Dynamic susceptibility study on the skyrmion phase

JOURNAL OF APPLIED PHYSICS 117, 123903 (2015)

Dynamic susceptibility study on the skyrmion phase stability of Fe0.7Co0.3Si T. Y. Ou-Yang,1,2 G. J. Shu,1 C. D. Hu,1,a) and F. C. Chou2,3,4,a) 1

Department of Physics, National Taiwan University, Taipei 10617, Taiwan Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan 3 National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan 4 Taiwan Consortium of Emergent Crystalline Materials, Ministry of Science and Technology, Taipei 10622, Taiwan 2

(Received 6 January 2015; accepted 11 March 2015; published online 23 March 2015) The AC susceptibilities of Fe1xCoxSi (0.1 x 0.7) alloys were measured and compared with that of MnSi. The range of skyrmion phase in the H-T phase space was enlarged and moved to higher temperatures when approximately 1/3 of the Fe was substituted with Co. Comparing with MnSi, the skyrmion phase of Fe0.7Co0.3Si was found thermodynamically more stable under a much lower and narrower critical field near 280 6 50 Oe. The stability range in the H-T phase space and the free energy reduction DE (as a function of the applied magnetic field) for both the Fe0.7Co0.3Si C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4915934] and MnSi were compared. V

I. INTRODUCTION

The skyrmion is a topologically stable, particle-like spin structure with a screw-like nanoscale spin configuration. Such spin texture has been detected by Lorentz transmission electron microscopy1 and neutron diffraction.2 The handedness of the chiral spin ordering induced by the Dzyaloshinskii-Moriya (DM) interaction for MnSi has attracted tremendous interest in the field of condensed matter physics.2–4 Additionally, the novel types of magnetic nano-structures under the controlled motion of magnetic domain walls have opened a new era for logic devices and information storage.5,6 In conventional information storage devices, magnetic domain walls are electrically controlled by spin transfer torques to read and write magnetic signals. For a more efficient operation of the devices, the key issue lies in reducing the driving current. Skyrmions are recommended as possible candidates for spin-based electronics, which can be manipulated by spin transfer torque with ultralow spin-polarized current density 106 A/m2.3 The skyrmion lattice has defects that often act as pinning centers that obstruct the current-driven motion of magnetic domain walls. However, the Magnus force and the flexible shape-deformation of individual skyrmions could be used to avoid pinning effects on the translational and rotational motions of the skyrmion lattice domain.5 Moreover, in the domain wall-based racetrack memory, the space between the bits of the domain walls and the magnetic domains for information storage is limited to 30–40 nm. Fert et al. proposed that the spacing between bits can be reduced to the magnitude of the skyrmion particle diameter (approximately 16 nm),6 which would enable faster information flow by condensing the storage density. However, the stability of the skyrmion state would need to be improved and its range of existence in the H-T phase space would need to be increased if the skyrmion is to be considered for practical use in spintronics. Fe1xCoxSi and MnSi compounds have the same cubic B20-type crystal structure of space group P213.7,8 The nona)

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centrosymmetric nature of the B20 symmetry renders the DM spin-orbital interaction nontrivial. The competing ferromagnetic (FM) coupling and the DM interaction lead to a ground state of long range helical spin ordering.9 The propagating directions of the spiral spins are along h100i for Fe1xCoxSi and h111i for MnSi and have been confirmed by small angle neutron scattering studies2,10 and Lorentz force microscopy.11,12 The multi-Q vectors of the helix in the skyrmion phase would be stabilized by thermal fluctuations under the applied magnetic fields. Notably, among the Fe1xCoxSi alloys, Fe0.7Co0.3Si possesses the highest Tc of helical ordering, in addition to the largest spin gap size and DM energy.10 In present study, we explored the physical properties of single crystal sample of Fe0.7Co0.3Si using AC susceptibility measurement and compared the stability range of the skyrmion in the H-T phase space with that of MnSi. II. EXPERIMENT

