magnetic-field-induced austenite phase of ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ is more unstable than that of ${\mathrm{Ni}}_{45}{\mathrm{Co}}_5{\mathrm{Mn}}_{36.7}{\mathrm{In}}_{13.3}$ and that it is sensitive to slight tetragonal distortion. We conclude that the inverse MCE in the magnetic-field-induced austenite phase is realized by marked change in the electronic entropy through tetragonal distortion induced by the externally applied magnetic field.

Figure 1

(a) M-T curves of ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ measured at various magnetic fields. (b) Temperature differential of the M-T curve at 0.5 T. (c) Temperature dependence of magnetic susceptibility for ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ measured at 0.1 T and its temperature differential.

Figure 2

(a) Magnetic phase diagram of ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ determined by magnetization and MCE measurements. (b) Temperature dependence of the total entropy change for ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ and for ${\mathrm{Ni}}_{45}{\mathrm{Co}}_5{\mathrm{Mn}}_{36.7}{\mathrm{In}}_{13.3}$ [23] estimated, respectively, from the magnetic phase diagrams and from the $\mathrm{\Delta }{T}_{\mathrm{MT}}$ presented in Fig. 3.

Figure 3

(a) Adiabatic temperature changes of ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ polycrystalline sample as functions of the applied magnetic field. The magnetic field profiles are shown in the inset. Also, (b) and (c) present enlarged views of the representative temperatures, in which the $T_{\mathrm{ini}}$ is subtracted from each datum. The gray dotted curve shows a result of ${\mathrm{Ni}}_{45}{\mathrm{Co}}_5{\mathrm{Mn}}_{36.7}{\mathrm{In}}_{13.3}$ measured at $T_{\mathrm{ini}}=280\mathrm{K}$ [23].

Figure 4

Specific heat of ${\mathrm{Ni}}_{40.3}{\mathrm{Co}}_{9.7}{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ shown as $C/T$ vs $T^2$. Data measured at 5, 10, and 16 T were taken after field cooling at 17.5 T (i.e., the sample is in A phase). The inset presents results obtained at around $T_{\mathrm{M}\to \mathrm{A}}$ for ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ (Co9) and ${\mathrm{Ni}}_{40.3}{\mathrm{Co}}_{9.7}{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ (Co9.7) taken using a DSC shown as C vs T.

Figure 5

Magnetostrictions of ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ polycrystalline sample measured along the applied magnetic field (${\mu }_{0}H\left|\right|\mathrm{\Delta }L$).

Figure 6

Total energy shown as a function of the ratio of the tetragonality ($c/a$) for (a) ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{32}{\mathrm{Ga}}_{18}$ and for (b) ${\mathrm{Ni}}_{45}{\mathrm{Co}}_5{\mathrm{Mn}}_{37}{\mathrm{In}}_{13}$. FM, FIM, and AFM, respectively, denote the ferromagnetic, ferrimagnetic, and antiferromagnetic. The origin of the energy scale is set to the energy at $c/a=1$ for FM. The inset of (a) portrays the crystal structure of cubic ($L{2}_1$) A phase in the Heusler alloy ($X_1{X}_2)YZ$ ($X_1$, blue; $X_2$, green; Y, red; Z, brown).

Figure 7

Density of states calculated for ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ [(a)–(e)] and for ${\mathrm{Ni}}_{45}{\mathrm{Co}}_5{\mathrm{Mn}}_{36.7}{\mathrm{In}}_{13.3}$ [(f)-(j)]. Solid and dotted curves represents, respectively, cubic (ferromagnetic, FM) and tetragonal (ferrimagnetic, FIM) phases. Gray solid and brown dotted curves are the DOSs of ${\mathrm{Ni}}_2$ and ${\mathrm{Mn}}_2$.

Figure 8

$c/a$ dependence of the DOS for ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ [(a) and (b)] and for ${\mathrm{Ni}}_{45}{\mathrm{Co}}_5{\mathrm{Mn}}_{36.7}{\mathrm{In}}_{13.3}$ [(c) and (d)]. Also, (b) and (d) present the enlarged views of the minority spin band at around the Fermi level.

Figure 9

$c/a$ dependence of the change in DOS $\left[\mathrm{\Delta }{D}_{\mathrm{FE}}=D_{\mathrm{FE}}\left(1.00\right)-D_{\mathrm{FE}}\left(c/a\right)\right]$ for ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$.

Figure 10

M-H curve of ${\mathrm{Ni}}_{41}{\mathrm{Co}}_9{\mathrm{Mn}}_{31.5}{\mathrm{Ga}}_{18.5}$ measured at 4.2 K [38]. The insets are projection of the crystal structure along the $a$ axis, where the red and brown circles, respectively, denote ${\mathrm{Mn}}_1$ and ${\mathrm{Mn}}_2$ atoms.