We have found several errors in our previously published paper [1]. It is redundant to provide the plus terms in Eqs. (8) and (9), as the corresponding heat loads have been included in Eq. (7). Equations (8)–(10) should be replaced, respectively, by the following equations:

The simulation results alter with the changes of Eqs. (8)–(10). Figures 3–5 in [1] should be replaced by the following Figs. 1–3, respectively. Figure 1 shows that, at a pump wavelength of 2070 nm, the optimal dopant concentration for the ${\mathrm{Ho}}^{3+}\text{:}{\mathrm{YLiF}}_4$ crystal is 0.54%, the maximum achievable cooling power density is $9.7\times {10}^4\mathrm{W}·{\mathrm{m}}^{-3}$, and the corresponding cooling efficiency is 0.29%. Figure 3 shows that, for ${\mathrm{YLiF}}_4$ crystal with background absorption of $4.0\times {10}^{-4}{\mathrm{cm}}^{-1}$, the ideal pump wavelength is around 2067 nm. A cooling power density of about $1.1\times {10}^5\mathrm{W}·{\mathrm{m}}^{-3}$ is expected in $\sim 0.47\%{\mathrm{Ho}}^{3+}$ doped samples. If the background absorption is reduced by 1 order of magnitude, the maximum cooling power density could exceed $7.5\times {10}^5\mathrm{W}·{\mathrm{m}}^{-3}$ in $\sim 0.41\%$ ${\mathrm{Ho}}^{3+}$ doped samples, and the corresponding optimal pump wavelength redshifts to $\sim 2083\mathrm{nm}$.

 

Fig. 1. (a) Cooling power density and (b) the cooling efficiency of ${\mathrm{Ho}}^{3+}\text{:}{\mathrm{YLiF}}_4$ crystal as functions of pump intensity and dopant concentration. The pump wavelength is 2070 nm, and the background absorption is $4.0\times {10}^{-4}{\mathrm{cm}}^{-1}$.

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Fig. 2. Comparison among M1 (dotted curves), M2 (solid curves), and M3 (dashed curves). (a) The cooling power density and (b) the cooling efficiency. The dopant concentration is 0.54%, the pump wavelength is 2070 nm, and the background absorption is $4.0\times {10}^{-4}{\mathrm{cm}}^{-1}$.

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Fig. 3. Maximum cooling power density and the corresponding optimal dopant concentration of ${\mathrm{Ho}}^{3+}\text{:}{\mathrm{YLiF}}_4$ crystal versus pump wavelength at background absorptions of (a) $4.0\times {10}^{-4}{\mathrm{cm}}^{-1}$ and (b) $4.0\times {10}^{-5}{\mathrm{cm}}^{-1}$.

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A few clerical errors repeatedly emerge in Section 2 of [1]. The variable symbols $\upsilon$, ${\upsilon }_{10}$, ${\upsilon }_{20}$, ${\upsilon }_{30}$, ${\upsilon }_{31}$, and $V_u$ should be replaced by $\nu$, ${\nu }_{10}$, ${\nu }_{20}$, ${\nu }_{30}$, ${\nu }_{31}$, and ${\nu }_u$, respectively.

These changes do not affect the qualitative conclusions of our paper [1].