Table 1 Hyperfine properties of the used materials R2Ti2O7 (R = Ho, Dy)

From: Nuclear spin assisted quantum tunnelling of magnetic monopoles in spin ice

R

I

μ N

A (K)

BN (T)

|μ| (K)

ΔE (K)

Ho

7/2

4.17

0.3

0.034

5.7

1 × 10−5

161Dy(≈19% in natDy2Ti2O7)

5/2

−0.48

0.0216

−0.0039

4.35

6 × 10−6

163Dy (≈25% in natDy2Ti2O7)

5/2

0.67

0.0216

0.0054

4.35

6 × 10−6

otherDy(≈66% in natDy2Ti2O7)

0

0

0.0216

0

4.35

6 × 10−6

162Dy

0

0

0

0

4.35

6 × 10−6

163Dy

5/2

0.67

0.0599

0.0054

4.35

6 × 10−6

  1. Here, I is the nuclear spin, μN the nuclear moment, A the hyperfine coupling constant, BN the effective field due to the nuclear moment at r = 0.5 Å, μ is the monopole chemical potential (conventionally negative, hence we quote |μ|) and ΔE is the tunnel splitting for a typical transverse field of 0.5 T14. The A = 0.0216 K coefficient for Dy is the average for natDy2Ti2O7. Note that about 13% of Ti ions have a nuclear moment giving approximately 20 μT field at the site of a Ho or Dy ion
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