npsm 새물리 New Physics : Sae Mulli

pISSN 0374-4914 eISSN 2289-0041


Research Paper

New Phys.: Sae Mulli 2022; 72: 96-99

Published online February 28, 2022

Copyright © New Physics: Sae Mulli.

Out-of-plane Magnetic Anisotropy in Cleaved and Uncleaved CoS2

Mariam OMRAN1, Joonyoung CHOI1, Younjung JO1*, Mi Kyung KIM2,3, Changyoung KIM2,3

1Department of Physics, Kyungpook National University, Deague 41566, Korea
2Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Korea
3Department of Physics and Astronomy, Seoul National University (SNU), Seoul 08826, Korea


Received: January 3, 2022; Revised: January 14, 2022; Accepted: January 14, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Magnetic anisotropy is an important phenomenon driven by a strong electron correlation. It is defined as the magnetization tendency of magnetic material in a particular crystallographic direction. In this paper, we investigated the magnetic anisotropy of CoS2 single crystal. Here, torque magnetometry was used to determine the magnetocrystalline anisotropy of the crystal. The angle dependence of torque τ(θ) for CoS2 was measured at several temperatures above and below the ferromagnetic order transition Tc. To verify the effect of surface morphology on magnetic properties, we compared the τ(θ) of uncleaved and cleaved pure CoS2. Results show that two-fold symmetry was equally dominant in both. Furthermore, we compared higher orders of magnetic anisotropy to track the intrinsic and shape anisotropies. All amplitudes showed the same behavior for cleaved and uncleaved samples, but the higher orders were more dominatant in the cleaved sample.

Keywords: Torque magnetometry, Ferromagnet, Magnetic anisotropy

Magnetic anisotropy is an important phenomenon driven by a strong electron correlation. It is a factor that influences the magnetization tendency of materials, implying the dependency of magnetic properties on the direction of the applied field [1-4]. Magnetic anisotropy can be classified into crystal (magnetocrystalline), shape, and exchange anisotropies. Additionally, external factors such as annealing and irradiation can create anisotropy. Crystal anisotropy is a force that maintains the magnetization in a specific crystallographic direction, known as the easy direction of magnetization, and consequently regulates the magnetization strength. Applying the magnetic field in an easy direction of ferromagnet requires only a few tens of Oersteds to achieve saturation. However, when the field is applied in a hard axis direction, the domain movement structure changes and domain rotation occurs in the high field instead[5]. Anisotropic interactions heavily depend on the crystal morphology, symmetry, and content of the magnetic substance. Furthermore, robust magnetic anisotropy dependence on crystal cleavage has been reported[6].

CoS2 belongs to ferromagnetic materials with a cubic pyrite structure, with its ferromagnetic transition temperature Tc at 122 K. It is classified into the Pa3¯ space group, where the cations(Co) are enclosed by six anions (S), forming a trigonal distorted octahedron[7]. The d-electron level in the transition metal disulfides is split by the octahedral crystal field into eg and t2g orbitals. Due to the trigonal distortion, the t2g orbital splits further into ag and eg levels. Sulfur atoms have a robust covalent σ bond[8]. However, the cobalt-sulfur bond is ionic, primarily with a crucial covalent bond present. This covalent bond between Co eg and S 3p orbitals triggers the formation of the narrow band ferromagnet. Conversely, the antibonding S 3pσ* has the cobalt d feature represented by eg*, which is sufficiently narrow to facilitate magnetic ordering. The electrical and magnetic properties of the transition metal disulfides originate from the filling of the antibonding band eg*. Thus, CoS2 exhibits metallic ferromagnetism connected with the unpaired spin of the dϵ6dγ1 levels[9]. Therefore, CoS2 is a half-metallic ferromagnet with high spin polarization as the exchange splitting induces a decrease in the minority spins at the Fermi level[10-13]. Although CoS2 magnetic anisotropy has been investigated only once, it was concluded that it is responsive to sample shape [14].

In our study, we verified out-of-plane (OOP) magnetic anisotropy before and after the ferromagnetic transition of cleaved and uncleaved CoS2 single crystals. Furthermore, higher-order anisotropic contributions have been evaluated and compared for both cases. Results show that compared with the uncleaved sample, the cleavage sample showed a larger higher-order anisotropic constant and a significant contribution to the torque signal.

