Session S02: Topological Antiferromagnets and Altermagnets

Exploring Topological Phases and Spin Group Protection in Two-Dimensional Altermagnets

In magnetic materials containing light elements, where neglecting relativistic spin-orbit coupling (SOC) is a reasonable approximation, the crystalline symmetry groups are considerably larger than those of conventional magnetic materials. This expansion results from the decoupling of nontrivial spin degrees of freedom from the orbital part, which is known to be relevant in the newly proposed class of magnetic materials called 'altermagnets.' Here, we systematically study the description of spinful electrons in 2D magnetic lattices using spin groups, focusing on topological phases protected by order-two nonsymmorphic spin group elements in coplanar magnetic textures. Within the spin group framework, we explore intrinsic topological phases by considering one of the spin group elements that acts solely in spin space, effectively serving as a time-reversal symmetry in addition to the nonsymmorphic spin group element. This approach leads to the emergence of new topological phases, enriching the landscape of magnetic topological phases protected by magnetic space group symmetries. Furthermore, an important question to address is understanding the robustness of topological protection afforded by the spin group against SOC, which is inevitably present in all materials.   

Detecting Large Thermal Hall Effect in MnPS3

The phenomenon of thermal Hall effect in insulating materials has recently attracted the interest of the scientific community. In this talk, we expand on the thermal Hall measurement to low temperatures in an insulating antiferromagnet, MnPS₃. We discuss some possible origins causing our large observed thermal Hall signal, including intrinsic Berry curvature, magnon-phonon hybridization, and magnon-phonon skew scattering. Additionally, we discuss the temperature and magnetic field dependence of the Hall angle, k_xy, and k_xx in both antiferromagnetic order and spin-flop transition.   

Investigation of spin waves and magnetic structure of NiTiO3

Magnetoelectric multiferroics with coexisting magnetic and electric orders that can be manipulated by external electric and magnetic fields have wide-ranging applications. Investigating the origin of these magnetic and electric properties is crucial for understanding the intriguing underlying physics. NiTiO₃ is such a system with the honeycomb structure with R space group. It has an antiferromagnetic (AFM) stacking order along the c-axis and ferromagnetic (FM) in-plane. The Néel temperature is 22 K. The local structure, magnetism and exchange interactions were investigated by neutron scattering. The local structure obtained from the pair distribution function analysis of the diffraction data at high temperatures shows that the Ti-O bond length changes as a function of temperature and this could be linked to the ferroelectric properties above room temperature. At low temperatures, a negative thermal expansion is observed along a-axis that may be linked to magnetoelastic coupling and anisotropic exchange interactions in the system. From inelastic neutron scattering data, a single, broad magnon peak centered at ~ 2.5 meV is observed and calculations suggested considerable out of plane interactions.

Non-collinear spin structure of NdSb revealed by spin-polarized scanning tunneling microscopy

Rare-earth monopnictides are a family of materials simultaneously displaying complex magnetism, strong electronic correlation, and topological band structure. Emergent arc-like surface states driven by antiferromagnetic order have recently been discovered in these materials [1-2]. Their magnetic structure is still under debate and direct experimental observation has been elusive [3-6]. Here we report the observation of non-collinear antiferromagnetic order with multiple modulations using spin-polarized scanning tunneling microscopy. Moreover, we discover a hidden spin-rotation transition of single-to-multiple modulations 2 K below the Neel temperature. The hidden transition coincides with the onset of the surface states splitting observed by our angle-resolved photoemission spectroscopy measurements.

 

References

[1] B. Schrunk, et al., Nature 603, 610-615 (2022)

[2] Y. Kushnirenko, et al., Phys. Rev. B 106, 115112 (2022) 

[3] L.-L. Wang, et al., Commun. Phys. 6, 78 (2023)

[4] P. Li, et al., npj Quantum Mater. 8, 22 (2023).

[5] A. Honma, et al., Phys. Rev. B 108, 115118 (2023)

[6] Y. Kushnirenko, et al., arXiv:2305.17085   

Symmetry in chiral phonon and magnon.

Symmetry plays a critical role in determining physical properties. Recently, phonon chirality has become an important topic. The interest is driven partly by its relevance to giant phonon thermal hall conductivity in Cuprate high-Tc superconductors and partly by its promise for applications in producing a giant effective magnetic field in materials. On the other hand, the recent rapid development of spin and magnetic space groups makes it possible to classify chiral phonons in magnetic materials as well as understand magnon topology. Here, we present a study of chiral phonon and magnon topology, and relate them to crystal symmetries.   

