Prospects for electron spin-dependent short-range force experiments with rare earth iron garnet test masses

T. M. Leslie, E. Weisman, R. Khatiwada, and J. C. Long

Phys. Rev. D 89, 114022 – Published 24 June 2014

Abstract

A study of the possible interactions between fermions assuming only rotational invariance has revealed 15 forms for the potential involving the fermion spins. We review the experimental constraints on unobserved macroscopic, spin-dependent interactions between electrons in the range below 1 cm. An existing experiment, using 1 kHz mechanical oscillators as test masses, has been used to constrain mass-coupled forces in this range. With suitable modifications, including spin-polarized test masses, this experiment can be used to explore all 15 possible spin-dependent interactions between electrons in this range with unprecedented sensitivity. Samples of ferrimagnetic dysprosium iron garnet have been fabricated in the suitable test mass geometry and shown to have spin densities on the order of $10^{20} ℏ / {cm}^{3}$ with very low intrinsic magnetism.

Received 26 January 2014

DOI:https://doi.org/10.1103/PhysRevD.89.114022

Authors & Affiliations

T. M. Leslie^1,*, E. Weisman¹, R. Khatiwada^1,2, and J. C. Long^1,†

¹Department of Physics, Indiana University, Bloomington, Indiana 47405, USA and IU Center for Exploration of Energy and Matter, Bloomington, Indiana 47408, USA
²Department of Physics, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana 46202, USA

^*Present address: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA.
^†Corresponding author.

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Vol. 89, Iss. 11 — 1 June 2014

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Figure 1
Projected sensitivity of the proposed experiment to static spin-spin interactions [Eq. (1)], with current limits and theoretical prediction. Interaction strength according to all parametrizations in Table 1 is plotted vs the range $λ$ (lower axes) and the mass of an unobserved boson (upper axes). Excluded regions are above the curves. For $V_{2}$ , the solid curve is the $1 σ$ direct limit on $(g_{A}^{e})^{2}$ [12], also expressed as $f_{2}^{e e}$ . The dashed curve is the limit from Ref. [13] reinterpreted in terms of Eq. (1). For $V_{3}$ , the bold solid curve is the direct limit on $(g_{P}^{e})^{2}$ [12], also rescaled to $f_{3}^{e e}$ in Eq. (1). Dashed curves are the limit from Ref. [14] and the anomaly from Refs. [15, 16] reinterpreted in terms of Eq. (1); the thin solid curve is the prediction for the axion [9]. For $V_{11}$ , the solid curve is the direct limit on $g_{A}^{e} g_{V}^{e}$ [12], also expressed as $f_{11}^{e e}$ .
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Figure 2
Projected sensitivity of proposed experiment to velocity-dependent spin-spin interactions [Eq. (2)]. For comparison, the solid curve in the $V_{8}$ plot is an extension of the $2 σ$ limit on $g_{V}^{n} g_{V}^{p}$ for nucleons [7], also rescaled to $f_{8}^{n p}$ in Eq. (2).
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Figure 3
Projected sensitivity of the proposed experiment to interactions between polarized and unpolarized particles [Eq. (3)], with current limits and theoretical prediction. For comparison, solid curves in the $V_{4 + 5}$ and $V_{12 + 13}$ plots are the direct limits ( $2 σ$ and $1 σ$ , respectively) for the case of polarized neutrons [29, 30]. For $V_{9 + 10}$ , the bold solid curve is the $2 σ$ direct limit on $g_{S}^{N} g_{P}^{e}$ [31], also rescaled to $f_{r}^{e e} + f_{r}^{e p} + f_{r}^{e n}$ in Eq. (3); the bold dashed curve is the projected thermal limit. The thin solid curve is the prediction for the axion [9]. Lower solid curves in the $V_{4 + 5}$ and $V_{9 + 10}$ plots are the indirect limits inferred from stellar cooling arguments [32]; the additional projected curves show expected improvements from the proposed experiment with unpolarized test masses [10].
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Figure 4
(adapted from [8] and [39]) Basic test mass geometry of the proposed experiment. In the particular configuration, a thin sample of spin-polarized material (here DyIG) covers half of the small forward rectangle of the detector mass. In other configurations, a similar sample is attached to the underside of the forward part of the source mass. The thin, stiff, conducting shield between the test masses is not shown.
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Figure 5
Left: Magnetization of DyIG vs temperature, from the results of the molecular field calculation described in the text. Contributions from the ions on each sublattice are shown (bold curves), together with the sum (dashed curve). Right: Magnetization vs temperature of the particular DyIG samples fabricated for the proposed experiment. At each temperature investigated, there are two data points for each sample, one taken as the sample is cooled from 295 K, the other as the sample warmed from 200 K. The dashed line is the (negative of the) calculated total magnetization in the left-hand plot, for comparison with the slope of the experimental curves at $T c$ .
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Figure 6
Test mass and spin polarization configurations used to search for interactions $V_{2}$ – $V_{16}$ as assumed in the sensitivity calculations. Here, $σ_{1}$ is the net polarization direction of the spins in the detector mass and $σ_{2}$ in the source mass. The relative velocity of the spins in each test mass is strongly dominated by the velocity of the source, $v$ . The detector torsion axis is along $x$ . $C 1$ : polarization in plane, parallel ( $V_{2}$ , $V_{3}$ ). $C 2$ : polarization normal ( $V_{2}$ , $V_{3}$ , $V_{6 + 7}$ , $V_{8}$ ). $C 3$ : polarization normal, detector only ( $V_{9 + 10}$ , $V_{12 + 13}$ ). $C 4$ : polarization in plane, crossed ( $V_{11}$ , $V_{14}$ ). $C 5$ : polarization in plane, detector only ( $V_{4 + 5}$ ). $C 6$ : polarization mixed ( $V_{15}$ , $V_{16}$ ). Note that in $C_{1}$ – $C_{4}$ the source subtends half the detector area, and the polarized material $σ_{1}$ covers only the detector area subtended. In $C_{5}$ and $C_{6}$ , the source mass is centered over the detector, and $σ_{1}$ covers the entire detector area.
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