Fe1xCoxSi (x ¼ 0.7 0.1) and MnSi single crystal samples used in the present work were grown by the modified Bridgman method with an optical floating-zone furnace. The initial polycrystalline samples were prepared from pure (4N) elements of iron, cobalt, manganese, and (5N) silicon powder at the designated ratios. Precursor feed rods were synthesized in an arc melting furnace in an argon atmosphere. The ingots were crushed and re-loaded into a quartz tube. The cone-shaped bottom-sealed quartz tube was suspended and used as the feed rod in an optical floating zone furnace, and single crystals were grown using a modified Bridgman method, i.e., nucleation and solidification were performed by passing the feed rod through the hot zone of a sharp thermal gradient provided by the optical floating zone furnace. Feed rods of different Co (with x ¼ 0.7, 0.5, 0.3, and 0.1) were grown under 1 atm argon gas. Similar crystal growth condition for MnSi has been summarized in Ref. 23. The as-grown crystals had a typical size of approximately 8 8 7 mm3, and the chemical compositions of the grown crystals were analyzed using electron probe microanalysis

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C 2015 AIP Publishing LLC V

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(EPMA). The crystal quality was confirmed by synchrotron X-ray power diffraction (NSRRC, Taiwan) and Laue backreflection methods; no impurities were detected. The AC susceptibility and DC magnetization measurements were conducted with a magnetic property measurement system (MPMS, Quantum Design). The AC field used in the AC susceptibility measurement was 3 Oe at 30 Hz. III. RESULTS AND DISCUSSION

J. Appl. Phys. 117, 123903 (2015) TABLE I. Curie-Weiss law (vðTÞ ¼ v þ C=ðT HÞ) fitting results for Fe1xCoxSi between 2 Tc and 400 K.

Co content Tc x (K) 0.7 0.5 0.3 0.1

7.07 38.06 46.07 15.07

Fitting range v0 C (K) (104 cm3/mol) (cm3 K/mol) 25–400 80–400 100–400 35–400

2.69(1) 6.47(1) 3.79(3) 12.30(1)

0.1475(3) 0.2648(1) 0.2827(8) 0.0973(7)

H (K)

leff (lB /f.u.)

12.6(3) 54.4(2) 49.7(9) 25.0(9)

1.0863(3) 1.4554(1) 1.5041(8) 0.8824(7)

A. Magnetic phase transitions: M(H) and vac ðT ; HÞ

The AC susceptibilities as a function of temperature for various Co substitutions are shown in Fig. 1. The cusps shown in v0ðTÞ indicate the onsets of a helical spin ordering. To determine a precise transition temperature Tc for the helical spin ordering, we used the peak value of the first derivative of v0 (i.e., dv0 =dT) to define Tc of the phase transition of a long range helical spin ordering, i.e., at the sharpest drop of v0ðTÞ on cooling.13 Fe0.7Co0.3Si showed the highest Tc among the Fe1xCoxSi series. To confirm the quality of our crystal samples, the Co substitution level, and sample homogeneity, we found that the measured Tc ðxÞ were consistent with those reported in the literature, as compared in the inset of Fig. 1.7,10,14–17 Paramagnetic behavior was observed above the Tc and can be fitted with a Curie-Weiss law and the fitted parameters are summarized in Table I, where positive H values indicate the existence of FM coupling among localized spins. Both Tc and Curie constant peak at x 0.3, which implies that Co substitution introduces more localized spins on approaching x 0.3 but the itinerant electron density outgrows the localized spins above x 0.3. Current results of Curie-Weiss analysis on the localized spins agree with the evolution of transport properties of Fe1xCoxSi in transition from the semiconducting FeSi to the metallic CoSi qualitatively.17 In the cubic B20-type compounds of Fe1xCoxSi and MnSi, the long range helical spin ordering is the ground state