Spontaneous Hall effect in an antiferromagnet Mn11Ge8 with broken time-reversal symmetry

In conventional ferromagnets, the magnitude of anomalous Hall effect is proportional to net magnetization. On the other hand, in recent times, it was theoretically proposed that some antiferromagnets with broken time-reversal symmetry (TRS) can induce large spontaneous Hall effect despite vanishingly small net magnetization. In this study, we investigated the properties of Mn₁₁Ge₈ as a candidate of TRS-broken antiferromagnet. This material was reported to show weak spontaneous magnetization along b-axis, which implies the realization of antiferromagnetic order with broken TRS. By performing detailed magnetization measurement, we identified four distinctive magnetic phases as a function of temperature and magnetic field. We also found that the Hall resistivity profile does not simply scale with net magnetization, implying the additional Hall contribution originating from TRS-broken antiferromagnetic order.   

Large-Scale Discovery of Topological Magnons

Progress over the past decade has given rise to emergence of topological magnon models that exhibit various topologically-nontrivial phases analogous to their electronic counterpart. However, to make predictions of material realization of such models is a severe challenge given the lack of neutron scattering data. Here, we utilize the recently-developed theories of Magnetic Topological Quantum Chemistry and Symmetry Indicators to perform an automated full search among all magnetic structures in Bilbao Crystallographic Server that, upon a perturbation, induce at least one nontrivial topological gap in all their possible allowed band structures compatible with symmetries. This gives a complete classification for current BCS magnetic materials with all different types of perturbation-induced topological features they exhibit. Our work results in the discovery of over 300 candidate materials to host field-induced topological magnons.   

Magnon-Electron Interaction in Magnetic Topological Materials

The recently identified magnetic Weyl semimetals Co₃Sn₂S₂ [1] and MnBi₂Te₄ [2] have drawn a lot of interest in the interplay between magnetism and topology. Giant anomalous transport has been detected in Co₃Sn₂S₂ while the manipulation of the Weyl nodes via the rotation of the magnetization has been identified as a possible source of large transport signatures [3]. Nonetheless, in these studies, magnetization is usually considered a classical and temperature-independent quantity, and inherent interaction between electrons and magnons is generally overlooked. Inspired by the prediction of electron-phonon interaction-driven topological phase transition predicted in Ref. [4], we examine the influence of electron-magnon interaction on the topology of selected topological magnetic materials. Using quantum field theory techniques, we compute the band renormalization induced by this interaction in both ferromagnetic and antiferromagnetic two-dimensional topological insulators as a function of the temperature, highlighting the impact of interactions on the lifetimes of magnons and electrons, their transport properties, and topological phase transitions.

[1] Wang et al. Nat. Comm. 9, 3681 (2018)

[2] Li et al. Science Advances, 5(6). (2019)

[3] Ghimire et al. Phys. Rev. Research 1, 032044(R) (2019) .

[4] I. Garate.  Phys. Rev. Let. 110 (4), 046402 (2013).   

Tunable Floquet topological magnons in a driven system

Topological magnon insulators are two-dimensional systems with an ordered magnetic ground state and gapped bosonic magnetic excitations (magnons). In the presence of an out-of-plane Dzyaloshinskii-Moriya interaction (DMI), a two-dimensional magnetic system may support excitations corresponding to bands of one-magnon and two-magnon modes.  These bands may be topologically non-trivial (characterized by non-zero Chern numbers) and therefore these systems support chiral magnon edge states. Recently, Ref. [1] studied magnetic systems where the (otherwise trivial) single-magnon and two-magnon bands are hybridized by in-plane DMI, resulting in a topologically non-trivial band structure. We aim to find magnetic systems in which such hybridization between (initially trivial) bands having a different magnon number is achieved by driving the system with time-dependent electromagnetic fields. The resulting bands may have non-zero Chern numbers that can be modified by varying the relative phase between ac magnetic fields driven at two distinct frequencies. Furthermore, we study the transverse thermal conductivity in this system and investigate its deviation from the case of static (topologically trivial) systems.

[1] Mook, Alexander, et al. Phys. Rev. B 107.6 064429 (2023).   

