BiXSE: Spintronics Material & Sentence Embeddings

• BiXSE is a dual-use term defined as both a sputtered Bi–Se thin film for efficient spin–orbit torque and a binary cross-entropy objective for graded sentence embeddings.
• In spintronics, sputtered BiXSe films exhibit strong spin Hall effects and optimized charge-to-spin conversion critical for SOT-MRAM applications.
• In dense retrieval, the BiXSE loss leverages graded relevance supervision, outperforming traditional contrastive methods under limited labeled data.

BiXSE is a term with two distinct meanings in recent arXiv literature. In spintronics and memory-device research, it denotes sputtered $\mathrm{Bi_xSe_{1-x}}$ thin films, a Bi–Se topological-insulator-like material used as a spin-current generator in spin–orbit-torque (SOT) heterostructures and benchmarked for SOT-MRAM integration. In dense retrieval and sentence-embedding research, BiXSE denotes “Binary Cross-Entropy Sentence Embeddings,” a pointwise dual-encoder training objective that optimizes binary cross-entropy against graded relevance targets. The two usages are unrelated in mechanism and application, but both are defined around an efficiency problem: charge-to-spin conversion and low-current switching in the former, and scalable graded-relevance supervision in the latter (DC et al., 2017, Tsirigotis et al., 9 Aug 2025).

1. Nomenclature and scope

In the literature represented here, “BiXSE” appears in two non-overlapping technical domains.

Domain	Meaning of “BiXSE”	Representative paper
Spintronics	Sputtered $\mathrm{Bi_xSe_{1-x}}$ thin film	(DC et al., 2017)
Dense retrieval	“Binary Cross-Entropy Sentence Embeddings”	(Tsirigotis et al., 9 Aug 2025)

In the spintronics usage, the term refers to a Bi–Se compound closely related to $\mathrm{Bi_2Se_3}$, with a stoichiometric $\mathrm{Bi_2Se_3}$-like top region and a Bi concentration gradient through the film thickness. In the retrieval usage, the term is an acronym for a training loss and model recipe for dense retrievers that replaces one-hot contrastive supervision with probabilistic graded relevance supervision (DC et al., 2017, Tsirigotis et al., 9 Aug 2025).

This dual usage matters because the same orthographic form labels both a material system and a learning objective. Any technical discussion therefore depends entirely on disciplinary context.

2. BiXSE as a Bi–Se spin–orbit-torque material

In the 2017 SOT study, BiXSE refers to magnetron-sputtered $\mathrm{Bi_xSe_{1-x}}$ thin films grown on $\mathrm{Si/SiO_2}$ with a $2 \,\mathrm{nm}$ MgO seed layer. Rutherford backscattering gives an average composition $x \approx 0.47 \pm 0.03$, while EDS line scans show that the top of the film is stoichiometric $\mathrm{Bi_2Se_3}$ and that a Bi concentration gradient extends from top to bottom. High-angle annular dark-field STEM shows that the films are polycrystalline, with continuous Bi and Se atomic layers in both $4 \,\mathrm{nm}$ and $\mathrm{Bi_xSe_{1-x}}$0 samples, and with weak $\mathrm{Bi_xSe_{1-x}}$1-axis texture: the mean tilt from the vertical $\mathrm{Bi_xSe_{1-x}}$2-axis is about $\mathrm{Bi_xSe_{1-x}}$3, with standard deviations of $\mathrm{Bi_xSe_{1-x}}$4 for BS4 and $\mathrm{Bi_xSe_{1-x}}$5 for BS8. AFM reports RMS roughness of about $\mathrm{Bi_xSe_{1-x}}$6 for $\mathrm{Bi_xSe_{1-x}}$7 BiXSE on $\mathrm{Bi_xSe_{1-x}}$8, and $\mathrm{Bi_xSe_{1-x}}$9 for the full $\mathrm{Bi_2Se_3}$0 stack (DC et al., 2017).

The material is explicitly treated as a topological-insulator-like spin Hall material. The paper compares it with crystalline $\mathrm{Bi_2Se_3}$1 and $\mathrm{Bi_2Se_3}$2, and argues that its large SOT is consistent with strong SOC and a strong intrinsic spin Hall effect. The authors do not independently resolve surface-state and bulk contributions, but the combination of Bi$\mathrm{Bi_2Se_3}$3Se$\mathrm{Bi_2Se_3}$4-like stoichiometry at the top surface, large spin Hall conductivity, and large effective spin Hall angle supports its use as a TI-like spin-current generator (DC et al., 2017).