FIG. 1. The AC susceptibilities of Fe1xCoxSi. Inset shows Co concentration dependence of Tc for Fe1xCoxSi series compared with those reported in Refs. 7, 10, and 14–17.

for the competition between the FM exchange and DM interactions.9,18,19 The anisotropic exchange interaction has been shown to pin the propagating direction of the spin spiral.9 The wave vector of the helical ordering was strongly pinned along the h111i direction for MnSi.2,12 On the other hand, the wave vector of the helix had a weaker tendency to propagate along the h100i axis for Fe1xCoxSi. With an increasing Co concentration, this weak tendency was suppressed by the Fe/Co site disordering and broke the local symmetry of Fe(Co)Si4 tetrahedron. For Fe0.7Co0.3Si without the perturbation of DM interaction, FM ordering is expected below 50 K based on the fitted Weiss temperature of H 49.7 K (Table I). Since DM interaction has been shown to be closely correlated with the transition temperature Tc of the helical ordering,10 the existence of DM interaction at the 0.24 meV

FIG. 2. Real part of AC susceptibilities (v0 ) for (a) Fe0.7Co0.3Si at various magnetic fields, and (b) dM/dH at various temperatures near Tc. The definitions of TA1 =TA2 from v0ðTÞ and HA1 =HA2 from dM/dH can be used to show A-phase boundaries in the H-T phase space, as described in Refs. 2 and 23.


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level7 could be used to reasonably explain the occurrence of helical spin ordering at Tc 46.07 K as a result of combined FM and DM interactions. Fig. 2(a) shows the temperature dependence of v0 for Fe0.7Co0.3Si at various fields. Fig. 2(b) displays the corresponding field-dependent dM/dH at temperatures in the vicinity of Tc. Following the definitions of critical temperature and field provided by Bauer et al. for MnSi and the measurement results of v0 ðT; HÞ and dMðH; TÞ=dH, we can extract the critical temperatures, TA1 and TA2 , and the critical fields, HA1 and HA2 , to define the transitions across the skyrmion state (Aphase) of Fe0.7Co0.3Si similarly.20 For example, the two consecutive peaks of v0 ðTÞ shown in Fig. 2(a) are used to define TA1 ðHÞ and TA2 ðHÞ for the crossovers from the Single Domain Cone (SDC) state to the skyrmion state and the PM state to the skyrmion state upon raising temperature, respectively.21,22 There are four peaks can be extracted from the dM/dH plot using the isotherms M(T, H) near Tc, as shown in Fig. 2(b). The highest critical field of the dM/dH represents the HC2 for SDC-PM transition, and the lowest HC1 represents the ROS-SDC state transition. The middle two peaks represent the critical fields HA1 ðTÞ and HA2 ðTÞ that define the crossovers from SDC to skyrmion states and from skyrmion to SDC states upon field increase, respectively. Given the definitions of the critical temperatures and fields as shown in Fig. 2, we can map out the H-T magnetic phase diagram for Fe0.7Co0.3Si and compare with the published H-T phase diagram for MnSi, as shown in Fig. 3. B. Magnetic phase diagram

We can categorize six magnetic phases for MnSi and five for Fe0.7Co0.3Si. The A-phase in Figs. 3(a) and 3(b) correspond to the skyrmion state.2 Here, IM (Fig. 3(a)) represents the intermediate spin fluctuation-disordered state; FM represents the saturated ferromagnetic state from the canting moment of the helically ordered spins; PM represents the paramagnetic state, where the localized spins under the applied field are randomized due to thermal fluctuations; ROS (Fig. 3(b)) represents the randomly oriented spiral state due to the weak pinning effect of the helix; and SDC represents a single domain cone.10 The local strain and electron doping introduced by Co substitution may cast complex pinning effects on the skyrmion state comparing to that of MnSi with insignificant amount of impurities. The A-phase of Fe0.7Co0.3Si is clearly stabilized at a much lower field and a higher temperature range than those of MnSi, which implies that the A-phase of Fe0.7Co0.3Si is more controllable than that of MnSi and a better candidate for spintronics applications. C. Stability of skyrmion state

