Canted antiferromagnetic order and spin dynamics in the honeycomb-lattice compound ${\mathrm{Tb}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Ga}}_{9}$

Canted antiferromagnetic order and spin dynamics in the honeycomb-lattice compound ${Tb}_{2} {Ir}_{3} {Ga}_{9}$

Feng Ye, Zachary Morgan, Wei Tian, Songxue Chi, Xiaoping Wang, Michael E. Manley, David Parker, Mojammel A. Khan, J. F. Mitchell, and Randy Fishman

Phys. Rev. B 103, 184413 – Published 12 May 2021

Abstract

Single-crystal neutron diffraction, inelastic neutron scattering, bulk magnetization measurements, and first-principles calculations are used to investigate the magnetic properties of the honeycomb lattice ${Tb}_{2} {Ir}_{3} {Ga}_{9}$ . While the $R ln 2$ magnetic contribution to the low-temperature entropy indicates a $J_{eff} = 1 / 2$ moment for the lowest-energy crystal-field doublet, the ${Tb}^{3 +}$ ions form a canted antiferromagnetic structure below 12.5 K. Due to the Dzyaloshinskii-Moriya interactions, the Tb moments in the $a b$ plane are slightly canted towards $b$ with a canted moment of 1.22 $μ_{B}$ per formula unit. A minimal $x x z$ spin Hamiltonian is used to simultaneously fit the spin-wave frequencies along the high-symmetry directions and the field dependence of the magnetization along the three crystallographic axes. Long-range magnetic interactions for both in-plane and out-of-plane couplings up to the second nearest neighbors are needed to account for the observed static and dynamic properties. The $z$ component of the exchange interactions between Tb moments is larger than the $x$ and $y$ components. This compound also exhibits bond-dependent exchange with negligible nearest-neighbor exchange coupling between moments parallel and perpendicular to the $4 f$ orbitals. Despite the $J_{eff} = 1 / 2$ moments, the spin Hamiltonian is denominated by a large in-plane anisotropy $K_{z} \sim - 1 meV$ . DFT calculations confirm the antiferromagnetic ground state and the substantial interplane coupling at larger Tb-Tb distances.

Received 3 March 2021
Accepted 19 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.184413

Physics Subject Headings (PhySH)

Dzyaloshinskii-Moriya interaction Frustrated magnetism Magnetic order Quantum spin liquid Spin dynamics

Density functional calculations Inelastic neutron scattering Magnetization measurements Neutron diffraction Neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Feng Ye ^1,*, Zachary Morgan ¹, Wei Tian ¹, Songxue Chi ¹, Xiaoping Wang ¹, Michael E. Manley ², David Parker ², Mojammel A. Khan ^3,†, J. F. Mitchell ³, and Randy Fishman ^2,‡

¹Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
²Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA

^*yef1@ornl.gov
^†Present address: Department of Physics and Astronomy and Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA.
^‡fishmanrs@ornl.gov

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 103, Iss. 18 — 1 May 2021

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) The crystal structure of TIG projected onto the $a c$ plane. The structure is composed of stacked ${(A B)}_{2}$ layers, where $A$ is a buckled ${IrGa}_{2}$ layer (Ir atoms form a triangle lattice), and $B$ is a ${Tb}_{2} {Ga}_{3}$ layer (Tb atoms form a pseudohoneycomb lattice). (b) The network of Tb ions viewed from the $c$ axis. The black rectangular box in panels (a) and (b) is the unit cell. (c), (d) The canted AFM spin configuration with magnetic space group $C m^{'} c m^{'}$ . $J_{1}$ , $J_{2}$ , $J_{3}$ , and $J_{4}$ are the in-plane exchange interactions with Tb-Tb distances of 4.28, 4.38, 7.52, and $7.54 Å$ , respectively; $J_{l 1}$ , $J_{l 2}$ , $J_{l 3}$ , and $J_{l 4}$ are the interlayer exchange interactions with Tb-Tb distances of 5.36, 5.37, 6.86, and $6.89 Å$ , respectively, all at room temperature.
Reuse & Permissions
Figure 2
(a) Contour plot of the neutron-diffraction data in the $(H, 0, L)$ scattering plane collected on CORELLI at $T = 7 K$ . (b) $T$ dependence of the (0,0,2) Bragg peak measured at HB1A. The solid line is a guide to the eye. (c) Comparison between the observed and calculated structure factors, $F_{obs}$ and $F_{calc}$ . The (red) line is a linear fit to the data points. (d) The $T$ dependence of the $L$ scan across the (2,0,0) Bragg point. The inset shows the representative line cut along the $[0, 0, L]$ direction at 11, 12, and 13 K, with prominent short-range correlation at 12 K.
Reuse & Permissions
Figure 3
(a) Contour plot of the neutron-diffraction data in the $(H, 0, L)$ scattering plane. A rod-like feature along $[0, 0, L]$ indicates the short-range magnetic correlations along the $c$ axis. (b) For the line cut along $[2, 0, L]$ , Lorentzian profiles appear at even indices. (c) Monte Carlo simulation of the magnetic diffuse scattering just above the transition using the magnetic exchange parameters in Table I. (d) The corresponding line cut along $[2, 0, L]$ .
Reuse & Permissions
Figure 4
SW dispersion spectra of ${Tb}_{2} {Ir}_{3} {Ga}_{9}$ along (a) $[ξ, 0, 3]$ , (b) $[η, 0, 4 - η]$ , and (c) $[0, 0, L]$ . The corresponding calculated spectra are shown in panels (d)–(f). Individual scans at constant moment transfer are measured from $E = 1$ to 7 meV with step of 0.25 meV. The solid circles in panels (a)–(c) specify the measured momentum transfer. Insets show the schematics of the scan directions in the $(H, 0, L)$ scattering plane. In untwinned samples, only red dots are allowed Bragg reflections $(H, L = 2 n)$ , the blue dots represent the observed Bragg peaks contributed from twinned domains, as shown in Fig. 2. The dispersion-like feature for energy transfer below 3 meV in panel (a) arises from the tail of the resolution function sweeping through the neighboring Bragg peak in the focusing geometry.
Reuse & Permissions
Figure 5
Magnetization $M (H)$ with field applied along the three crystallographic axes up to 7 T at 1.8 K. Open symbols are experimental data; solid lines are the best fits described in the text. The spin configurations in three distinct region with field $B ∥ a$ are sketched in panel (a).
Reuse & Permissions
Figure 6
The calculated density of states of ${Tb}_{2} {Ir}_{3} {Ga}_{9}$ in the ${AF}_{1}$ phase.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Canted antiferromagnetic order and spin dynamics in the honeycomb-lattice compound ${Tb}_{2} {Ir}_{3} {Ga}_{9}$

Feng Ye, Zachary Morgan, Wei Tian, Songxue Chi, Xiaoping Wang, Michael E. Manley, David Parker, Mojammel A. Khan, J. F. Mitchell, and Randy Fishman

Phys. Rev. B 103, 184413 – Published 12 May 2021

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

Supplemental Material (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review B

covering condensed matter and materials physics

Canted antiferromagnetic order and spin dynamics in the honeycomb-lattice compound Tb2Ir3Ga9

Feng Ye, Zachary Morgan, Wei Tian, Songxue Chi, Xiaoping Wang, Michael E. Manley, David Parker, Mojammel A. Khan, J. F. Mitchell, and Randy Fishman

Phys. Rev. B 103, 184413 – Published 12 May 2021

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

Supplemental Material (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Canted antiferromagnetic order and spin dynamics in the honeycomb-lattice compound ${Tb}_{2} {Ir}_{3} {Ga}_{9}$