The device stacks are correspondingly standard for SOT characterization. The in-plane SOT-characterization heterostructures are $\mathrm{Bi_2Se_3}$5 with $\mathrm{Bi_2Se_3}$6, and the perpendicular-magnetization switching stack is $\mathrm{Bi_2Se_3}$7. This geometry is technologically important because the films are deposited by sputtering on oxidized Si rather than by MBE on single-crystal substrates (DC et al., 2017).

3. Spin–orbit torque, magnetization switching, and SOT-MRAM benchmarking

For BiXSE/$\mathrm{Bi_2Se_3}$8 heterostructures with in-plane easy axis, the 2017 paper quantifies SOT by a dc planar Hall method under $\mathrm{Bi_2Se_3}$9, extracting the effective out-of-plane field $\mathrm{Bi_2Se_3}$0 from the differential Hall response. The damping-like torque is written as

$\mathrm{Bi_2Se_3}$1

with

$\mathrm{Bi_2Se_3}$2

and the spin Hall angle is defined by

$\mathrm{Bi_2Se_3}$3

No significant $\mathrm{Bi_2Se_3}$4 or Oersted field is observed under the measurement conditions, so the response is interpreted as dominated by damping-like spin-Hall torque. For the $\mathrm{Bi_2Se_3}$5 film, $\mathrm{Bi_2Se_3}$6, and the extracted spin Hall angle is $\mathrm{Bi_2Se_3}$7. The thickness dependence is strong: BS6 gives $\mathrm{Bi_2Se_3}$8, BS8 gives $\mathrm{Bi_2Se_3}$9, BS16 gives $\mathrm{Bi_xSe_{1-x}}$0, and BS40 gives $\mathrm{Bi_xSe_{1-x}}$1. For BS4, the electrical conductivity is about $\mathrm{Bi_xSe_{1-x}}$2 and the spin Hall conductivity is about $\mathrm{Bi_xSe_{1-x}}$3. A scaling fit,

$\mathrm{Bi_xSe_{1-x}}$4

yields $\mathrm{Bi_xSe_{1-x}}$5, which the authors interpret as evidence that the intrinsic term dominates (DC et al., 2017).

The same study demonstrates room-temperature deterministic switching of perpendicular magnetization in a CoFeB/Gd/CoFeB multilayer driven by a $\mathrm{Bi_xSe_{1-x}}$6 BiXSE layer. With $\mathrm{Bi_xSe_{1-x}}$7 in-plane bias field, switching occurs at about $\mathrm{Bi_xSe_{1-x}}$8 on the negative sweep and $\mathrm{Bi_xSe_{1-x}}$9 on the return sweep, corresponding to a BiXSE current density of about $\mathrm{Si/SiO_2}$0 at room temperature. The switching efficiency,

$\mathrm{Si/SiO_2}$1

is about $\mathrm{Si/SiO_2}$2 per $\mathrm{Si/SiO_2}$3, compared with about $\mathrm{Si/SiO_2}$4 per $\mathrm{Si/SiO_2}$5 for Ta. The anomalous Hall loop orientation is opposite to that of Ta, indicating opposite spin Hall polarity (DC et al., 2017).

The 2020 SOT-MRAM study embeds sputtered $\mathrm{Si/SiO_2}$6 into a realistic $\mathrm{Si/SiO_2}$7 in-plane type-Y cell model and treats the apparent spin Hall conductivity,

