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Deciphering structural and magnetic disorder in the chiral skyrmion host materials CoxZnyMnz (x+y+z=20)

Joshua D. Bocarsly, Colin Heikes, Craig M. Brown, Stephen D. Wilson, and Ram Seshadri
Phys. Rev. Materials 3, 014402 – Published 9 January 2019
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  • INTRODUCTION
  • METHODS
  • RESULTS AND DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    CoxZnyMnz (x+y+z=20) compounds crystallizing in the chiral β-Mn crystal structure are known to host skyrmion spin textures even at elevated temperatures. As in other chiral cubic skyrmion hosts, skyrmion lattices in these materials are found at equilibrium in a small pocket just below the magnetic Curie temperature. Remarkably, CoxZnyMnz compounds have also been found to host metastable nonequlibrium skyrmion lattices in a broad temperature and field range, including down to zero field and low temperature. This behavior is believed to be related to disorder present in the materials. Here, we use neutron and synchrotron diffraction, density functional theory calculations, and dc and ac magnetic measurements to characterize the atomic and magnetic disorder in these materials. We demonstrate that Co has a strong site preference for the diamondoid 8c site in the crystal structure, while Mn tends to share the geometrically frustrated 12d site with Zn, due to its ability to develop a large local moment on that site. This magnetism-driven site specificity leads to distinct magnetic behavior for the Co-rich 8c sublattice and the Mn on the 12d sublattice. The Co-rich sublattice orders at high temperatures (compositionally tunable between 210 and 470 K) with a moment around 1μB/atom and maintains this order to low temperature. The Mn-rich sublattice holds larger moments (about 3μB) which remain fluctuating below the Co moment ordering temperature. At lower temperature, the fluctuating Mn moments freeze into a reentrant disordered cluster-glass state with no net moment, while the Co moments maintain order. This two-sublattice behavior allows for the observed coexistence of strong magnetic disorder and ordered magnetic states such as helimagnetism and skyrmion lattices.

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    • Received 15 October 2018

    DOI:https://doi.org/10.1103/PhysRevMaterials.3.014402

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Frustrated magnetismGlass transitionMagnetic phase transitionsMagnetismSkyrmions
    1. Techniques
    Density functional theoryMagnetization measurementsNeutron diffractionX-ray powder diffraction
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Joshua D. Bocarsly1,*, Colin Heikes2, Craig M. Brown2, Stephen D. Wilson1, and Ram Seshadri1

    • 1Materials Department and Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
    • 2Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA

    • *jdbocarsly@mrl.ucsb.edu

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    Vol. 3, Iss. 1 — January 2019

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    • Figure 1
      Figure 1

      The β-Mn crystal structure, comprising 8c and 12d atomic sites, is displayed in its two chiral enantiomers P4132 (a) and P4332 (b). The two structures differ only in handedness, and therefore should have the same formation energy, with individual crystallites of a sample forming in one or the other configuration. The origin of each cell has been translated by 1/4 of a unit cell from the standard setting such that the chiral fourfold screw axis (41 or 43) is centered in the cube face. The connecting lines indicate 12d−12d contacts of length ≈2.7Å, showing how the 12d sublattice is constructed of equilateral triangles arranged in a helix. The 8c sublattice, on the other hand, can be viewed as a distorted diamond lattice.

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    • Figure 2
      Figure 2

      Synchrotron and paramagnetic neutron diffraction patterns for (a) Co10Zn10, (b) Co8Zn9Mn3, and (c) Co7Zn7Mn6. For Co10Zn10 (a), the synchrotron diffraction pattern is shown along with Rietveld fit to the P4132β-Mn structure (i). A 0.25 wt.% ZnO secondary phase is observed, which can be seen in an expanded view (ii). Refined structures are shown both with partial occupancies indicated by the atom coloring (iii) and anisotropic atomic displacement parameters displayed as 90% probability ellipsoids (iv). For Co8Zn9Mn3 (b) and Co7Zn7Mn6 (c), combined synchrotron (i) and neutron (ii) Rietveld refinements above the magnetic Curie temperatures are shown. The Co8Zn9Mn3 shows only the β-Mn phase, while the Co7Zn7Mn6 sample shows a 3.12(3) wt.% MnO secondary phase, which, due to structure factor differences between x-ray and neutron diffraction, appears much stronger in the neutron pattern. The refined structural details are described in Tables 1 and 2.

