Stockholders' Equity - Other Comprehensive Income (Loss) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	$ 306.6	$ 134.5
Balance at end of period	203.2	306.6
Unamortized benefit plan credits
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	15.1	16.8
Other comprehensive income (loss) before reclassification	0.0	0.0
(Gain) loss reclassified out of accumulated other comprehensive income	(2.2)	(2.2)
Tax benefit (expense)	0.5	0.5
Balance at end of period	13.4	15.1
Currency translation adjustments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	(49.7)	(10.1)
Other comprehensive income (loss) before reclassification	13.1	(40.0)
(Gain) loss reclassified out of accumulated other comprehensive income	30.7	0.0
Tax benefit (expense)	(0.1)	0.4
Balance at end of period	(6.0)	(49.7)
Changes in fair value of cash flow hedges
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	13.3	0.8
Other comprehensive income (loss) before reclassification	(22.8)	15.4
(Gain) loss reclassified out of accumulated other comprehensive income	12.7	1.4
Tax benefit (expense)	2.6	(4.3)
Balance at end of period	5.8	13.3
Total
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	(21.3)	7.5
Other comprehensive income (loss) before reclassification	(9.7)	(24.6)
(Gain) loss reclassified out of accumulated other comprehensive income	41.2	(0.8)
Tax benefit (expense)	3.0	(3.4)
Balance at end of period	$ 13.2	$ (21.3)