Stripe antiferromagnetism in van der Waals metal HoTe3 decoupled from charge density wave order

Neutron diffraction studies on single-crystal HoTe3 reveal two distinct antiferromagnetic phases with specific stripe motifs and stacking orders that are decoupled from the charge density wave order, suggesting that the alignment of propagation vectors and single-ion anisotropy are critical for spin-charge coupling in van der Waals systems.

The Gist

Imagine a microscopic city built from layers of atomic Lego bricks. This city is made of a material called HoTe₃ (Holmium Telluride), which belongs to a family of materials known as "van der Waals metals." Think of these materials like a stack of pancakes: the pancakes (atomic layers) are held together loosely, so you can peel them apart easily, but inside each pancake, the atoms are tightly bonded.

In this atomic city, two major events are happening simultaneously, like two different types of traffic patterns:

1. The Charge Density Wave (CDW): Imagine the electrons (the city's citizens) organizing themselves into a giant, repeating grid pattern, like a checkerboard on a chessboard. This is the "Charge Density Wave."
2. Magnetism: The atoms themselves act like tiny compass needles (spins). Usually, in these materials, the compass needles want to align with the checkerboard pattern, creating a complex, intertwined dance between the electrons and the magnets.

The Big Discovery: Two Different Magnetic Dances

The scientists in this paper wanted to see how the compass needles (magnetism) behaved in HoTe₃. They expected the needles to dance in sync with the checkerboard electron pattern, just like they do in similar materials (like DyTe₃).

Instead, they found something surprising: The magnetism and the electron checkerboard are completely ignoring each other.

They discovered that HoTe₃ has two distinct "magnetic seasons" (phases) as it gets colder, and in both seasons, the compass needles form a very specific, simple pattern: Up, Up, Down, Down (↑↑↓↓).

Think of this pattern like a row of soldiers standing in a line:

• Two soldiers face North.
• The next two face South.
• The next two face North.
• And so on.

This is called a "Stripe" pattern.

The Two Seasons: Vertical vs. Tilted

While the soldiers in a single layer all stand in the same Up-Up-Down-Down line, the way these layers stack on top of each other changes depending on the temperature.

1. The "Vertical Stripe" Phase (Hotter):
   Imagine stacking your pancakes. In this phase, the soldiers in the pancake directly above are standing in the exact same direction as the ones below. If the bottom layer has "North-North-South-South," the layer above it also has "North-North-South-South."

   • Analogy: It's like a perfectly aligned tower of books where the spines all face the same way.

2. The "Tilted Stripe" Phase (Coldest/Ground State):
   As the material gets colder, the stacking changes. Now, the layer above flips its pattern. If the bottom layer is "North-North-South-South," the layer above becomes "South-South-North-North."

   • Analogy: It's like a stack of books where every other book is flipped upside down. This creates a "tilted" or zigzag effect when you look at the whole stack from the side.

The Plot Twist: The "Checkerboard" Problem

Here is the most exciting part of the story. In other similar materials (like DyTe₃), the electron checkerboard and the magnetic stripes are best friends; they lock arms and move together, creating exotic, complex shapes.

But in HoTe₃, they are strangers.

The scientists found that because the electron pattern in HoTe₃ is a checkerboard (a complex 2D grid) rather than a simple line (unidirectional), it actually prevents the magnetism from locking onto it.

• The Metaphor: Imagine trying to dance with a partner. If they are walking in a straight line, you can easily match their steps. But if they are suddenly jumping in a complex 2D grid pattern (the checkerboard), you can't keep up, so you just do your own simple dance (the stripes) and ignore them.

Why Does This Matter?

This is a big deal for future technology. Scientists hope to build "spintronic" devices (computers that use magnetism instead of electricity) by stacking these materials like Lego. Usually, they want the magnetism and electricity to be tightly coupled so they can control one with the other.

This paper tells us: "Hey, if you use a material with a checkerboard electron pattern, the magnetism might just ignore you."

It suggests that to get the "coupled" behavior scientists love, we need to avoid the checkerboard pattern and stick to simpler, straight-line patterns. It's a crucial rule for engineers trying to build the next generation of quantum computers using these atomic pancakes.

Summary in One Sentence

Scientists discovered that in HoTe₃, the magnetic atoms form simple "Up-Up-Down-Down" stripes that stack in two different ways, but they completely ignore the complex electron checkerboard pattern, proving that not all atomic dances are partners.

Technical Summary

1. Problem Statement

Rare-earth tritellurides ($RTe_3$) are a family of layered van der Waals (vdW) compounds known for hosting coexisting Charge Density Wave (CDW) and magnetic orders. In heavy rare-earth members like DyTe$_3$, TbTe$_3$, and GdTe$_3$, these two orders are strongly coupled, leading to exotic magnetic states (e.g., helimagnetic cones) driven by the CDW. However, the interplay between magnetism and CDW in the presence of a checkerboard-type CDW (a superposition of two orthogonal charge modulations) remains largely unexplored. The central question is whether the complex checkerboard CDW in HoTe$_3$ facilitates or suppresses the coupling between spin and charge degrees of freedom compared to the unidirectional CDW found in other $RTe_3$ members.

