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In Nd2 CuO4, one cannot use very low-temperature specific-heat data for analyzing the phonon term because of the appearance of a magnetic peak, so in Ref. the β value was obtained from the simple fitting of T3 to the data at intermediate temperature. It is known that in the temperature range 0.02
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In Nd2 CuO4, one cannot use very low-temperature specific-heat data for analyzing the phonon term because of the appearance of a magnetic peak, so in Ref. the β value was obtained from the simple fitting of T3 to the data at intermediate temperature. It is known that in the temperature range 0.02
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14
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0033689586
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This formula is commonly used for analyzing the phonon specific heat at this intermediate temperature range. [See, for example, the papers on the specific heat of La2 CuO4; 10.1103/PhysRevLett.84.5612;
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This formula is commonly used for analyzing the phonon specific heat at this intermediate temperature range. [See, for example, the papers on the specific heat of La2 CuO4; C. F. Chang, J. Y. Lin, and H. D. Yang, Phys. Rev. Lett. 84, 5612 (2000) 10.1103/PhysRevLett.84.5612
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65649118103
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It is important to recognize that the correction to the simple T3 analysis can decrease the β value, but it can never change the β value by as much as a factor of two, as can be seen in these reference papers. More importantly, if the specific-heat data in the intermediate temperature range can still be well fitted to the simple T3 law, which is actually the case for Nd2 CuO4, it means that the higher-power terms are effectively negligible in this material. (In Ref., the T3 law fits the data well from ∼15 to 25 K or even higher temperature.) This is not surprising, because the higher-power term β5 is usually found to be a small positive value in La2 CuO4, but it can even be a small negative value in some other materials [e.g., see the data for Nax CoO2;
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It is important to recognize that the correction to the simple T3 analysis can decrease the β value, but it can never change the β value by as much as a factor of two, as can be seen in these reference papers. More importantly, if the specific-heat data in the intermediate temperature range can still be well fitted to the simple T3 law, which is actually the case for Nd2 CuO4, it means that the higher-power terms are effectively negligible in this material. (In Ref., the T3 law fits the data well from ∼15 to 25 K or even higher temperature.) This is not surprising, because the higher-power term β5 is usually found to be a small positive value in La2 CuO4, but it can even be a small negative value in some other materials [e.g., see the data for Nax CoO2
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Also, it is useful to note that one can neglect the possibility that the β value determined at 15-25 K for Nd2 CuO4 might be enhanced by a magnon contribution, because it is established that in the Néel state of Nd2 CuO4, Cu magnons (which are the only possibility at 15-25 K) are gapped although it is still an open question whether the Nd magnons (which can only be relevant below 3 K) are gapped as well (Ref.).
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Also, it is useful to note that one can neglect the possibility that the β value determined at 15-25 K for Nd2 CuO4 might be enhanced by a magnon contribution, because it is established that in the Néel state of Nd2 CuO4, Cu magnons (which are the only possibility at 15-25 K) are gapped although it is still an open question whether the Nd magnons (which can only be relevant below 3 K) are gapped as well (Ref.).
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While the averaged sound velocity v̄ is a rather complicated average over all acoustic branches in all directions, this issue was carefully studied by Casimir and has been well sorted out; 10.1016/S0031-8914(38)80162-2
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