Magnetic field induced phase transitions in disordered altermagnets

In altermagnets (AM), flipping spins can be compensated by a rotation, similar to antiferromagnets, where this is accomplished by a translation or by inversion. Even though AM are states of homogeneous order, their symmetry requires that, in sharp contrast to ferromagnets, there is no direct bilinear coupling to a homogeneous magnetic field. However, since many altermagnets display piezomagnetism, a trilinear coupling with magnetic field and strain is generally allowed. This is the case for externally applied, for dynamic, and for random strain. Consequently, in the presence of random strain, a magnetic field behaves as an effective random field conjugate to the AM order parameter, providing a rare realization of a tunable random-field Ising model. Here, we solve the corresponding transverse-field Ising model in the presence of random longitudinal fields via mean-field to gain insight into the impact of a magnetic field on the AM phase diagram. We find two competing effects enabled by an increasing magnetic field: an increasing random-field disorder, which suppresses long-range AM order, and an enhanced coupling to elastic fluctuations, which favors AM order. We discuss the outcome of this competition and determine its fingerprints in various experimentally-accessible quantities, such as the magnetic susceptibility, the elastocaloric effect, the shear modulus, and the AM order parameter.   

Topological altermagnetic to ferromagnetic transition promoted by spin-orbit coupling

The defining property of an altermagnetic state is that the symmetry that leaves the state unchanged when combined with flipping the magnetic moments is a rotation, which can be proper or improper. Because of this symmetry, the band structure of altermagnets displays a Zeeman splitting that vanishes in certain regions of momentum space. In this talk, we will discuss the impact of spin-orbit coupling on the properties of altermagnets. We will show that the magnetic moments in an altermagnetic state become intrinsically non-collinear, and that the Zeeman splitting acquires nodal lines protected by mirror symmetries of the lattice. This symmetry protection ensures that the nodal lines are stable against magnetic fields applied perpendicular to such mirrors. Consequently, a critical magnetic field needs to be applied for the nodal loops to collapse, resulting in a topological transition between a state with nodal Zeeman splitting, which is characteristic of an altermagnet, and a state with nodeless Zeeman splitting, which is charactertistic of a ferromagnet.   

Quantum Spin Hall Effect in an Altermagnet

Altermagnetism was recently proposed as a framework to describe a class of spin-orbit-coupling free magnetic systems with broken time-reversal symmetry and perfect compensation of spin-up/down species due to a crystal symmetry different from translation or inversion. It has been shown that if spin-orbit coupling is restored as a perturbation, the system may exhibit weak ferromagnetism and anomalous Hall effect. In our work, we employ a minimal tight-binding model for a square-lattice altermagnet and show that the system can also realize the quantum spin Hall effect. We further explore what types of altermagnetism can be stabilized by correlation-driven orbital order, and employ group theory to predict which orders are stable with respect to inclusion of spin-orbit coupling and which ones exhibit weak ferromagnetism.   

Mechanisms for stabilizing altermagnetism: applications to material candidates

Altermagnetism has been proposed as a new magnetic phase that has a vanishing net magnetization, like antiferromagnets, but shows time-reversal symmetry breaking, associated with ferromagnets. In this work, we study the 2D and 3D mechanisms giving rise to altermagnetism by examining the altermagnetic susceptibility and comparing it to the usual spin susceptibility. In particular, in the 2D case we study the effect of Van Hove singularities and propose a mechanism to stabilize altermagnetism. Finally, we discuss these findings in terms of relevant tight-binding models for altermagnetic materials candidates, including the rutile metal RuO2. We demonstrate that the minimal tight-binding models are sufficient to capture a leading altermagnetic instability.   

Magnon-phonon coupling in a Dirac magnet CoTiO3

Magnon-phonon coupling has been an intense research topic due to its numerous applications in spintronics and magnonics. Recently, cobalt titanate (CoTiO₃), an easy-plane quantum antiferromagnet, has been found to host topological magnons and has been predicted to have a relatively large phonon magnetic moment. We have investigated the effect of coherent chiral phonons on the magnetic properties of CoTiO₃ using terahertz pump-optical Faraday rotation probe spectroscopy. Our results showed phonon-driven excitation of the antiferromagnetic magnon mode and a gradual increase in the Faraday as a function of pump-probe delay time with no measurable decay. We found that the observed THz-induced rotation was highly temperature dependent, and thus, we conclude that it is related to the magnetic order in this material. We will discuss the possible origins of the observed phenomena.