2. Methodology

The authors employed a comprehensive experimental and theoretical approach to determine the magnetic structure and its relationship with the CDW in single-crystal HoTe$_3$:

• Neutron Diffraction:
  • Polarized Neutron Scattering: Used to determine the orientation of magnetic moments (spin direction) relative to the crystallographic axes. The experiment utilized the $hk0$ scattering plane with the neutron spin quantization axis aligned along the crystallographic $c$-axis to distinguish between spin-flip (SF) and non-spin-flip (NSF) channels.
  • Unpolarized Time-of-Flight (TOF) Laue Diffraction: Performed using the SENJU diffractometer at J-PARC to map magnetic superlattice reflections and refine the magnetic structure factor.
• Symmetry Analysis: Theoretical modeling based on the paramagnetic space group ($Cmcm$) to identify maximal magnetic subgroups (mSGs) compatible with the observed propagation vectors and moment orientations.
• Magnetization Measurements: Used to construct the magnetic phase diagram in the magnetic field ($B$) vs. temperature ($T$) plane.

3. Key Contributions

• Identification of Two Distinct AFM Phases: The study reveals two successive antiferromagnetic (AFM) phases in HoTe$_3$ (AFM-I ground state and AFM-II high-temperature phase), both characterized by a collinear $\uparrow\uparrow\downarrow\downarrow$ motif within individual vdW layers.
• Structural Differentiation via Stacking: The two phases are distinguished solely by the stacking sequence of magnetic layers along the $b$-axis:
  • AFM-II: "Vertical-stripe" phase with Ferromagnetic (FM) stacking of magnetic layers.
  • AFM-I: "Tilted-stripe" phase with Antiferromagnetic (AFM) stacking of magnetic layers.
• Decoupling of Spin and Charge: The paper provides definitive evidence that, unlike in DyTe$_3$, the magnetic order in HoTe$_3$ is decoupled from the CDW order.
• Role of Checkerboard CDW: The authors propose that the checkerboard nature of the CDW in HoTe$_3$ is detrimental to the formation of coupled spin-charge order parameters, contrasting with the unidirectional CDW in other $RTe_3$ compounds.

4. Detailed Results

Magnetic Structure of AFM-I (Ground State)

• Propagation Vector: $\mathbf{q}_{m1} = (0.5, 0.5, 0)$.
• Moment Orientation: Polarized neutron data showed exclusively Non-Spin-Flip (NSF) scattering in the $hk0$ plane, indicating that the Ho$^{3+}$ moments are fully aligned along the crystallographic $c$-axis (Ising-like anisotropy).
• Symmetry and Model: Symmetry analysis narrowed the candidates to the magnetic space group $Pa2_1/m$. Refinement of unpolarized data confirmed Model 1, where:
  • Within a single vdW layer, spins form a $\uparrow\uparrow\downarrow\downarrow$ pattern (tilted stripes).
  • Adjacent layers separated by $b/3$ are FM coupled.
  • Adjacent layers separated by $2b/3$ are AFM coupled.
• Refined Moment: The ordered moment is $7.89 \mu_B$/Ho (at 1.5 K), reduced from the free-ion value of $10 \mu_B$ due to proximity to the critical temperature ($T_N \approx 3.2$ K).

Magnetic Structure of AFM-II

• Propagation Vector: $\mathbf{q}_{m2} = (0.48, 0, 0)$, indicating a slight incommensurability (magnetic discommensuration) along the $a$-axis.
• Moment Orientation: Moments remain collinear along the $c$-axis (Ising-like).
• Structure: The symmetry group is identified as $Pcnma$. The stacking is Ferromagnetic along the $b$-axis, resulting in a "vertical-stripe" pattern ($\uparrow\uparrow\downarrow\downarrow$ within layers, FM between layers).

Coupling with CDW

• In DyTe$_3$, the CDW and AFM orders are coupled, evidenced by coupled magnetic reflections ($\mathbf{q}_{CDW} \pm \mathbf{q}_{AFM}$).
• In HoTe$_3$, no such coupled reflections were observed. The magnetic propagation vectors are independent of the CDW wavevectors.
• The authors attribute this decoupling to the checkerboard character of the CDW in HoTe$_3$ (involving modulations along both $a$ and $c$ axes), which differs from the predominantly unidirectional CDW in DyTe$_3$.

5. Significance

• Fundamental Physics: This work challenges the assumption that CDW and magnetic orders in $RTe_3$ are always strongly coupled. It demonstrates that the specific geometry of the charge order (unidirectional vs. checkerboard) dictates the nature of the spin-charge interaction.
• Material Design: The findings suggest that the checkerboard CDW acts as a "detrimental" factor for realizing coupled spin/charge order parameters in layered vdW systems. This insight is crucial for engineering vdW heterostructures where specific magnetic or electronic functionalities are desired.
• Systematic Evolution: The study maps a systematic evolution across the $RTe_3$ series, linking lanthanide-controlled lattice volume changes to the transition from unidirectional to checkerboard CDWs and the subsequent decoupling of magnetic orders.
• Experimental Benchmark: The precise determination of the magnetic space groups ($Pa2_1/m$ and $Pcnma$) and the distinction between "tilted" and "vertical" stripe phases provide a critical benchmark for theoretical models of correlated electron systems in low-dimensional materials.