[Paper Review] Investigation of the Anomalous and Topological Hall Effects in Layered Monoclinic Ferromagnet Cr$_{2.76}$Te$_4$

Shubham Purwar, Achintya Low+3 more|arXiv (Cornell University)|Sep 16, 2023

2D Materials and Applications4 citations

TL;DR

This study investigates the anomalous and topological Hall effects in monoclinic Cr₂.₇₆Te₄, a layered ferromagnet with strong magnetocrystalline anisotropy. The system exhibits a large extrinsic anomalous Hall effect due to skew-scattering and a significant topological Hall effect arising from non-coplanar spin structures stabilized by strong anisotropy, with maximum topological Hall resistivity reaching ~1.1 μΩ·cm between 50 K and 150 K.

ABSTRACT

We studied the electrical transport, Hall effect, and magnetic properties of monoclinic layered ferromagnet Cr$_{2.76}$Te$_4$. Our studies demonstrate Cr$_{2.76}$Te$_4$ to be a soft ferromagnet with strong magnetocrystalline anisotropy. Below 50 K, the system shows an antiferromagnetic-like transition. Interestingly, between 50 and 150 K, we observe fluctuating magnetic moments between in-plane and out-of-plane orientations, leading to non-coplanar spin structure. On the other hand, the electrical resistivity data suggest it to be metallic throughout the measured temperature range, except a $kink$ at around 50 K due to AFM ordering. The Rhodes-Wohlfarth ratio $\frac{μ_{eff}}{μ_{s}}=1.89 (>1)$ calculated from our magnetic studies confirms that Cr$_{2.76}$Te$_4$ is an itinerant ferromagnet. Large anomalous Hall effect has been observed due to the skew-scattering of impurities and the topological Hall effect has been observed due to non-coplanar spin-structure in the presence of strong magnetocrystalline anisotropy. We examined the mechanism of anomalous Hall effect by employing the first principles calculations.

Motivation & Objective

• To investigate the electrical transport, Hall effect, and magnetic properties of monoclinic Cr₂.₇₆Te₄ as a candidate for 2D spintronic materials.
• To determine the origin of the anomalous Hall effect (AHE) and topological Hall effect (THE) in this layered ferromagnet.
• To clarify the role of magnetocrystalline anisotropy and spin fluctuations in stabilizing non-coplanar spin textures.
• To establish whether Cr₂.₇₆Te₄ is a itinerant ferromagnet based on magnetic and transport measurements.
• To correlate experimental Hall responses with first-principles calculations of Berry curvature and spin texture.

Proposed method

• High-quality single crystals of Cr₂.₇₆Te₄ were grown via chemical vapor transport (CVT) with iodine as a transport agent.
• X-ray diffraction (XRD) and Rietveld refinement were used to confirm the monoclinic crystal structure and phase purity.
• Electrical resistivity and Hall measurements were performed using the standard four-probe technique to extract transport and Hall responses.
• Magnetic measurements were conducted using a physical property measurement system (PPMS) to determine saturation fields, coercivity, and magnetic anisotropy.
• First-principles calculations were employed to evaluate the intrinsic AHE contribution via Berry curvature near the Fermi level.
• Magnetocrystalline anisotropy energy (Kᵤ) was extracted from field-dependent magnetization and resistivity data to correlate with topological Hall response.

Figure 1: (a) XRD pattern from Cr 2.76 Te 4 single crystals. Inset in (a) shows the photographic image of the single crystals. (b) X-ray diffraction pattern from the crushed Cr 2.76 Te 4 single crystals, overlapped with Rietveld refinement. (c) Schematic crystal structure of Cr 2.76 Te 4 obtained fr

Experimental results

Research questions

• RQ1 What is the origin of the large anomalous Hall effect in Cr₂.₇₆Te₄, and is it intrinsic or extrinsic?
• RQ2 What causes the topological Hall effect in this monoclinic CrₓTeᵧ system, which is centrosymmetric and lacks inversion symmetry?
• RQ3 How does the magnetocrystalline anisotropy influence the stabilization of non-coplanar spin structures in Cr₂.₇₆Te₄?
• RQ4 What is the role of spin fluctuations between in-plane and out-of-plane orientations in the 50–150 K temperature range?
• RQ5 How do the experimental Hall responses compare with first-principles predictions of Berry curvature and spin chirality?

Key findings

• Cr₂.₇₆Te₄ is a soft ferromagnet with negligible coercivity and strong magnetocrystalline anisotropy, with the easy axis of magnetization aligned along the bc-plane.
• Below 50 K, the system exhibits an antiferromagnetic-like transition, indicated by a kink in resistivity and changes in magnetic susceptibility.
• Between 50 K and 150 K, Cr magnetic moments fluctuate between in-plane and out-of-plane orientations, indicating dynamic non-coplanar spin structure.
• The electrical resistivity is metallic across the entire measured temperature range, with a kink at ~50 K corresponding to the AFM-like transition.
• The topological Hall resistivity reaches a maximum value of ~1.1 μΩ·cm in the 50–150 K range, indicating strong spin chirality and finite Berry curvature.
• First-principles calculations predict intrinsic AHE due to non-zero Berry curvature near the Fermi level, but experimentally the AHE is dominated by extrinsic skew-scattering mechanisms.

Figure 2: (a) Temperature dependent magnetization $M(T)$ measured under ZFC and FC modes with a magnetic field $H$ =1000 Oe for $H\parallel\it{a}$ and $H\parallel\it{bc}$ . (b) Variation of magnetization $\Delta$ M=(M FC -M FC ) plotted as a function of temperature. Inset in (b) shows first derivati