For a more detailed study of Fe0.7Co0.3Si, we analyzed the AC susceptibility data under various external magnetic fields, as shown in Figs. 4(a) and 4(b). The area under the v00 ðT; HÞ peak was shown to correspond to the entropy change for phase transitions between A-phase and its neighboring state within H-T phase space. The crossover of the opposite field dependency of v00 occurred at approximately 270–290 Oe, i.e.,

FIG. 3. Magnetic phase diagrams of (a) MnSi adapted from Refs. 2 and 23, and (b) Fe0.7Co0.3Si in this study. The phases of Random Oriented Spiral (ROS) and Single Domain Cone (SDC) in (b) are defined in Ref. 8. The phase boundaries are defined using TA1 ; TA2 ; HA1 ; HA2 ; HC1 , and HC2 described in Fig. 2.

v00 increased with the field for H ⲏ 290 Oe, but decreased with the field for H ⱗ 270 Oe, which implied that spin entropy increased for phase transition from the A-phase to the neighboring SDC phase, i.e., the phase transition from A-phase to SDC phase is always endothermic thermodynamically, as indicated in the inset of Figs. 4(a) and 4(b). These observations confirm the hypothesis that the A-phase is a new ground state via additional symmetry breaking in the spin space beyond the original SDC state of Fe0.7Co0.3Si, similar to that of the Aphase as a ground state sitting within the conical state of MnSi within H-T phase space (see Fig. 3). Interestingly, there was almost no change in v00 for the transitions under the critical fields near 270–290 Oe, which strongly suggested the existence of multiple degenerate spin configurations within the HT space under quantum fluctuation. Cimpoesu et al.24 showed that the reduction in the free energy DE ð/ DGÞ can be evaluated from the imaginary part 2 00 vT ðHÞ, where of the ACÐ susceptibility with DEðHÞ ¼ pl0 Hac 00 TA2 00 vT ðHÞ ¼ TA1 v ðT; HÞdT=ðTA2 TA1 Þ can be determined from the experimental results of v00 ðT; HÞ, as shown in Fig. 4. The DE for both MnSi and Fe0.7Co0.3Si are plotted as functions of H in Fig. 4(c), where detailed analysis for MnSi is shown in Ref. 23. Our experimental results were qualitatively consistent with the thermal fluctuation model, as evidenced


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FIG. 4. The real (v0 ) and imaginary (v00 ) parts of AC susceptibility for Fe0.7Co0.3Si at fields (a) below and (b) above a critical field near 280 Oe. (c) The free energy reduction DE for the A-phase of Fe0.7Co0.3Si and MnSi are compared, DE of MnSi is scaled up ten times for clarity.

by the local minima that occurred near H ’ 270–290 Oe for Fe0.7Co0.3Si and ’ 1600–1700 Oe for MnSi. Although the skyrmion state of Fe0.7Co0.3Si survived at relatively higher temperatures and more stable in the H-T phase space than that of MnSi, its critical field range was relatively narrower.

ACKNOWLEDGMENTS

F.C.C. acknowledges the support provided by the Ministry of Science and Technology in Taiwan under Project No. MOST-102-2119-M-002-004. 1

IV. CONCLUSIONS

In summary, we conducted a thorough magnetization and AC susceptibility study for Fe0.7Co0.3Si to verify the stability of the skyrmion state in the H-T phase space. Fe0.7Co0.3Si crystals displayed a larger area of stable skyrmion state than that of MnSi crystals within the H-T phase space. The higher transition temperatures plus the lower and narrower critical magnetic fields for the Fe0.7Co0.3Si crystal make it a potential candidate for using the skyrmion phase in applications as a novel spintronic device.

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