The crystal structure of CoS2 has a cubic structure with cut corners a cross-section, as shown in the inset of Fig. 4(b). The length of each side is approximately 1 mm. To verify the effect of surface morphology on magnetic properties, we compared the torque signal of uncleaved and cleaved CoS2. Cleaved CoS2 was prepared by parallelly cutting the crystal plane with a razor. The thickness is about 0.3 mm, and the shape of the shortened cross-section is shown in the inset of Fig. 2(b). Torque measurement for CoS2single crystal was performed using the membrane-type surface stress (MSS) device[15]. CoS2 was mounted on the MSS using vacuum grease by aligning the crystal direction. Moreover, the torque change was measured through the change in the resistance of the piezo material comprising a Wheatstone bridge circuit. This is a non-destructive and reliable technique for detecting spin alignment. Here, the magnetic field direction with respect to the crystal axis was controlled using a rotator. We measured the OOP torque while rotating the field through angle θ, with respect to the c-axis. The rotating angle θ is defined as the angle between the applied field and c-axis of the crystal (Fig. 1(a) (Inset)).

Figure 1. (Color online) Angle-dependent torque curves τ(θ) for cleaved CoS2 at different magnetic fields and temperatures above and below Tc = 122 K, (a) T = 10 K, (Inset) Sketch of out-of-plane rotation for torque measurements, the angle θ is the direction of the field with respect to the c-axis. (b) T = 50 K, (c) T = 100 K, and (d) T = 130 K.

Figure 2. (Color online) τ(θ) for uncleaved CoS2 at different magnetic fields and temperatures above and below Tc.

Figure 4. (Color online) (a) Normalized amplitude An(H)/A2(1 T) versus magnetic field at T = 10 K solid symbols for cleaved CoS2 and open symbols for uncleaved CoS2.

We performed the angle-dependent torque τ(θ) at diverse magnetic fields H and temperature T. Figure 1 shows the torque curvature for cleaved CoS2 after removing the background. Data consistency was confirmed with other cleaved samples and no change was observed. All data exhibited two-fold symmetry and torque values decreased as T increased. At low temperatures below Tc, the sawtooth-like curve occurred at approximately 0.05 - 0.2 T. Meanwhile, the saturation field of ferromagnetic CoS2 is approximately 0.2 T, and a sine wave appeared in a larger field. The sawtooth pattern at low fields steadily transforms into a sinusoidal pattern as H rises. By applying a high magnetic field, we overcome all magnetic correlations, to restore the sinusoidal pattern due to the contribution of the Zeeman energy. The maximum amplitude shifts with the field strength until it overlaps in a high field. Conversely, at T = 130 K above Tc, no signal was observed at very low fields and a very small signal was detected at higher fields.

Since CoS2 has a cubic crystal structure, the rotating plane on which θ changes includes two main principal crystal directions. Considering the symmetry of the crystal, odd coefficients corresponding to A3, A5...[16,17]. So, τ(θ) has a sin 2nθ angular dependence and can be fitted with higher coefficients only. Accordingly, τ(θ) was fitted using the following equation:


where A2, A4, and A6 are the coefficients of sin 2θ, sin 4θ, and sin 6θ, respectively.

In Fig. 2(a), the red lines indicate the fitted result of τ(θ) at 0.2 T, from Eq. (1). The fitted torque curves can be classified into three regions: low-, intermediate-, and high-field regions. The fitted curves fit perfectly only for the significantly low- and high-field regions, whereas, for the intermediate-field regions, a higher-order is required.

Based on the fitted curves, the amplitudes of the higher-order corrections were extracted. The An behavior pattern with H and T is displayed in Figs. 2(b) and (c), respectively. The all symmetry fold increases with the field up to 0.2 T, then it saturates or gradually reduces. The two-fold symmetry is more predominant than the four- and six-fold symmetries. The temperature dependence of the amplitude diminishes for all A2, A4, and A6 beyond Tc.