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    • Figure 3
      Figure 3

      Magnetization data for CoxZnyMnz samples. The top row shows susceptibility M/H as a function of temperature under an applied field H=20mT, showing both zero-field-cooled (ZFC, dashed dashed lines) and field-cooled (FC, solid lines) measurements. For Co8Zn9Mn3 (d) and Co7Zn7Mn6 (e), measurements taken at H=200mT, are also shown. For all samples except Co10Zn10, the high-temperature magnetization, taken under an applied field H=1T is shown as inverse susceptibility (χ−1, dotted lines), demonstrating Curie-Weiss behavior at high temperature. The bottom row shows magnetization M as a function of applied field H at various temperatures for each material. For each temperature, a full five-branch hysteresis loop is shown, although no significant magnetic hysteresis is observed in any loop except for at 2 K in Co7Zn7Mn6. The unit emumol−1Oe−1 is equal to 4π×10−6m3.

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    • Figure 4
      Figure 4

      ac magnetic susceptibility measurements of Co7Zn7Mn6. (a) Shows the real (in-phase, χ′) part of the ac susceptibility, while (b) shows the imaginary (out-of-phase, χ′′) part. At high temperatures, the ac susceptibility resembles the dc susceptibility shown in Fig. 3. However, at low temperatures, χ′ drops and there is a peak in χ′′ indicating glassy dynamics of the spins. The right side of the figure shows the dependence of this feature on the frequency of the applied ac field. The locations of the peak in χ′′ increase by about 4.5 K as the excitation field frequency is increased from 1 to 997 Hz. The measurements were collected while warming, after cooling under a dc field H=20mT. The unit emumol−1Oe−1 is equal to 4π×10−6m3.

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    • Figure 5
      Figure 5

      Magnetic properties of CoxZnyMnz alloys derived from the data in Fig. 3. (a) and (b) Shows properties as a function of the amount of Mn relative to Co in the sample. (a) With increasing Mn, the Curie temperature drops from 470 K (Co10Zn10) to 210 K (Co7Zn7Mn6). (b) Upon addition of Mn into Co10Zn10, the average saturated moment on the magnetic ions (Mn and Co) initially increases until Mn makes up about 20% of the magnetic ions in the structure. Adding additional Mn results in a decrease in the average moment. The average moments are obtained from the magnetization at T=2K and H=5T. For (a) and (b), the data points correspond to, in order from left to right, Co10Zn10, Co9Zn9Mn2, Co8Zn10Mn2, Co8Zn9Mn3, and Co7Zn7Mn6. (c) Shows a comparative view of the high-field portions of the 2-K M(H) loops that are shown in Fig. 3. For each sample, the magnetization at 2 K is expressed in units of μB per magnetic ion and the magnetization at H=1T is subtracted in order to highlight the size of the moment change experienced by the material at high field. For Co10Zn10, only a small moment change is seen, indicating that the moments in Co10Zn10 are (very nearly) completely polarized by a 1-T field. For Co7Zn7Mn6, on the other hand, the moment rises by about 0.08μB per magnetic ion (around 14%) between 1 and 5 T, indicating that the material still contains unpolarized spins at 1 T. Samples with smaller amounts of Mn fall in-between Co10Zn10 and Co7Zn7Mn6.