$\mathrm{Si/SiO_2}$8

together with sheet resistance,

$\mathrm{Si/SiO_2}$9

as the key material figures of merit. Bi$2 \,\mathrm{nm}$0Se$2 \,\mathrm{nm}$1 is benchmarked against Pt and $2 \,\mathrm{nm}$2-W. Table II reports $2 \,\mathrm{nm}$3, $2 \,\mathrm{nm}$4, $2 \,\mathrm{nm}$5, and $2 \,\mathrm{nm}$6 for one Bi$2 \,\mathrm{nm}$7Se$2 \,\mathrm{nm}$8 point, while the Table III optimization example uses $2 \,\mathrm{nm}$9, $x \approx 0.47 \pm 0.03$0, and $x \approx 0.47 \pm 0.03$1. At $x \approx 0.47 \pm 0.03$2, the chosen low-write-energy case gives $x \approx 0.47 \pm 0.03$3, requires 3 fins in the weak write path, and yields $x \approx 0.47 \pm 0.03$4, $x \approx 0.47 \pm 0.03$5, and total $x \approx 0.47 \pm 0.03$6. In the same model, $x \approx 0.47 \pm 0.03$7-W gives about $x \approx 0.47 \pm 0.03$8 total and Pt about $x \approx 0.47 \pm 0.03$9. The authors’ general design rule is that the best cell-level operation requires large $\mathrm{Bi_2Se_3}$0 and moderate $\mathrm{Bi_2Se_3}$1, with an optimal window of about $\mathrm{Bi_2Se_3}$2. The benchmarked $\mathrm{Bi_2Se_3}$3 Bi$\mathrm{Bi_2Se_3}$4Se$\mathrm{Bi_2Se_3}$5 case lies on the very low-$\mathrm{Bi_2Se_3}$6 side of that window, so it is competitive but not optimal in the transistor-limited regime (Li et al., 2020).

4. BiXSE as “Binary Cross-Entropy Sentence Embeddings”

In dense retrieval, BiXSE is a pointwise training objective for dual-encoder sentence-embedding models that uses graded relevance labels $\mathrm{Bi_2Se_3}$7 rather than strictly binary labels. Query and document encoders produce normalized embeddings,

$\mathrm{Bi_2Se_3}$8

and the relevance logit is

$\mathrm{Bi_2Se_3}$9

where $4 \,\mathrm{nm}$0 is a logit scale and $4 \,\mathrm{nm}$1 is a learned logit bias. The model prediction is

$4 \,\mathrm{nm}$2

For a batch $4 \,\mathrm{nm}$3, BiXSE defines

$4 \,\mathrm{nm}$4

so that non-diagonal query–document pairs are treated as in-batch negatives, and optimizes

$4 \,\mathrm{nm}$5

Binary relevance is recovered as the special case $4 \,\mathrm{nm}$6 (Tsirigotis et al., 9 Aug 2025).

The method is explicitly designed for settings in which LLMs can generate graded relevance judgments cheaply enough to supervise dense retrievers, but not cheaply enough to label many documents per query. Its main structural property is therefore economy of supervision: one labeled query–document pair per query, plus implicit in-batch negatives. The paper interprets the graded targets as probabilities of relevance, which makes the objective naturally compatible with partial relevance and less tied to winner-takes-all batch softmax normalization than InfoNCE (Tsirigotis et al., 9 Aug 2025).

The training data construction reflects that interpretation. In the LightBlue dataset, Qwen2.5-32B-Instruct-GPTQ-Int4 rates query–text pairs on a five-point scale $4 \,\mathrm{nm}$7. If $4 \,\mathrm{nm}$8 denotes the normalized probability assigned by the LLM to label $4 \,\mathrm{nm}$9, then the expected score is

$\mathrm{Bi_xSe_{1-x}}$00

and the normalized target is $\mathrm{Bi_xSe_{1-x}}$01. This normalized score is used directly as the BiXSE target. The paper reports that a learned bias term $\mathrm{Bi_xSe_{1-x}}$02, trained with a higher learning rate than the encoder, is important because the batch labels are highly imbalanced: each query has one supervised diagonal pair and $\mathrm{Bi_xSe_{1-x}}$03 implicit negatives (Tsirigotis et al., 9 Aug 2025).

5. Empirical profile in dense retrieval and sentence embedding

BiXSE is evaluated on BEIR, MMTEB/MTEB, and TREC-DL, and is compared primarily against InfoNCE, Soft InfoNCE, MarginMSE, pairwise BCE, and LambdaLoss variants. The central empirical result is that BiXSE consistently outperforms InfoNCE across all tested backbones and is especially strong on graded-relevance evaluation. For ModernBERT-base, the reported aggregated scores are 42.29 versus 41.32 on BEIR, 41.11 versus 39.17 on MTEB English-v2 Retrieval, 47.67 versus 42.32 on TREC-DL 2019–2023, and 55.66 versus 51.79 on MTEB English-v2 All tasks. For multilingual Qwen2.5, the BEIR scores are 40.49 versus 38.25 for 0.5B, 48.08 versus 43.66 for 1.5B, and 50.55 versus 48.83 for 3B. The paper describes these gains as consistent across model sizes and benchmark families (Tsirigotis et al., 9 Aug 2025).

