Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (2024)

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Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${Ni}_{2} MnSb$ polycrystalline Heusler alloy

Fanghua Tian, Qizhong Zhao, Jiale Guo, Yin Zhang, Minxia Fang, Tieyan Chang, Zhiyong Dai, Chao Zhou, Kaiyan Cao, and Sen Yang

Phys. Rev. B 109, 224405 – Published 4 June 2024

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Abstract

In this work, the phenomenon of downward deviations from the Curie-Weiss law is found above the Curie temperature (329–458 K) in ${Ni}_{2} MnSb$ polycrystalline Heusler alloy, and it was confirmed by the change in inverse magnetic susceptibility under different magnetic fields that it is the Griffiths phase. This abnormal phenomenon can be attributed to short-range nanoferromagnetic clusters caused by local lattice distortion within the paramagnetic state. The ac magnetic susceptibility further showed characteristics of long-range disordered and short-range ordered glassy magnetic states in Griffiths phase range, where the magnetization intensity of the spin glass state has a frequency dependence. This work revealed the nature of the Griffiths phase in Heusler alloys and observed the characteristics of spin glass at high temperatures, providing experimental evidence and support for the study of high-temperature spintronics.

$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (1)$
$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (2)$
$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (3)$
$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (4)$
$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (5)$
$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (6)$
$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (7)$

Received 23 November 2023
Accepted 23 May 2024

DOI:https://doi.org/10.1103/PhysRevB.109.224405

Physics Subject Headings (PhySH)

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Magnetic phase transitions

Authors & Affiliations

Fanghua Tian^1,*, Qizhong Zhao¹, Jiale Guo¹, Yin Zhang¹, Minxia Fang¹, Tieyan Chang², Zhiyong Dai¹, Chao Zhou¹, Kaiyan Cao¹, and Sen Yang^1,†

¹MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
²NSF's ChemMatCARS, The University of Chicago, Lemont, Illinois 60439, USA

^*Corresponding author: tfh2017@xjtu.edu.cn
^†Corresponding author: yangsen@xjtu.edu.cn

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Vol. 109, Iss. 22 — 1 June 2024

$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (8)$

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$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (9)$

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$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (12)$

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$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (13)$
Figure 1
(a) EDS analyzed the element ratio of alloy. The element ratio is calculated by the software that comes with the instrument according to the intensity ratio to standard samples. Inset: Backscattered electron testing of alloy. (b) EDS mapping for the SEM image [inset Fig.1]; the corresponding elemental mapping images of the Ni, Mn, and Sb, atoms, respectively. (c) The high-resolution XRD spectra of the ${Ni}_{2} MnSb$ alloy were measured at room temperature; the partial enlarged view is shown in the right of (c), and the $L 2_{1}$ structure is illustrated in the inset.
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$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (14)$
Figure 2
(a) Field-cooled warming magnetization of ${Ni}_{2} MnSb$ measured under different magnetic fields. Inset: (Top) Magnetization as a function of temperature for ${Ni}_{2} MnSb$ measured at a low magnetic field of 10 Oe under the ZFC and FC processes. (Bottom) dM/dT curves for ${Ni}_{2} MnSb$ measured at a low magnetic field of 10 Oe. (b) Temperature dependence of inverse susceptibility $χ^{- 1}$ under different fields for ${Ni}_{2} MnSb$ . (c) $\log_{10} χ^{- 1}$ vs ${log}_{10} (T / T_{C} - 1)$ plots for the ${Ni}_{2} MnSb$ alloy. Black lines are the fitting for data using Eq.(1).
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$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (15)$
Figure 3
(a) Isothermal magnetizations for the ${Ni}_{2} MnSb$ alloy at $T_{C} < T < T_{G}$ . (b) Arrott plot of isotherms at $T_{C} < T < T_{G}$ .
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$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (16)$
Figure 4
TEM characterizations of the ${Ni}_{2} MnSb$ alloy at 350 K. (a) SAED pattern, (b) HRTEM image, (c) the corresponding FFT pattern extracted from the square marked region, and the corresponding IFFT images obtained by circling fundamental reflections. (d) Two (200) spots and (e) two (022) spots marked in (c) to reveal the modulation waves. (f) IFFT image filtered using all four spots.
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$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (17)$
Figure 5
(a) The temperature dependence of magnetization (M-T) curves measured under 200 Oe with the sequences of ZFC and FC. (b),(c) Temperature dependence of the real part and imaginary part of an ac susceptibility measured at different frequencies under an ac field of 2 Oe. In the enlarged part in the insets of (b) and (c), the arrows indicate the direction of high frequencies. (d) Correlation between angular frequency and $T_{f}$ . The frequency ( $ω$ ) dispersion behavior of $T_{f}$ conforms to the Vogel-Fulcher relationship.
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$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (18)$
Figure 6
(a) The time dependence magnetization, M( $t$ ) with a 50-Oe dc magnetic field at 350, 360, and 370 K. The red solid lines exhibit the fit by stretched exponential relation. (b) The change of $τ_{dc}$ and $M_{0} / M_{r}$ with temperature.
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$Griffiths phase arising from local lattice distortion and spin glass above the Curie temperature in ${\mathrm{Ni}}_{2}\mathrm{MnSb}$ polycrystalline Heusler alloy (19)$
Figure 7
(a) The transition temperature of the magnetic state of ${Ni}_{2} MnSb$ dependent on temperature. (b) Simplified schematic diagrams of the evolution of the magnetic behavior from PM to nano-FM and SG then to FM, as a function of temperature. (I) FM, (II) SG and nano-FM, (III) nano-FM, and (IV) PM. PM is represented by black spots, spins are represented by arrows, and frustrated sites are represented by open circles. The yellow region is the Griffiths phase.
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