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    • Figure 6
      Figure 6

      Magnetic neutron Rietveld refinements for the Co8Zn9Mn3 sample at 100 and 14 K. (a) Shows how a magnetic contribution to the pattern grows in below the magnetic ordering temperature. Tick marks underneath the 350-K pattern indicate allowed nuclear peaks for the β-Mn structure; no magnetic intensity is seen at forbidden peak positions, however, some magnetic peaks occur at allowed structural peak positions which have nearly zero intensity in the paramagnetic pattern. (b), (c) Show a close view of the temperature evolution of the largest structural peaks, the (221) and (310). In both cases, the peak is seen to have a larger intensity at 100 K than 14 K, driven by the larger magnetic contribution (orange) at 100 K than 14 K.

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    • Figure 7
      Figure 7

      Magnetic neutron Rietveld refinements for the Co7Zn7Mn6 sample at 100 and 14 K. Below the observed magnetic ordering temperature (210 K), a small magnetic contribution is found to grow in to the β-Mn structure. The paramagnetic to antiferromagnetic transition of MnO at 118 K is also seen. This transition is accompanied by a rhombohedral structural distortion, which, along with the magnetic ordering, changes the space group from Fm3¯m to the monoclinic group Cc2/c′ [40].

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    • Figure 8
      Figure 8

      Magnetocaloric evaluation of CoxZnyMnz. ΔSM(T,H), the entropy change of the material upon isothermal magnetization to magnetic field H, is calculated from magnetization data using Eq. (2). Larger |ΔSM| values indicate a larger magnetocaloric effect. (a) ΔSM as a function of temperature for several applied field values for three CoxZnyMnz compositions. The largest effect is seen at the Curie temperature for each material. (b) Peak values of ΔSM as a function of applied field for five CoxZnyMnz compositions. (c) Peak ΔSM for different CoxZnyMnz compositions as a function of magnetic saturation of the composition. There is a clear relationship between magnetocaloric effect and magnetic moment in these samples.

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    • Figure 9
      Figure 9

      (a) Temperature dependence of the power-law exponent n of the magnetocaloric effect [ΔSM(H)∝Hn]. This exponent is obtained from linear fits of log-log plots of ΔSM vs field for applied fields between 500 mT and 5 T, as shown for the critical temperatures in (b). For all samples, the power-law exponents are found to show a standard shape, characteristic of a continuous magnetic transition. The minimum n in each curve is the critical exponent nc, which occurs at the critical temperature Tc. The dashed line shows the expected critical exponent for the mean field model nc=23. As Mn content increases, nc increases relative to the mean field model value, suggesting increasingly disordered magnetic interactions.

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    • Figure 10
      Figure 10

      Magnetoentropic analysis of the low-field behavior of Co8Zn9Mn3. (a) Representative M vs T data under three different applied fields. The slope of many such curves ∂M/∂T=∂S/∂H is shown as a heat map in (b), with color bar chosen symmetrically about zero to highlight the areas of conventional (negative, blue) and inverse (positive, red) magnetocaloric effect. (c) Heat map of the isothermal entropy change upon application of a given magnetic field at a given temperature ΔSM(T,H), which is obtained by integrating (b) in the field direction [Eq. (2)]. This analysis reveals three clear areas: (i) A blue region at high temperature and field representing the region in which the sample is behaving as a conventional field-polarized ferromagnet or paramagnet. In this regime, application of a magnetic field suppresses fluctuations and decreases entropy. (ii) A white region at low temperatures and fields, where the system shows a long-period helimagnetic or partially polarized conical magnetic phase. In this region, application of a magnetic field causes the planes of spins in the conical structure to progressively cant in the direction of the field, but has little effect on the entropy of the system. (iii) A red pocket just below the Curie temperature. This corresponds to the phase region where a hexagonal skyrmion lattice has been observed in this class of materials and other cubic skyrmion hosts. The increased entropy in this region is due to increased entropy in the skyrmion lattice relative to the helical or conical phases. However, due to the disorder in the sample, it is difficult to resolve this feature into clear phase boundaries, and differentiate it from a Brazovskii transition.

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