Transdimensional anomalous Hall effect in rhombohedral thin graphite | Nature

Subjects

- Ferromagnetism

- Quantum Hall

Abstract

Anomalous Hall effect (AHE), occurring in materials with broken time-reversal symmetry, epitomizes the interplay between magnetic order and electron orbital motions1,2,3,4. In two-dimensional (2D) systems, AHE is coupled with out-of-plane orbital magnetization associated with in-plane chiral orbital motions. In three-dimensional (3D) systems, in which sample thickness far exceeds a vertical coherence-transport length lz, the AHE is effectively a thickness-averaged 2D counterpart4—still governed by out-of-plane orbital magnetization arising from in-plane orbital motions. Here we report the experimental observation of a fundamentally new type of AHE that couples both in-plane and out-of-plane orbital magnetizations in multilayer rhombohedral graphene, shown by pronounced Hall resistance hysteresis under both in-plane and out-of-plane magnetic fields. This state emerges from a peculiar metallic phase that spontaneously breaks time-reversal, mirror and rotational symmetries driven by electron–electron interactions. By measuring multiple devices spanning 3–15 layers, we find that this phenomenon emerges only within an intermediate thickness of 2–5 nm. Theoretical calculations show that carriers within this window can sustain coherent orbital motions both within and across the 2D plane. Together, these identify an uncharted ‘transdimensional’ regime between 2D and 3D, in which the sample thickness is much larger than atomic spacing yet remains comparable to lz, for the emergence of this new state of matter—transdimensional AHE. Our findings point to a distinct class of AHE, opening an unexplored model for correlated and topological physics in transdimensional landscapes.

Access through your institution

Buy or subscribe

This is a preview of subscription content, access via your institution

Access options

Access through your institution

Access Nature and 54 other Nature Portfolio journals

Get Nature+, our best-value online-access subscription

$32.99 / 30 days

cancel any time

Learn more

Subscribe to this journal

Receive 51 print issues and online access

$199.00 per year

only $3.90 per issue

Learn more

Buy this article

- Purchase on SpringerLink

- Instant access to the full article PDF.

USD 39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Dimensionality perspective of AHE and basic characterizations on rhombohedral ennealayer graphene.The alternative text for this image may have been generated using AI.

Fig. 2: Phase diagram and fermiology in the conduction band.The alternative text for this image may have been generated using AI.

Fig. 3: TDAHE with unique in-plane orbital magnetization and out-of-plane magnetization.The alternative text for this image may have been generated using AI.

Fig. 4: Temperature dependence of in-plane magnetic hysteresis and Hartree–Fock calculations.The alternative text for this image may have been generated using AI.

Data availability

The data that support the findings of this study are available from the corresponding authors upon request.

References

- Hall, E. On the possibility of transverse currents in ferromagnets. Philos. Mag 12, 157–172 (1881).

Article

Google Scholar

- Karplus, R. & Luttinger, J. M. Hall effect in ferromagnetics. Phys. Rev. 95, 1154–1160 (1954).

Article

ADS

Google Scholar

- Yao, Y. et al. First principles calculation of anomalous Hall conductivity in ferromagnetic bcc Fe. Phys. Rev. Lett. 92, 037204 (2004).

Article

ADS

PubMed

Google Scholar

- Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).

Article

ADS

Google Scholar

- Hall, E. H. On a new action of the magnet on electric currents. Am. J. Math. 2, 287–292 (1879).

Article

Google Scholar

- Smit, J. The spontaneous Hall effect in ferromagnetics I. Physica 21, 877–887 (1955).

Article

ADS

CAS

Google Scholar

- Berger, L. Side-jump mechanism for the Hall effect of ferromagnets. Phys. Rev. B 2, 4559–4566 (1970).

Article

ADS

Google Scholar

- Jungwirth, T., Niu, Q. & MacDonald, A. H. Anomalous Hall effect in ferromagnetic semiconductors. Phys. Rev. Lett. 88, 207208 (2002).

Article

ADS

CAS

PubMed

Google Scholar

- Burkov, A. A. Anomalous Hall effect in Weyl metals. Phys. Rev. Lett. 113, 187202 (2014).

Article

ADS

CAS

PubMed

Google Scholar

- Ghimire, N. J. et al. Large anomalous Hall effect in the chiral-lattice antiferromagnet CoNb3S6. Nat. Commun. 9, 3280 (2018).

Article

ADS

PubMed

PubMed Central

Google Scholar

- Chang, C.-Z. et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340, 167–170 (2013).

Article

ADS

CAS

PubMed

Google Scholar

- Liu, J. & Dai, X. Orbital magnetic states in moiré graphene systems. Nat. Rev. Phys. 3, 367–382 (2021).

Article

CAS

Google Scholar

- Sharpe, A. L. et al. Emergent ferromagnetism nea