Magnetic monopole relaxation effects in spin ice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Dy</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Ti</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi

Spin-ice compounds enable the exploration of the dynamics of magnetic monopoles in condensed matter systems. In this study, we use AC calorimetry to probe the dynamic heat capacity response of the classical spin-ice compound <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>Dy</a:mi><a:mn>2</a:mn></a:msub><a:msub><a:mi>Ti</a:mi><a:mn>2</a:mn></a:msub><a:msub><a:mi mathvariant="normal">O</a:mi><a:mn>7</a:mn></a:msub></a:mrow></a:math> at low temperatures (0.5–5 K). Using frequencies of 0.01–500 Hz, we observe a strong frequency dependence in the measured heat capacity, allowing us to study thermal-relaxation effects on the corresponding timescales. The relaxation time <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>τ</c:mi></c:math> is determined from the frequency dependence of the heat capacity as the characteristic frequency below which the heat capacity saturates. Specific heat shows a maximum around 1 K. The extracted <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>τ</d:mi></d:math> shows divergent behavior below this temperature, reaching <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mo>∼</e:mo><e:mn>6</e:mn><e:mspace width="0.28em"/><e:mi mathvariant="normal">s</e:mi></e:mrow></e:math> at 0.65 K, similar to the relaxation time seen in previous studies. Performing dynamic Monte Carlo simulations, we verify that the specific heat frequency response has its origin in the slow magnetic monopole dynamics indigenous to spin ice. We find a timescale of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mn>20</h:mn><h:mspace width="4.pt"/><h:mtext>ms</h:mtext></h:mrow></h:math> per Monte Carlo step at <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mn>4</j:mn><j:mspace width="4.pt"/><j:mtext>K,</j:mtext></j:mrow></j:math> in contrast to <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:mn>2.5</l:mn><l:mspace width="4.pt"/><l:mtext>ms</l:mtext></l:mrow></l:math> mentioned in previous studies by other techniques.