Phase separation and superparamagnetism in the martensitic phase of $\mathrm{N}{\mathrm{i}}_{50\text{\ensuremath{-}}x}\mathrm{C}{\mathrm{o}}_{x}\mathrm{M}{\mathrm{n}}_{40}\mathrm{S}{\mathrm{n}}_{10}$

Phase separation and superparamagnetism in the martensitic phase of $N i_{50 − x} C o_{x} M n_{40} S n_{10}$

S. Yuan, P. L. Kuhns, A. P. Reyes, J. S. Brooks, M. J. R. Hoch, V. Srivastava, R. D. James, and C. Leighton

Phys. Rev. B 93, 094425 – Published 21 March 2016

Abstract

$N i_{50 − x} C o_{x} M n_{40} S n_{10}$ shape memory alloys in the approximate range $5 \leq x \leq 8$ display desirable properties for applications as well as intriguing magnetism. These off-stoichiometric Heusler alloys undergo a martensitic phase transformation at a temperature $T_{M}$ of 300–400 K, from ferromagnetic (FM) to nonferromagnetic, with unusually low thermal hysteresis and a large change in magnetization. The low temperature magnetic structures in the martensitic phase of such alloys, which are distinctly inhomogeneous, are of great interest but are not well understood. Our present use of spin echo nuclear magnetic resonance in the large hyperfine fields at ${}^{55}{Mn}$ sites provides compelling evidence that nanoscale magnetic phase separation into FM and antiferromagnetic (AFM) regions occurs below $T_{M}$ in alloys with $x$ in the range 0 to 7. At finite Co substitution, the FM regions are found to be of two distinct types, corresponding to high and low local concentrations of Co on Ni sites. Estimates of the size distributions of both the FM and AFM nanoregions have been made. At $x = 7$ , the AFM component is not long-range ordered, even below 4 K, and is quite different from the AFM component found at $x = 0$ ; by $x = 14$ , the FM phase is completely dominant. Of particular interest, we find for $x = 7$ that field cooling leads to dramatic changes in the AFM regions. These findings provide insight into the origins of magnetic phase separation and superparamagnetism in these complex alloys, particularly their intrinsic exchange bias, which is of considerable current interest.

Received 11 December 2015
Revised 25 February 2016

DOI:https://doi.org/10.1103/PhysRevB.93.094425

Physics Subject Headings (PhySH)

Ferromagnetism Martensitic phase transition Superparamagnetism

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S. Yuan¹, P. L. Kuhns¹, A. P. Reyes¹, J. S. Brooks^1,2,*, M. J. R. Hoch^1,†, V. Srivastava³, R. D. James³, and C. Leighton⁴

¹National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
²Department of Physics, Florida State University, Tallahassee, Florida 32310, USA
³Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455, USA
⁴Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA

^*Deceased
^†Corresponding author: hoch@magnet.fsu.edu

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Vol. 93, Iss. 9 — 1 March 2016