The retrieval paper also frames BiXSE as a graded-relevance distillation method. A direct 32B LLM ranker, Qwen2.5-32B-Instruct, reaches $\mathrm{Bi_xSe_{1-x}}$04 on TREC-DL with a graded 0–3 prompt and 62.86 with a binary prompt, while a BiXSE-trained Qwen2.5-3B encoder reaches 62.06. This places a much smaller bi-encoder within about three points of the graded LLM teacher and within 0.8 points of its binary-prompt score (Tsirigotis et al., 9 Aug 2025).

Several analyses in the same study explain why the method behaves differently from InfoNCE. Because BCE applies independently to each pair, it can use graded targets without forcing the labels for a fixed query to sum to 1. The authors argue that this makes BiXSE more robust to label noise: under simulated label flips between positives and hard negatives on the E5 data, BiXSE degrades more gracefully than InfoNCE. They also report that BiXSE benefits from keeping moderately relevant pairs: when the minimum retained relevance cutoff is varied on LightBlue, InfoNCE improves monotonically as the retained pairs become more strongly relevant, whereas BiXSE follows a reverse-U curve and peaks at a moderate cutoff, showing that it can exploit low- and medium-relevance supervision rather than only very high-relevance pairs (Tsirigotis et al., 9 Aug 2025).

Relative to pairwise and listwise graded-ranking objectives, BiXSE is positioned as a lower-cost alternative. The paper states that pairwise or listwise methods require multiple labeled documents per query, whereas BiXSE needs only one labeled pair per query and still uses in-batch negatives. It also emphasizes memory scaling: pairwise/listwise losses over all pair combinations scale as $\mathrm{Bi_xSe_{1-x}}$05, whereas BiXSE scales as $\mathrm{Bi_xSe_{1-x}}$06. The paper gives a concrete comparison in which storing pairwise score tensors for LambdaLoss at large batch size can exceed $\mathrm{Bi_xSe_{1-x}}$07, whereas BiXSE requires about $\mathrm{Bi_xSe_{1-x}}$08 (Tsirigotis et al., 9 Aug 2025).

6. Ambiguities, limitations, and related terms

The most immediate source of confusion is terminological. In the literature summarized here, BiXSE names both a Bi–Se thin-film material and a sentence-embedding loss. A separate 2025 paper introduces the “bixplot,” a univariate exploratory display for bimodal and multimodal data; despite superficial similarity in spelling, that term denotes a visualization method rather than either the spintronic material or the retrieval objective (Montalcini et al., 10 Oct 2025).

The spintronics literature is explicit about several unresolved issues. The sputtered $\mathrm{Bi_xSe_{1-x}}$09 films have a Bi concentration gradient, are polycrystalline rather than single-crystalline, and do not cleanly separate bulk and surface contributions to the observed giant SOT. The PMA switching stack inserts a $\mathrm{Bi_xSe_{1-x}}$10 Ta layer between BiXSE and CoFeB, so interface engineering remains a live variable even though the Ta control indicates that BiXSE dominates the torque. The 2017 paper also does not provide detailed endurance, retention, nanosecond pulsed switching, or variability data. The 2020 MRAM benchmarking paper adds a different limitation: for sputtered Bi$\mathrm{Bi_xSe_{1-x}}$11Se$\mathrm{Bi_xSe_{1-x}}$12, “spin diffusion length cannot be defined because its resistivity and band structures change drastically as a function of thickness,” so the material cannot be reduced to the simple thickness-scaling model used for heavy metals (DC et al., 2017, Li et al., 2020).

The retrieval literature likewise states clear constraints. BiXSE still assumes that in-batch negatives are non-relevant; when semantically overlapping queries share relevant documents, that assumption can fail. The method also inherits the quality and calibration of the LLM-generated relevance targets it distills. The reported scaling experiments go up to 3B-parameter student models, so larger-model behavior is left open. These limitations do not negate the method’s empirical performance, but they delimit the conditions under which its pointwise probabilistic formulation should be interpreted (Tsirigotis et al., 9 Aug 2025).

Taken together, the two BiXSE literatures illustrate a rare case of exact terminological overlap across unrelated research communities. In spintronics, BiXSE denotes a sputtered Bi–Se spin Hall material whose utility depends on the co-optimization of $\mathrm{Bi_xSe_{1-x}}$13, $\mathrm{Bi_xSe_{1-x}}$14, thickness, and transistor-loaded cell resistance. In dense retrieval, BiXSE denotes a BCE-based graded-relevance distillation objective whose utility depends on probabilistic supervision, in-batch negatives, and logit-bias calibration. The shared name is accidental; the technical content is not.