An alternative way to see this uses the Koenigsberger ratio \(Q_n = I_r/(k H)\), which measures how much of a rock's total magnetization is remanent versus induced, for a given ambient field \(H\). Rapidly chilled/quenched volcanic rocks (glassy or fine-grained basalts, pillow-lava rinds) are well known in rock-magnetism to have very high \(Q_n\) values (often \(Q_n \gg 1\)), while slowly cooled, coarse-grained intrusive rocks (e.g. gabbros) have low \(Q_n\) (often \(Q_n < 1\)).
Since \(Q_n = I_r/(kH)\) being large for rapidly-cooled rock directly requires \(I_r\) to be large relative to \(k\) — i.e., as the cooling rate increases, \(I_r\) must rise and/or \(k\) must fall. Grain-size theory (Néel theory of single-domain relaxation vs. Weiss domain-wall theory for multidomain grains) explains why both happen simultaneously: fast cooling biases the grain population toward the fine, single-domain end, which is magnetically "hard" (low susceptibility, high remanence-retention), whereas slow cooling biases it toward coarse multidomain grains, which are magnetically "soft" (high susceptibility, poor remanence retention). This grain-size argument independently confirms \(k\) decreases and \(I_r\) increases on rapid cooling.