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Figure 1
Frequency $(f)$ scanned ${}^{55}{Mn}$ zero applied field NMR spectra in polycrystalline $N i_{50 – x} C o_{x} M n_{40} S n_{10}$ at 1.6 K for $x = 0$ , 7, and 14. Spectra associated with ferromagnetic regions (FM, red) and antiferromagnetic regions (AFM, blue) are indicated. The amplitude of the dominant AFM component has been reduced by a factor 10 in the $x = 7$ spectrum. Comparison of the spectra reveals that substitution of Co on Ni sites at $x = 7$ and 14 produces ferromagnetic regions or clusters with enhanced hyperfine fields and spectral features above 350 MHz, compared to $x = 0$ . The spectra can be well fit using multiple Gaussian curves. The spectral region below 350 MHz is designated L (low frequency) and the region above 350 MHz is designated H (high frequency), as discussed in the text.
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Figure 2
The ratio, $f / f_{0}$ , of the ${}^{55}{Mn}$ NMR resonance peak center frequency $(f)$ to the resonance frequency $(f_{0})$ at 1.6 K, as a function of $T$ , for the principal FM component in Region H (i.e., the highest frequency in Fig. 1) for $N i_{43} C o_{7} M n_{40} S n_{10}$ . The frequency decreases approximately linearly at temperatures in the range 3–70 K and then more rapidly at higher temperatures. The decrease in frequency is produced by averaging of the hyperfine field by collective cluster spin fluctuations in their anisotropy fields. The slope of the straight line fit through the points provides an estimate of the average cluster size, as discussed in the text. The small reproducible increase in $f / f_{0}$ at the lowest temperatures (<3 K), as shown in the inset, is attributed to the freezing of very small clusters and a possible change in the spectral lineshape.
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Figure 3
Curie-law-corrected ${}^{55}{Mn}$ NMR peak areas for the high frequency (region H in Fig. 1) ferromagnetic components (black circles) in $N i_{43} C o_{7} M n_{40} S n_{10}$ as a function of temperature. The fitted curve is based on a cluster dynamics model, with a distribution of cluster sizes, as described in the text. The inset shows the log-normal cluster radius distribution used in the fit; assuming spherical clusters, the most probable diameter is 4.4 nm. For comparison the Curie-law-corrected areas for the AFM component (region L in Fig. 1) are also shown (blue triangles). This AFM component cannot be detected at $T$ > 10 K.
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Figure 4
${}^{55}{Mn}$ spin-lattice relaxation times $T_{1}$ for (a) the principal FM spectral component in Region H and (c) the AFM components in Region L (see Fig. 1) as a function of temperature in $N i_{43} C o_{7} M n_{40} S n_{10}$ . Measurements were made in both zero field and in an applied field of 1 T. Comparison of the FM and AFM $T_{1}$ values shows that the AFM relaxation times are substantially shorter than those of the FM component and that they decrease more rapidly as $T$ increases. The field dependence seen in Fig. 4 is discussed in the text. (b), (d) Korringa plots of 1/ $T_{1}$ $T$ versus $T$ for the FM and AFM components, respectively. An estimate of the density of states at the Fermi level for the FM components is given in the text.
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Figure 5
(a) ${}^{55}{Mn}$ zero field spectra in the range 150–375 MHz, obtained in various RF fields, $H_{1}$ , optimized for the 240 MHz AFM component, following field cooling to 1.7 K in varied applied fields up to 6 T. (b) ${}^{55}{Mn}$ zero field spectra, obtained in a fixed low RF field optimized for the 435 MHz component, over the range 150–500 MHz, following field cooling to 1.7 K in fields up to 6 T. (c) Spin echo amplitude response curves at 275 MHz and 1.7 K, obtained in zero field as a function of $H_{1}$ , following field cooling in fields up to 6 T. The marked decrease in the optimal $H_{1}$ with increase in the $μ_{0} H$ used during field cooling is due to an unexpected large increase in the enhancement factor $η$ , as discussed in the text. (d) Plot of $η$ versus $μ_{0} H$ following field cooling to 1.7 K, as obtained from Fig. 5. The dramatic increase in $η$ is attributed to exchange bias linked interactions between the FM and AFM regions across their interfaces.
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Physical Review B

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Phase separation and superparamagnetism in the martensitic phase of $N i_{50 − x} C o_{x} M n_{40} S n_{10}$

S. Yuan, P. L. Kuhns, A. P. Reyes, J. S. Brooks, M. J. R. Hoch, V. Srivastava, R. D. James, and C. Leighton

Phys. Rev. B 93, 094425 – Published 21 March 2016

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Physical Review B

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Phase separation and superparamagnetism in the martensitic phase of Ni50−xCoxMn40Sn10

S. Yuan, P. L. Kuhns, A. P. Reyes, J. S. Brooks, M. J. R. Hoch, V. Srivastava, R. D. James, and C. Leighton

Phys. Rev. B 93, 094425 – Published 21 March 2016

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Phase separation and superparamagnetism in the martensitic phase of $N i_{50 − x} C o_{x} M n_{40} S n_{10}$