TABLE I: Magnetic moments µ of several target nuclei used in cryogenic detectors. Here, µ$_{N}$ is the proton Bohr magneton µ$_{N}$ = e/ 2 m$_{p}$ . The nuclear spin is denoted as superscripts. F$_{2}$ is the half of the conventional definition, F$_{2}$ = 1 $_{2}$F st 2 , which is related to the effective anomalous magnetic moment corresponding to the equivalent particle that has the same mass, charge and magnetic dipole moment as the target nucleus. FIG. 5: The allowed region of the DM magnetic moment f vs. the DM mass m$_{N}$ . The upper colored regions are excluded for F$_{2}$ = 0 and F$_{2}$ = 0, respectively, with the 90 % confidence level for the CDMS II data [6]. FIG. 4: WIMP( N )–nucleus detection rate as a function of the recoil energy, normalized at E$_{rec}$ = 10 keV. The solid line corresponds to the magnetic moment and the dashed line corresponds to the SI interaction. The MDM graph and the SI graph meet at two points due to our normalization to their equality at 10 keV. So, at very low Q $^{2}$, the MDM is bigger than SI as expected. such a divergent effect is diminished by small velocity of WIMP, v 2 ∼ 10 − 6 which appears in the coefficient of the 1 /E$_{rec}$ -term as follows: used to estimate the proper allowed region with a 90% confidence level. The most stringent bound appears as f ≲ 2 . 88 × 10 − 3 for m$_{N}$ ≃ 21 GeV and F$_{2}$ = 0. When we ignore the contributions of nucleus anomalous mag- netic moment, F$_{2}$ = 0, then the upper-bound of f is 1 . 16 × 10 − 2 for m$_{N}$ ∼ 100 GeV. Taking into account the non-zero F$_{2}$ , the upper-bound goes down to 1 . 04 × 10 − 2 for m$_{N}$ ∼ 100 GeV. The event rate becomes larger with non-zero F$_{2}$ so that the allowed region is more con- strained, producing 1 − 10% of difference in f . However, we can easily expect that depending on the materials in direct detection experiments, the difference can be sig- nificantly amplified due to the enhanced magnetic dipole moment effect. Thus, it is worthwhile to study the DM multi-pole interactions with nuclei more carefully. Due to the suppression of the IR divergent feature in non-relativistic scattering, the dR $^{MDM}$/dE$_{rec}$ diver- gently larger than dR $^{SI}$/dE$_{rec}$ only in the region below E$_{rec}$ ∼ 10 keV, while the slope of the dR $^{MDM}$/dE$_{rec}$ above E$_{rec}$ ∼ 10 keV becomes eventually more flatter than the SI. This is why the dR $^{MDM}$/dE$_{rec}$ distribu- tion looks larger than dR $^{SI}$/dE$_{rec}$ above E$_{rec}$ 10 keV in Fig. (4). This non-relativistic v $^{2}$- suppression in the 1 /E$_{rec}$ -term might result in further interesting possibil- ity. Due to the suppression, ‘ Z terms’ can be comparable to each other, even with ‘ F$_{2}$ terms’. In this regard, we obtain the upper-bound on the DM magnetic moment from the recent CDMS II data for both of the F$_{2}$ = 0 and F$_{2}$ = 0 cases. The “maximal gap method”[16] is We considered a Dirac or an almost-Dirac DM N which may acquire a large magnetic moment. Using the possible dipole interactions, we estimated the signal event rate which is expected in the CDMS II experiment. Using the recent report of the CDMS II experiment, we present the upper-bound of the magnetic dipole moment. The most stringent bound appears for m$_{N}$ ≃ 21 GeV and F$_{2}$ = 0: f ≲ 1 . 4 × 10 − 3 with a sizable nucleus anomalous V. CONCLUSION 5 O(8,16) 3 Na(11.23) 3 2 Si(14,28) 2 Ge(32,73) 9 2 I(53,127) 5 2 Xe(54,131) 3 2 Cs(55,133) 7 2 W(74,183) 1 2 µ/µ$_{N}$ 1.66812 2.21752 1.1218 − 0 . 879467 2.81327 0.692 2.58 0.117785 F$_{2}$ 4.83 13.36 4.02 − 36 . 32 94.56 6.52 83.93 − 26 . 30 Λ$_{−}$ 2 ME$_{rec}$ = 2 M | ⃗p | 2 E$_{rec}$ ≃ 2 M 3 v 2 E$_{rec}$ ≃ 2 M 3 10 − 6 10 ( − 5 ∼− $^{4)}$( GeV) . (12) m$_{N}$ = 70 GeV 32 Ge 73 for C DMS I I f = 10 − $^{5}$↪ F$_{2}$ = − 36.  Dash : σ SI , Solid : σ MDM E rec [keV] dR◁d E rec (Arbitrary Unit) 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5