To validate the surface shape influence of the crystal on their characteristics[18], an uncleaved CoS2 single crystal was measured via the same procedure. τ(θ) was measured at the same fields (H) and temperatures (T) as cleaved samples. Figure 3 presents the normalized torque curvatures. Generally, two-fold constituents for curves remain unchanged, which is the same case for the maximum values of torque. It keeps decreasing as the T increases toward 300 K. Contrary to the cleaved samples, data at low temperatures below Tc, a sawtooth pattern at low field vanishs. All peak positions are similar, except for a 0.1 T low-magnetic field. At T = 130 K, the amplitude decreases rapidly, but no significant transformation occurs.

Figure 3. (Color online) (a) τ(θ) and a fitting curve for uncleaved CoS2 at T = 10 K and H = 0.2 T using Eq. (1). Anisotropy amplitudes An for uncleaved CoS2 (b) at different fields at T = 10 K, (c) and temperatures at H = 1 T.

Figure 4(a) illustrates the fitted torque curves for the uncleaved CoS2. The fitting curve fits reasonably well for all H and T, but it is not perfect. The behavior pattern with the T and H of the extracted values of A2, A4, and A6 are presented in Figs. 4(b) and (c). All symmetry fold An increases with the field below 0.2 T, then saturates. Furthermore, the two-fold symmetry is predominant. A6 is very small, A4 is quickly suppressed as the temperature increases, and all Ans diminish at Tc.

To summerize the effect of crystal cleavage on CoS2 magnetic anisotropy, all the extracted amplitudes from the fitted data at T = 10 K were normalized with A2(1 T), An(H)A2(1T), and plotted together in Fig. . Figure 5 clearly demonstrates the effect of crystal cleavage on the anisotropy order amplitudes. The transtion in the cleaved crystal is broad compaerd to the uncleaved sample. The strain created on the atoms due to cleavage may lead to the broad transition and higher saturation field. All amplitudes show same behavior for cleaved and uncleaved samples. For the uncleaved samlpe, the saturation occurs at 0.2 T, while it increases up to 0.4 T for the cleaved sample. All anisotropic orders are observed for both cleaved and uncleaved samples. However, higher orders, including A4 and A6, are dominant in the cleaved sample.

This research was supported by Kyungpook National University Research Fund, 2019

  1. P. Gambaredella et al, Science 300, 1130 (2003).
  2. K. Adachi et al, Phys. Rev. Lett. 95, 197202 (2005).
  3. S. Ouazi et al, Nat. Commun. 3, 1313 (2012).
  4. M. Nauman et al, Phys. Rev. B 96(15), 155102 (2017).
  5. S. Blundell, Magnetism in Condensed Matter. (OUP Oxford2001).
  6. N. Ouarab and A. Haroun, J. Mag. Magn. Mater. 443, 300 (2017).
  7. V. N. Antonov et al, Phys. Rev. B 78, 094409 (2008).
  8. E. Nowack, D. Schwarzenbach and T. Hahn, Acta Cryst. B47, 650 (1991).
  9. R. A. Munson, W. DeSorbo and J. S. Kouvel, J. Chem. Phys. 47, 1769 (1967).
  10. L. Wang, T. Y. Chen and C. Leighton, Phys. Rev. B 69, 094412 (2004).
  11. P. J. Brown et al, J. Phys. Condens. Matter 17, 1583 (2005).
  12. S. N. Kane, A. Mishra and A. K. Dutta, J. Phys. Conf. Ser. 755, 011001 (2016).
  13. N. V. Mushnikov, T. Goto, A. V. Andreev and S. M. Zadvorkin, Philos. Mag. B 80(1), 81 (2000).
  14. K. Adachi et al, J. Phys. Soc. Jpn. 38, 81 (1975).
  15. H. Takahashi et al, J. Phys. Soc. Jpn. 86, 063002 (2017).
  16. B. D. Cullity and C. D. Graham, Introduction to Magnetic Materials, Second. (John Wiley & Sons2011).
  17. H. Xiao et al, J. Phys. Condens. Matter 28, 325701 (2016).
  18. R. Masutomi, M. Hio, T. Mochizuki and T. Okamoto, Appl. Phys. Lett. 90, 202104 (2007).

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